Update and Resolve conflicts

paddle/framework/CMakeLists.txt

@@ -45,8 +45,9 @@ add_custom_command(TARGET framework_py_proto POST_BUILD
 
 cc_library(backward SRCS backward.cc DEPS net_op)
 cc_test(backward_test SRCS backward_test.cc DEPS backward recurrent_op device_context fill_constant_op)
+cc_library(lod_rank_table SRCS lod_rank_table.cc DEPS lod_tensor)
 
-cc_library(executor SRCS executor.cc DEPS op_registry device_context scope framework_proto backward glog)
+cc_library(executor SRCS executor.cc DEPS op_registry device_context scope framework_proto backward glog lod_rank_table)
 
 cc_library(prune SRCS prune.cc DEPS framework_proto)
 cc_test(prune_test SRCS prune_test.cc DEPS op_info prune recurrent_op device_context)

paddle/framework/executor.cc

@@ -21,7 +21,9 @@ limitations under the License. */
 #include <vector>
 
 #include "paddle/framework/feed_fetch_type.h"
+#include "paddle/framework/lod_rank_table.h"
 #include "paddle/framework/lod_tensor.h"
+#include "paddle/framework/lod_tensor_array.h"
 #include "paddle/framework/op_registry.h"
 #include "paddle/framework/scope.h"
 
@@ -70,10 +72,14 @@ static void CreateTensor(Variable* var, VarDesc::VarType var_type) {
     var->GetMutable<FeedFetchList>();
   } else if (var_type == VarDesc::STEP_SCOPES) {
     var->GetMutable<std::vector<framework::Scope>>();
+  } else if (var_type == VarDesc::LOD_RANK_TABLE) {
+    var->GetMutable<LoDRankTable>();
+  } else if (var_type == VarDesc::LOD_TENSOR_ARRAY) {
+    var->GetMutable<LoDTensorArray>();
   } else {
     PADDLE_THROW(
         "Variable type %d is not in "
-        "[LoDTensor, SelectedRows, FEED_MINIBATCH, FETCH_LIST]",
+        "[LoDTensor, SelectedRows, FEED_MINIBATCH, FETCH_LIST, LOD_RANK_TABLE]",
         var_type);
   }
 }

paddle/framework/framework.proto

@@ -109,6 +109,11 @@ message LoDTensorDesc {
   optional int32 lod_level = 2 [ default = 0 ];
 }
 
+message LoDTensorArrayDesc {
+  required TensorDesc tensor = 1;
+  optional int32 lod_level = 2 [ default = 0 ];
+}
+
 message VarDesc {
   enum VarType {
     LOD_TENSOR = 1;
@@ -116,11 +121,14 @@ message VarDesc {
     FEED_MINIBATCH = 3;
     FETCH_LIST = 4;
     STEP_SCOPES = 5;
+    LOD_RANK_TABLE = 6;
+    LOD_TENSOR_ARRAY = 7;
   }
   required string name = 1;
   required VarType type = 2;
   optional LoDTensorDesc lod_tensor = 3;
   optional TensorDesc selected_rows = 4;
+  optional LoDTensorArrayDesc tensor_array = 6;
   optional bool persistable = 5 [ default = false ];
 }
 

paddle/framework/lod_rank_table.cc

+/* Copyright (c) 2016 PaddlePaddle Authors. All Rights Reserved.
+
+   Licensed under the Apache License, Version 2.0 (the "License");
+   you may not use this file except in compliance with the License.
+   You may obtain a copy of the License at
+
+   http://www.apache.org/licenses/LICENSE-2.0
+
+   Unless required by applicable law or agreed to in writing, software
+   distributed under the License is distributed on an "AS IS" BASIS,
+   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+   See the License for the specific language governing permissions and
+   limitations under the License. */
+
+#include "paddle/framework/lod_rank_table.h"
+
+namespace paddle {
+namespace framework {
+void LoDRankTable::Reset(const LoD& lod, size_t level) {
+  this->coarse_lod_.clear();
+  this->items_.clear();
+  PADDLE_ENFORCE(level < lod.size(),
+                 "Cannot rank lod since the level %d is less than lod size %d",
+                 level, lod.size());
+  coarse_lod_.reserve(level);
+  for (size_t i = 0; i < level; ++i) {
+    coarse_lod_.push_back(lod[i]);
+  }
+  auto& vec = lod[level];
+  for (size_t i = 0; i < vec.size() - 1; ++i) {
+    TableItem item;
+    item.index = i;
+    item.length = vec[i + 1] - vec[i];
+    items_.emplace_back(item);
+  }
+  // NOTE(yuyang18):
+  //
+  // The time complexity of stable_sort is O(N*log(N)) if additional memory is
+  // available. It is easy to debug and unit test when using `stable_sort`
+  // instead of `sort`. Also, the items of a rank table will not be too large.
+  std::stable_sort(items_.begin(), items_.end(),
+                   [](const TableItem& a, const TableItem& b) {
+                     return a.length > b.length;
+                   });
+}
+
+}  // namespace framework
+}  // namespace paddle

paddle/framework/lod_rank_table.h

+/* Copyright (c) 2016 PaddlePaddle Authors. All Rights Reserved.
+
+   Licensed under the Apache License, Version 2.0 (the "License");
+   you may not use this file except in compliance with the License.
+   You may obtain a copy of the License at
+
+   http://www.apache.org/licenses/LICENSE-2.0
+
+   Unless required by applicable law or agreed to in writing, software
+   distributed under the License is distributed on an "AS IS" BASIS,
+   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+   See the License for the specific language governing permissions and
+   limitations under the License. */
+
+#pragma once
+#include "paddle/framework/lod_tensor.h"
+
+namespace paddle {
+namespace framework {
+
+// LoD Rank Table stores the `level` of `lod` which is ordered by sequence
+// length in descending order. It is useful when implement dynamic RNN and is
+// shared by dynamic RNN memory, dynamic RNN slice input and dynamic RNN slice
+// output operators.
+//
+// The table item contains two element. The length of sequence and the index of
+// sequence in that level.
+//
+// LoDRankTable also stores the coarse_lod, which is the lod information whose
+// level is less than input level, in order to restore the output LoD
+// information.
+class LoDRankTable {
+ public:
+  struct TableItem {
+    size_t index;
+    size_t length;
+  };
+
+  LoDRankTable() {}
+
+  void Reset(const LoD& lod, size_t level);
+
+  const std::vector<TableItem>& items() const { return this->items_; }
+
+  const LoD& coarse_lod() const { return this->coarse_lod_; }
+
+  size_t level() const { return coarse_lod_.size(); }
+
+ private:
+  LoD coarse_lod_;
+  std::vector<TableItem> items_;
+};
+
+}  // namespace framework
+}  // namespace paddle

paddle/framework/lod_tensor.cc

@@ -135,5 +135,43 @@ void LoDTensor::ShrinkInLevel(size_t level, size_t elem_begin,
   PADDLE_ENFORCE_LT(begin, end, "Cannot shrink, the result tensor is empty.");
   ShareDataWith(Slice(begin, end));
 }
+
+void GetFineGrainedLoDLength(const LoD& lod, size_t start_idx, size_t end_idx,
+                             std::vector<std::vector<size_t>>* lod_length,
+                             size_t* start_offset) {
+  lod_length->clear();
+  PADDLE_ENFORCE(start_idx < lod.size() - 1,
+                 "start_idx should be >= 0 and < lod.size() - 1.");
+  PADDLE_ENFORCE(end_idx < lod.size(),
+                 "end_idx should be >= 0 and < lod.size().");
+  PADDLE_ENFORCE_LE(start_idx, end_idx,
+                    "start_idx should be less than end_idx.");
+  for (size_t level_idx = 0; level_idx < lod.size(); ++level_idx) {
+    std::vector<size_t> level_lens;
+    for (size_t i = start_idx; i < end_idx; ++i) {
+      level_lens.push_back(lod[level_idx][i + 1] - lod[level_idx][i]);
+    }
+    lod_length->emplace_back(level_lens);
+    start_idx = lod[level_idx][start_idx];
+    end_idx = lod[level_idx][end_idx];
+  }
+  *start_offset = start_idx;
+}
+
+void AppendLoD(LoD* lod, const std::vector<std::vector<size_t>>& lod_length) {
+  PADDLE_ENFORCE_EQ(
+      lod->size(), lod_length.size(),
+      "The lod_length should has the same size with the appended lod.");
+  for (size_t i = 0; i < lod->size(); ++i) {
+    auto& level = (*lod)[i];
+    if (level.empty()) {
+      level.push_back(0);
+    }
+    for (size_t len : lod_length[i]) {
+      level.push_back(level.back() + len);
+    }
+  }
+}
+
 }  // namespace framework
 }  // namespace paddle

paddle/framework/lod_tensor.h

@@ -181,5 +181,11 @@ LoDTensor LodExpand(const LoDTensor& source, const LoD& lod, size_t level,
   return tensor;
 }
 
+void GetFineGrainedLoDLength(const LoD& lod, size_t start_idx, size_t end_idx,
+                             std::vector<std::vector<size_t>>* lod_length,
+                             size_t* start_offset);
+
+void AppendLoD(LoD* lod, const std::vector<std::vector<size_t>>& lod_length);
+
 }  // namespace framework
 }  // namespace paddle

paddle/framework/lod_tensor_array.h

+/* Copyright (c) 2016 PaddlePaddle Authors. All Rights Reserved.
+
+   Licensed under the Apache License, Version 2.0 (the "License");
+   you may not use this file except in compliance with the License.
+   You may obtain a copy of the License at
+
+   http://www.apache.org/licenses/LICENSE-2.0
+
+   Unless required by applicable law or agreed to in writing, software
+   distributed under the License is distributed on an "AS IS" BASIS,
+   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+   See the License for the specific language governing permissions and
+   limitations under the License. */
+
+#pragma once
+#include <vector>
+#include "paddle/framework/lod_tensor.h"
+
+namespace paddle {
+namespace framework {
+using LoDTensorArray = std::vector<LoDTensor>;
+}
+}  // namespace paddle

paddle/framework/lod_tensor_test.cc

@@ -144,5 +144,47 @@ TEST(LodExpand, test) {
   }
 }
 
+TEST(LoD, GetFineGrainedLoDLength) {
+  LoD lod;
+  lod.push_back(std::vector<size_t>{0, 2, 4, 5});
+  lod.push_back(std::vector<size_t>{0, 1, 6, 8, 10, 11});
+  lod.push_back(
+      std::vector<size_t>{0, 2, 5, 7, 10, 12, 15, 17, 20, 24, 26, 29});
+
+  std::vector<std::vector<size_t>> lod_length;
+  size_t start_offset;
+  paddle::framework::GetFineGrainedLoDLength(lod, 1, 2, &lod_length,
+                                             &start_offset);
+
+  std::vector<std::vector<size_t>> expected;
+  expected.push_back(std::vector<size_t>{2});
+  expected.push_back(std::vector<size_t>{2, 2});
+  expected.push_back(std::vector<size_t>{2, 3, 4, 2});
+  EXPECT_EQ(lod_length, expected);
+  EXPECT_EQ(start_offset, 15UL);
+}
+
+TEST(LoD, AppendLoD) {
+  std::vector<std::vector<size_t>> lod_lens;
+  lod_lens.push_back(std::vector<size_t>{2});
+  lod_lens.push_back(std::vector<size_t>{2, 2});
+  lod_lens.push_back(std::vector<size_t>{2, 3, 4, 2});
+
+  LoD origin;
+  origin.push_back(std::vector<size_t>{0, 2});
+  origin.push_back(std::vector<size_t>{0, 1, 6});
+  origin.push_back(std::vector<size_t>{0, 2, 5, 7, 10, 12, 15});
+
+  paddle::framework::AppendLoD(&origin, lod_lens);
+
+  LoD expected;
+  expected.push_back(std::vector<size_t>{0, 2, 4});
+  expected.push_back(std::vector<size_t>{0, 1, 6, 8, 10});
+  expected.push_back(
+      std::vector<size_t>{0, 2, 5, 7, 10, 12, 15, 17, 20, 24, 26});
+
+  EXPECT_EQ(origin, expected);
+}
+
 }  // namespace framework
 }  // namespace paddle

paddle/framework/operator.h

@@ -408,7 +408,6 @@ class OperatorWithKernel : public OperatorBase {
   // indicate kernel DataType by input data. Defaultly all input data must be
   // same.
   virtual DataType IndicateDataType(const ExecutionContext& ctx) const {
-    VLOG(3) << "Default IndicateDataType " << this->Type();
     auto& scope = ctx.scope();
     int data_type = -1;
     for (auto& input : this->inputs_) {
@@ -425,7 +424,6 @@ class OperatorWithKernel : public OperatorBase {
           }
           if (t != nullptr) {
             int tmp = static_cast<int>(ToDataType(t->type()));
-            VLOG(3) << "Input " << ipt_name << " with data_type " << tmp;
             PADDLE_ENFORCE(tmp == data_type || data_type == -1,
                            "DataType of Paddle Op %s must be the same.",
                            Type());

paddle/framework/var_desc.cc

@@ -37,13 +37,27 @@ std::vector<int64_t> VarDescBind::Shape() const {
 DataType VarDescBind::GetDataType() const { return tensor_desc().data_type(); }
 
 void VarDescBind::SetLoDLevel(int32_t lod_level) {
-  PADDLE_ENFORCE(desc_.type() == VarDesc::LOD_TENSOR);
-  desc_.mutable_lod_tensor()->set_lod_level(lod_level);
+  switch (desc_.type()) {
+    case VarDesc::LOD_TENSOR:
+      desc_.mutable_lod_tensor()->set_lod_level(lod_level);
+      break;
+    case VarDesc::LOD_TENSOR_ARRAY:
+      desc_.mutable_tensor_array()->set_lod_level(lod_level);
+      break;
+    default:
+      PADDLE_THROW("Tensor type=%d does not support LoDLevel", desc_.type());
+  }
 }
 
 int32_t VarDescBind::GetLodLevel() const {
-  PADDLE_ENFORCE(desc_.type() == VarDesc::LOD_TENSOR);
-  return desc_.lod_tensor().lod_level();
+  switch (desc_.type()) {
+    case VarDesc::LOD_TENSOR:
+      return desc_.lod_tensor().lod_level();
+    case VarDesc::LOD_TENSOR_ARRAY:
+      return desc_.tensor_array().lod_level();
+    default:
+      PADDLE_THROW("Tensor type=%d does not support LoDLevel", desc_.type());
+  }
 }
 
 const TensorDesc &VarDescBind::tensor_desc() const {
@@ -53,6 +67,8 @@ const TensorDesc &VarDescBind::tensor_desc() const {
       return desc_.selected_rows();
     case VarDesc::LOD_TENSOR:
       return desc_.lod_tensor().tensor();
+    case VarDesc::LOD_TENSOR_ARRAY:
+      return desc_.tensor_array().tensor();
     default:
       PADDLE_THROW("Unexpected branch.");
   }
@@ -66,6 +82,8 @@ TensorDesc *VarDescBind::mutable_tensor_desc() {
       return desc_.mutable_selected_rows();
     case VarDesc::LOD_TENSOR:
       return desc_.mutable_lod_tensor()->mutable_tensor();
+    case VarDesc::LOD_TENSOR_ARRAY:
+      return desc_.mutable_tensor_array()->mutable_tensor();
     default:
       PADDLE_THROW("Unexpected branch.");
   }

paddle/framework/var_desc.h

@@ -15,6 +15,7 @@ limitations under the License. */
 #pragma once
 
 #include <vector>
+#include "glog/logging.h"
 #include "paddle/framework/framework.pb.h"
 
 namespace paddle {

paddle/gserver/layers/MKLDNNAddtoLayer.cpp

+/* Copyright (c) 2017 PaddlePaddle Authors. All Rights Reserve.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License. */
+
+#include "MKLDNNAddtoLayer.h"
+
+using namespace mkldnn;  // NOLINT
+
+namespace paddle {
+
+REGISTER_LAYER(mkldnn_addto, MKLDNNAddtoLayer);
+
+bool MKLDNNAddtoLayer::init(const LayerMap& layerMap,
+                            const ParameterMap& parameterMap) {
+  if (!MKLDNNLayer::init(layerMap, parameterMap)) {
+    return false;
+  }
+
+  layerSize_ = getSize();
+  for (size_t i = 0; i < inputLayers_.size(); i++) {
+    CHECK_EQ(layerSize_, inputLayers_[i]->getSize()) << "input size must equal";
+  }
+  if (biasParameter_.get() != NULL) {
+    biases_ =
+        std::unique_ptr<Weight>(new Weight(1, layerSize_, biasParameter_, 0));
+  }
+  return true;
+}
+
+void MKLDNNAddtoLayer::reshape(
+    int& bs, int& ic, int& ih, int& iw, int oc, int& oh, int& ow) {
+  CHECK_EQ(layerSize_, getSize()) << "this layer size can not be changed";
+  reshapeInput(bs, ih, iw);
+  ic = inputLayers_[0]->getSize() / ih / iw;
+  CHECK_EQ((size_t)ic * ih * iw, inputLayers_[0]->getSize());
+  CHECK_EQ(inputElemenCnt_, (size_t)bs * ic * ih * iw);
+  for (size_t i = 0; i < inputLayers_.size(); i++) {
+    CHECK_EQ(int64_t(bs), inputLayers_[i]->getOutput().getBatchSize());
+    CHECK_EQ(layerSize_, inputLayers_[i]->getSize());
+  }
+
+  oc = ic;
+  oh = ih;
+  ow = iw;
+  reshapeOutput(oh, ow);
+  resizeOutput(bs, oc * oh * ow);
+  printSizeInfo();
+}
+
+void MKLDNNAddtoLayer::resetFwd(std::vector<primitive>& pipeline,
+                                MKLDNNMatrixPtr& in,
+                                MKLDNNMatrixPtr& wgt,
+                                MKLDNNMatrixPtr& bias,
+                                MKLDNNMatrixPtr& out) {
+  if (biases_) {
+    LOG(FATAL) << "not implemented yet";
+  }
+  resetFwdBuffers(inVals_, out);
+  in = inVals_[0];
+
+  std::shared_ptr<sum::primitive_desc> fwdPD;
+  resetFwdPD(fwdPD, inVals_, out);
+
+  resetFwdPipeline(pipeline, fwdPD, inVals_, out);
+}
+
+void MKLDNNAddtoLayer::resetBwd(std::vector<primitive>& pipeline,
+                                MKLDNNMatrixPtr& in,
+                                MKLDNNMatrixPtr& wgt,
+                                MKLDNNMatrixPtr& bias,
+                                MKLDNNMatrixPtr& out) {
+  resetBwdBuffers(inGrads_, out);
+  in = inGrads_[0];
+
+  // backward only need share output grad to input grad
+  for (size_t i = 0; i < inGrads_.size(); i++) {
+    if (inGrads_[i] != nullptr) {
+      inGrads_[i] = out;
+      inputLayers_[i]->getOutputGrad()->setData(inGrads_[i]->getData());
+    }
+  }
+}
+
+void MKLDNNAddtoLayer::updateWeights(const UpdateCallback& callback) {
+  if (biases_ && biases_->getWGrad()) {
+    biases_->getParameterPtr()->incUpdate(callback);
+  }
+}
+
+void MKLDNNAddtoLayer::resetFwdBuffers(std::vector<MKLDNNMatrixPtr>& inputs,
+                                       MKLDNNMatrixPtr& out) {
+  inputs.resize(inputLayers_.size());
+  for (size_t i = 0; i < inputs.size(); i++) {
+    resetInValue(inputs[i], nullptr, i);
+    CHECK(inputs[i]);
+    inputs[i]->downSpatial();
+  }
+  for (size_t i = 1; i < inputs.size(); i++) {
+    CHECK_PRIMITIVE_DESC_EQ(inputs[i], inputs[0]->getPrimitiveDesc());
+  }
+
+  resetOutValue(out, inputs[0]->getPrimitiveDesc());
+}
+
+void MKLDNNAddtoLayer::resetFwdPD(std::shared_ptr<sum::primitive_desc>& pd,
+                                  std::vector<MKLDNNMatrixPtr>& inputs,
+                                  MKLDNNMatrixPtr out) {
+  std::vector<double> scales(inputs.size(), 1.0);
+  std::vector<memory::primitive_desc> srcPDs;
+  for (size_t i = 0; i < inputs.size(); i++) {
+    srcPDs.push_back(inputs[i]->getPrimitiveDesc());
+  }
+  CHECK(out);
+  pd.reset(new sum::primitive_desc(out->getMemoryDesc(), scales, srcPDs));
+  CHECK_PRIMITIVE_DESC_EQ(out, pd->dst_primitive_desc());
+}
+
+void MKLDNNAddtoLayer::resetFwdPipeline(
+    std::vector<primitive>& pipeline,
+    std::shared_ptr<sum::primitive_desc>& pd,
+    std::vector<MKLDNNMatrixPtr>& inputs,
+    MKLDNNMatrixPtr& out) {
+  std::vector<primitive::at> srcs;
+  for (size_t i = 0; i < inputs.size(); i++) {
+    srcs.push_back(*(inputs[i]));
+  }
+  fwd_.reset(new sum(*pd, srcs, *out));
+  pipeline.push_back(*fwd_);
+}
+
+void MKLDNNAddtoLayer::resetBwdBuffers(std::vector<MKLDNNMatrixPtr>& inputs,
+                                       MKLDNNMatrixPtr& out) {
+  CHECK(outVal_);
+  resetOutGrad(out, outVal_->getPrimitiveDesc());
+  CHECK(out);
+
+  inputs.resize(inputLayers_.size());
+  for (size_t i = 0; i < inputs.size(); i++) {
+    resetInGrad(inputs[i], inVal_->getPrimitiveDesc(), i);
+    CHECK_PRIMITIVE_DESC_EQ(inputs[i], out->getPrimitiveDesc());
+  }
+}
+
+}  // namespace paddle

paddle/gserver/layers/MKLDNNAddtoLayer.h

+/* Copyright (c) 2017 PaddlePaddle Authors. All Rights Reserve.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License. */
+
+#pragma once
+
+#include "MKLDNNLayer.h"
+#include "mkldnn.hpp"
+
+namespace paddle {
+
+/**
+ * @brief A subclass of MKLDNNLayer Addto layer.
+ *
+ * The config file api is mkldnn_addto
+ */
+class MKLDNNAddtoLayer : public MKLDNNLayer {
+protected:
+  std::vector<MKLDNNMatrixPtr> inVals_;
+  std::vector<MKLDNNMatrixPtr> inGrads_;
+
+  // layer size == ic * ih * iw == oc * oh *ow, and can not be changed
+  size_t layerSize_;
+
+  // TODO(TJ): this part has not been optimized by MKL-DNN
+  std::unique_ptr<Weight> biases_;
+
+public:
+  explicit MKLDNNAddtoLayer(const LayerConfig& config) : MKLDNNLayer(config) {}
+
+  ~MKLDNNAddtoLayer() {}
+
+  bool init(const LayerMap& layerMap,
+            const ParameterMap& parameterMap) override;
+
+  void reshape(
+      int& bs, int& ic, int& ih, int& iw, int oc, int& oh, int& ow) override;
+
+  void resetFwd(std::vector<mkldnn::primitive>& pipeline,
+                MKLDNNMatrixPtr& in,
+                MKLDNNMatrixPtr& wgt,
+                MKLDNNMatrixPtr& bias,
+                MKLDNNMatrixPtr& out) override;
+
+  void resetBwd(std::vector<mkldnn::primitive>& pipeline,
+                MKLDNNMatrixPtr& in,
+                MKLDNNMatrixPtr& wgt,
+                MKLDNNMatrixPtr& bias,
+                MKLDNNMatrixPtr& out) override;
+
+  void updateWeights(const UpdateCallback& callback) override;
+
+  void printValueFormat() override {
+    for (size_t i = 0; i < inVals_.size(); ++i) {
+      VLOG(MKLDNN_FMTS) << i << " input: " << inVals_[i]->getFormat() << " >>>";
+    }
+    if (outVal_) {
+      VLOG(MKLDNN_FMTS) << outVal_->getFormat() << " >>> ";
+    }
+    if (extOutVal_) {
+      VLOG(MKLDNN_FMTS) << extOutVal_->getFormat();
+    }
+  }
+
+  void printGradFormat() override {
+    if (extOutGrad_) {
+      VLOG(MKLDNN_FMTS) << extOutGrad_->getFormat();
+    }
+    if (outGrad_) {
+      VLOG(MKLDNN_FMTS) << outGrad_->getFormat() << " <<< ";
+    }
+    for (size_t i = 0; i < inGrads_.size(); ++i) {
+      VLOG(MKLDNN_FMTS) << i << " input: " << inGrads_[i]->getFormat() << "<<<";
+    }
+  }
+
+protected:
+  /**
+   * Forward functions: reset buffers(inputs, output, bias),
+   *                    reset primitive descriptor,
+   *                    reset pipeline.
+   */
+  void resetFwdBuffers(std::vector<MKLDNNMatrixPtr>& inputs,
+                       MKLDNNMatrixPtr& out);
+  void resetFwdPD(std::shared_ptr<mkldnn::sum::primitive_desc>& pd,
+                  std::vector<MKLDNNMatrixPtr>& inputs,
+                  MKLDNNMatrixPtr out);
+  void resetFwdPipeline(std::vector<mkldnn::primitive>& pipeline,
+                        std::shared_ptr<mkldnn::sum::primitive_desc>& pd,
+                        std::vector<MKLDNNMatrixPtr>& inputs,
+                        MKLDNNMatrixPtr& out);
+
+  /**
+   * Backward functions: reset buffers(inputs, output, bias)
+   */
+  void resetBwdBuffers(std::vector<MKLDNNMatrixPtr>& inputs,
+                       MKLDNNMatrixPtr& out);
+};
+
+}  // namespace paddle

paddle/gserver/layers/MKLDNNLayer.cpp

@@ -77,7 +77,7 @@ void MKLDNNLayer::forward(PassType passType) {
       needResetBwd_ = true;
     }
 
-    if (inputLayers_[0]->getType() == "data") {
+    if (inputLayers_[0]->getType() == "data" && inputLayers_.size() == 1) {
       // Update input value data when input layer is "data" type,
       // since the input value data address might be changed.
       CHECK(extInVal_);
@@ -171,14 +171,16 @@ void MKLDNNLayer::resetWithMatrix(MKLDNNMatrixPtr& dnn,
 }
 
 void MKLDNNLayer::resetInValue(
-    MKLDNNMatrixPtr& in, const std::shared_ptr<memory::primitive_desc>& intPD) {
+    MKLDNNMatrixPtr& in,
+    const std::shared_ptr<memory::primitive_desc>& intPD,
+    size_t inputIdx) {
   cvtInVal_ = nullptr;
   extInVal_ = nullptr;
   in = nullptr;
   CHECK_GT(bs_ * ic_ * ih_ * iw_, 0);
   auto extPD = MKLDNNMatrix::createPrimitiveDesc(
       {bs_, ic_, ih_, iw_}, format::nchw, engine_);
-  const MatrixPtr& inMat = inputLayers_[0]->getOutputValue();
+  const MatrixPtr& inMat = inputLayers_[inputIdx]->getOutputValue();
   in = std::dynamic_pointer_cast<MKLDNNMatrix>(inMat);
   CHECK_EQ(inputIsOnlyMKLDNN(), in != nullptr);
   if (in == nullptr || in->getFormat() == format::nc) {
@@ -216,11 +218,12 @@ void MKLDNNLayer::resetOutValue(MKLDNNMatrixPtr& out,
 }
 
 void MKLDNNLayer::resetInGrad(MKLDNNMatrixPtr& in,
-                              memory::primitive_desc intPD) {
+                              memory::primitive_desc intPD,
+                              size_t inputIdx) {
   cvtInGrad_ = nullptr;
   extInGrad_ = nullptr;
   in = nullptr;
-  LayerPtr& input = inputLayers_[0];
+  LayerPtr& input = inputLayers_[inputIdx];
   if (input->getOutputGrad() == nullptr) {
     // no need input grad
     return;
@@ -245,7 +248,6 @@ void MKLDNNLayer::resetInGrad(MKLDNNMatrixPtr& in,
     return;
   }
   // need create reorder
-  // TODO(TJ): add macro definition to simplify it
   CHECK(extInVal_ != nullptr && isPaddleFormat(extInVal_->getFormat()))
       << "should have external input value and the format must be nchw(nc)";
   extInGrad_ = MKLDNNMatrix::create(extInVal_->getPrimitiveDesc(), inMat);

paddle/gserver/layers/MKLDNNLayer.h

@@ -199,7 +199,8 @@ protected:
    */
   void resetInValue(
       MKLDNNMatrixPtr& in,
-      const std::shared_ptr<mkldnn::memory::primitive_desc>& intPD = nullptr);
+      const std::shared_ptr<mkldnn::memory::primitive_desc>& intPD = nullptr,
+      size_t inputIdx = 0);
 
   /**
    * reset output value from internal primitive desc.
@@ -212,7 +213,9 @@ protected:
    * reset input grad from internal primitive desc.
    * reset both internal and external buffer and create reorder if necessary.
    */
-  void resetInGrad(MKLDNNMatrixPtr& in, mkldnn::memory::primitive_desc intPD);
+  void resetInGrad(MKLDNNMatrixPtr& in,
+                   mkldnn::memory::primitive_desc intPD,
+                   size_t inputIdx = 0);
 
   /**
    * reset output grad from internal primitive desc.

paddle/gserver/tests/MKLDNNTester.cpp

@@ -132,7 +132,7 @@ void MKLDNNTester::checkForward() {
   VLOG(MKLDNN_TESTS) << "Check Forward";
   printTopDatas();
   double delta =
-      compareMatrix(dnnLayer_->getOutputValue(), refLayer_->getOutputValue());
+      compareMatrix(refLayer_->getOutputValue(), dnnLayer_->getOutputValue());
   EXPECT_LE(fabs(delta), eps_);
 }
 
@@ -147,7 +147,7 @@ void MKLDNNTester::checkBackwardData() {
     VLOG(MKLDNN_ALL) << "Reference Backward Result: InputGrad " << i;
     printMatrix(refDiff);
 
-    double delta = compareMatrix(dnnDiff, refDiff);
+    double delta = compareMatrix(refDiff, dnnDiff);
     EXPECT_LE(fabs(delta), eps_);
     if (isBN) {
       // the other two inputs in batch norm are for moving mean and var
@@ -177,7 +177,7 @@ void MKLDNNTester::checkBackwardWgts() {
                      << parameters_[REF][i]->getName();
     printVector(ref);
 
-    double delta = compareVector(dnn, ref);
+    double delta = compareVector(ref, dnn);
     EXPECT_LE(fabs(delta), eps_);
   }
 

paddle/gserver/tests/test_MKLDNN.cpp

@@ -271,20 +271,53 @@ TEST(MKLDNNLayer, BatchNormLayer) {
   testBatchNormLayer({16, 32, 16, 16});
 }
 
-struct testActDesc {
+struct testImageDesc {
   int bs, ic, ih, iw;
 };
 
-static void getAddtoConfig(TestConfig& cfg, const testActDesc& pm) {
+static void getAddtoConfig(TestConfig& cfg,
+                           const testImageDesc& pm,
+                           const size_t nInputs = 1) {
   cfg.biasSize = 0;
   cfg.layerConfig.set_type("addto");
   size_t layerSize = pm.ic * pm.ih * pm.iw;
   cfg.layerConfig.set_size(layerSize);
-  cfg.inputDefs.push_back({INPUT_DATA, "layer_0", layerSize, 0});
-  cfg.layerConfig.add_inputs();
+  cfg.layerConfig.set_active_type("relu");
+  for (size_t i = 0; i < nInputs; ++i) {
+    std::stringstream ss;
+    ss << "layer_" << i;
+    cfg.inputDefs.push_back({INPUT_DATA, ss.str(), layerSize, 0});
+    LayerInputConfig* input = cfg.layerConfig.add_inputs();
+    ImageConfig* img_conf = input->mutable_image_conf();
+    img_conf->set_channels(pm.ic);
+    img_conf->set_img_size_y(pm.ih);
+    img_conf->set_img_size(pm.iw);
+  }
+}
+
+void testAddtoLayer(const testImageDesc& pm, const size_t nInputs) {
+  CHECK_GE(nInputs, 1);
+  TestConfig dnnConfig;
+  getAddtoConfig(dnnConfig, pm, nInputs);
+  dnnConfig.layerConfig.set_type("mkldnn_addto");
+  // TODO(TJ): test with bias
+  for (auto withBias : {false}) {
+    if (withBias) {
+      dnnConfig.biasSize = pm.ic * pm.ih * pm.iw;
+    } else {
+      dnnConfig.biasSize = 0;
+    }
+    RUN_MKLDNN_TEST_LAYER(dnnConfig, "addto", pm)
+  }
+}
+
+TEST(MKLDNNLayer, AddtoLayer) {
+  testAddtoLayer({16, 5, 14, 14}, 1);
+  testAddtoLayer({8, 10, 8, 8}, 2);
+  testAddtoLayer({4, 12, 1, 1}, 3);
 }
 
-void testActivation(std::string actType, const testActDesc& pm) {
+void testActivation(std::string actType, const testImageDesc& pm) {
   // TODO(TJ): remove me when paddle support elu activation
   if (actType == "mkldnn_elu") {
     return;

paddle/operators/CMakeLists.txt

@@ -142,6 +142,7 @@ set(DEPS_OPS
     nccl_op
     sequence_conv_op
     sequence_pool_op
+    lod_rank_table_op
     lstm_op)
 
 op_library(cond_op SRCS cond_op.cc DEPS framework_proto tensor operator net_op)
@@ -150,6 +151,7 @@ op_library(softmax_with_cross_entropy_op DEPS cross_entropy softmax)
 op_library(sum_op DEPS net_op selected_rows_functor)
 op_library(pool_op DEPS pooling)
 op_library(pool_with_index_op DEPS pooling)
+op_library(lod_rank_table_op SRCS lod_rank_table_op.cc DEPS lod_rank_table)
 if(WITH_GPU)
 op_library(nccl_op DEPS nccl_common)
 endif()

paddle/operators/accuracy_op.cc

@@ -33,7 +33,7 @@ class AccuracyOp : public framework::OperatorWithKernel {
 
     auto inference_dim = ctx->GetInputDim("Out");
     auto label_dim = ctx->GetInputDim("Label");
-    // Assume indices has same shape with infernece, because
+    // Assume indices has same shape as inference, because
     // it's the output of topk.
 
     PADDLE_ENFORCE_EQ(label_dim.size(), 2, "label's rank must be 2.");
@@ -60,20 +60,24 @@ class AccuracyOpMaker : public framework::OpProtoAndCheckerMaker {
                   framework::OpAttrChecker *op_checker)
       : OpProtoAndCheckerMaker(proto, op_checker) {
     // TODO(typhoonzero): support both inference value and indices.
-    AddInput("Out", "topk (inferences) the network output");
-    AddInput("Indices", "topk (indices) the network output");
+    AddInput("Out", "The network output of topk (inferences)");
+    AddInput("Indices", "The the network output of topk (indices)");
     AddInput("Label", "Label of the training data");
     // TODO(typhoonzero): AddInput("Weight", ...
     AddOutput("Accuracy", "The accuracy of current batch");
 
     AddComment(R"DOC(
-Accuracy. It will print accuracy rate for classification.
-The accuracy is:
-..  math::
-accuracy = \\frac{NumOfCorrectPredicts}{NumOfAllSamples})
+Accuracy Operator. 
+
+It will print accuracy rate for classification.
+The accuracy is calculated as follows:
+
+$$accuracy = \frac{NumOfCorrectPredicts}{NumOfAllSamples}$$
+
+Both the input Out and Label can carry the LoD (Level of Details)
+information, or not. But the output only shares the LoD information 
+with the input Out(Inference).
 
-Both the input `Out` and `Label` can carry the LoD (Level of Details)
-information, or not. But the output only shares the LoD with input `Inference`.
 )DOC");
   }
 };

paddle/operators/activation_op.cc

@@ -44,7 +44,7 @@ class SigmoidOpMaker : public framework::OpProtoAndCheckerMaker {
     AddInput("X", "Input of Sigmoid operator");
     AddOutput("Y", "Output of Sigmoid operator");
     AddComment(R"DOC(
-Sigmoid activation operator.
+Sigmoid Activation Operator.
 
 $y = 1 / (1 + e^{-x})$
 
@@ -60,7 +60,7 @@ class LogSigmoidOpMaker : public framework::OpProtoAndCheckerMaker {
     AddInput("X", "Input of LogSigmoid operator");
     AddOutput("Y", "Output of LogSigmoid operator");
     AddComment(R"DOC(
-Logsigmoid activation operator.
+Logsigmoid Activation Operator.
 
 $y = \log(1 / (1 + e^{-x}))$
 
@@ -75,7 +75,7 @@ class ExpOpMaker : public framework::OpProtoAndCheckerMaker {
     AddInput("X", "Input of Exp operator");
     AddOutput("Y", "Output of Exp operator");
     AddComment(R"DOC(
-Exp activation operator.
+Exp Activation Operator.
 
 $y = e^x$
 
@@ -90,7 +90,7 @@ class ReluOpMaker : public framework::OpProtoAndCheckerMaker {
     AddInput("X", "Input of Relu operator");
     AddOutput("Y", "Output of Relu operator");
     AddComment(R"DOC(
-Relu activation operator.
+Relu Activation Operator.
 
 $y = \max(x, 0)$
 
@@ -109,7 +109,7 @@ class LeakyReluOpMaker : public framework::OpProtoAndCheckerMaker {
     AddAttr<AttrType>("alpha", "The small negative slope")
         .SetDefault(static_cast<AttrType>(0.02f));
     AddComment(R"DOC(
-LeakyRelu activation operator.
+LeakyRelu Activation Operator.
 
 $y = \max(x, \alpha * x)$
 
@@ -128,7 +128,7 @@ class SoftShrinkOpMaker : public framework::OpProtoAndCheckerMaker {
     AddAttr<AttrType>("lambda", "non-negative offset")
         .SetDefault(static_cast<AttrType>(0.5f));
     AddComment(R"DOC(
-Softshrink activation operator.
+Softshrink Activation Operator.
 
 $$
 y = \begin{cases} 
@@ -149,7 +149,7 @@ class TanhOpMaker : public framework::OpProtoAndCheckerMaker {
     AddInput("X", "Input of Tanh operator");
     AddOutput("Y", "Output of Tanh operator");
     AddComment(R"DOC(
-Tanh activation operator.
+Tanh Activation Operator.
 
 $$y = \frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}$$
 
@@ -165,7 +165,7 @@ class TanhShrinkOpMaker : public framework::OpProtoAndCheckerMaker {
     AddInput("X", "Input of TanhShrink operator");
     AddOutput("Y", "Output of TanhShrink operator");
     AddComment(R"DOC(
-TanhShrink activation operator.
+TanhShrink Activation Operator.
 
 $$y = x - \frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}$$
 
@@ -184,7 +184,7 @@ class HardShrinkOpMaker : public framework::OpProtoAndCheckerMaker {
     AddAttr<AttrType>("threshold", "The value of threshold for HardShrink")
         .SetDefault(static_cast<AttrType>(0.5));
     AddComment(R"DOC(
-HardShrink activation operator.
+HardShrink Activation Operator.
 
 $$
 y = \begin{cases} 
@@ -205,7 +205,7 @@ class SqrtOpMaker : public framework::OpProtoAndCheckerMaker {
     AddInput("X", "Input of Sqrt operator");
     AddOutput("Y", "Output of Sqrt operator");
     AddComment(R"DOC(
-Sqrt activation operator.
+Sqrt Activation Operator.
 
 $y = \sqrt{x}$
 
@@ -220,7 +220,7 @@ class AbsOpMaker : public framework::OpProtoAndCheckerMaker {
     AddInput("X", "Input of Abs operator");
     AddOutput("Y", "Output of Abs operator");
     AddComment(R"DOC(
-Abs activation operator.
+Abs Activation Operator.
 
 $y = |x|$
 
@@ -236,7 +236,7 @@ class ReciprocalOpMaker : public framework::OpProtoAndCheckerMaker {
     AddInput("X", "Input of Reciprocal operator");
     AddOutput("Y", "Output of Reciprocal operator");
     AddComment(R"DOC(
-Reciprocal activation operator.
+Reciprocal Activation Operator.
 
 $$y = \frac{1}{x}$$
 
@@ -251,7 +251,7 @@ class LogOpMaker : public framework::OpProtoAndCheckerMaker {
     AddInput("X", "Input of Log operator");
     AddOutput("Y", "Output of Log operator");
     AddComment(R"DOC(
-Log activation operator.
+Log Activation Operator.
 
 $y = \ln(x)$
 
@@ -268,7 +268,7 @@ class SquareOpMaker : public framework::OpProtoAndCheckerMaker {
     AddInput("X", "Input of Square operator");
     AddOutput("Y", "Output of Square operator");
     AddComment(R"DOC(
-Square activation operator.
+Square Activation Operator.
 
 $y = x^2$
 
@@ -284,7 +284,7 @@ class SoftplusOpMaker : public framework::OpProtoAndCheckerMaker {
     AddInput("X", "Input of Softplus operator");
     AddOutput("Y", "Output of Softplus operator");
     AddComment(R"DOC(
-Softplus activation operator.
+Softplus Activation Operator.
 
 $y = \ln(1 + e^{x})$
 
@@ -300,7 +300,7 @@ class SoftsignOpMaker : public framework::OpProtoAndCheckerMaker {
     AddInput("X", "Input of Softsign operator");
     AddOutput("Y", "Output of Softsign operator");
     AddComment(R"DOC(
-Softsign activation operator.
+Softsign Activation Operator.
 
 $$y = \frac{x}{1 + |x|}$$
 
@@ -320,7 +320,7 @@ class BReluOpMaker : public framework::OpProtoAndCheckerMaker {
     AddAttr<AttrType>("t_max", "The max marginal value of BRelu")
         .SetDefault(static_cast<AttrType>(24));
     AddComment(R"DOC(
-BRelu activation operator.
+BRelu Activation Operator.
 
 $y = \max(\min(x, t_{min}), t_{max})$
 
@@ -339,7 +339,7 @@ class SoftReluOpMaker : public framework::OpProtoAndCheckerMaker {
     AddAttr<AttrType>("threshold", "The threshold value of SoftRelu")
         .SetDefault(static_cast<AttrType>(40));
     AddComment(R"DOC(
-SoftRelu activation operator.
+SoftRelu Activation Operator.
 
 $y = \ln(1 + \exp(\max(\min(x, threshold), threshold))$
 
@@ -357,7 +357,7 @@ class ELUOpMaker : public framework::OpProtoAndCheckerMaker {
     AddAttr<AttrType>("alpha", "The alpha value of ELU")
         .SetDefault(static_cast<AttrType>(1.0f));
     AddComment(R"DOC(
-ELU activation operator.
+ELU Activation Operator.
 
 Applies the following element-wise computation on the input according to
 https://arxiv.org/abs/1511.07289.
@@ -378,7 +378,7 @@ class Relu6OpMaker : public framework::OpProtoAndCheckerMaker {
     AddAttr<AttrType>("threshold", "The threshold value of Relu6")
         .SetDefault(static_cast<AttrType>(6));
     AddComment(R"DOC(
-Relu6 activation operator.
+Relu6 Activation Operator.
 
 $y = \min(\max(0, x), 6)$
 
@@ -396,7 +396,7 @@ class PowOpMaker : public framework::OpProtoAndCheckerMaker {
     AddAttr<AttrType>("factor", "The exponential factor of Pow")
         .SetDefault(static_cast<AttrType>(1));
     AddComment(R"DOC(
-Pow activation operator.
+Pow Activation Operator.
 
 $y = x^{factor}$
 
@@ -416,7 +416,7 @@ class STanhOpMaker : public framework::OpProtoAndCheckerMaker {
     AddAttr<AttrType>("scale_b", "The scale parameter of b for the input")
         .SetDefault(static_cast<AttrType>(1.7159));
     AddComment(R"DOC(
-STanh activation operator.
+STanh Activation Operator.
 
 $$y = b * \frac{e^{a * x} - e^{-a * x}}{e^{a * x} + e^{-a * x}}$$
 
@@ -435,7 +435,7 @@ class ThresholdedReluOpMaker : public framework::OpProtoAndCheckerMaker {
     AddAttr<AttrType>("threshold", "The threshold location of activation")
         .SetDefault(static_cast<AttrType>(1.0));
     AddComment(R"DOC(
-ThresholdedRelu activation operator.
+ThresholdedRelu Activation Operator.
 
 $$
 y = \begin{cases} 
@@ -461,7 +461,7 @@ class HardSigmoidOpMaker : public framework::OpProtoAndCheckerMaker {
     AddAttr<AttrType>("offset", "Offset for linear approximation of sigmoid")
         .SetDefault(static_cast<AttrType>(0.5));
     AddComment(R"DOC(
-HardSigmoid activation operator.
+HardSigmoid Activation Operator.
 
 Segment-wise linear approximation of sigmoid(https://arxiv.org/abs/1603.00391), 
 which is much faster than sigmoid.

paddle/operators/adadelta_op.cc

@@ -64,16 +64,15 @@ class AdadeltaOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("Param", "(Tensor) Input parameter");
     AddInput("Grad", "(Tensor) Input gradient");
-    AddInput("AvgSquaredGrad",
-             "(Tensor) Input expectation of squared gradient");
+    AddInput("AvgSquaredGrad", "(Tensor) Input average of squared gradient");
     AddInput("AvgSquaredUpdate",
-             "(Tensor) Input expectation of squared parameter updates");
+             "(Tensor) Input average of squared parameter updates");
 
     AddOutput("ParamOut", "(Tensor) Output parameter");
     AddOutput("AvgSquaredGradOut",
-              "(Tensor) Output expectation of squared gradient");
+              "(Tensor) Output average of squared gradient");
     AddOutput("AvgSquaredUpdateOut",
-              "(Tensor) Output expectation of squared parameter updates");
+              "(Tensor) Output average of squared parameter updates");
 
     AddAttr<float>("rho",
                    "(float, default 0.95) Exponential decay rate "
@@ -84,22 +83,21 @@ class AdadeltaOpMaker : public framework::OpProtoAndCheckerMaker {
                    "numerical stability")
         .SetDefault(1.0e-6f);
     AddComment(R"DOC(
-Adadelta Updates Operator.
+Adadelta Optimizer.
 
-This implements the Adadelta optimizer[1]. Adadelta is a per-dimension
-adaptive learning rate method for gradient descent.
+Adadelta optimizer is implemented as explained in:
+https://arxiv.org/abs/1212.5701
+Adadelta is a per-dimension adaptive learning rate method used
+for gradient descent.
 
-Adadelta updates:
+Adadelta updates are as follows:
 
-avg_squared_grad_out = rho * avg_squared_grad + (1 - rho) * grad * grad
-param_update =  - sqrt((avg_squared_update + epsilon) /
-                       (avg_squared_grad_out + epsilon)) * grad
-avg_squared_update_out = rho * avg_squared_update + (1 - rho) * param_update**2
-param_out = param + param_update
-
-References:
-  [1] ADADELTA: An Adaptive Learning Rate Method
-      https://arxiv.org/abs/1212.5701
+$$avgSquaredGradOut = \rho * avgSquaredGrad + (1 - \rho) * grad * grad \break
+paramUpdate =  - $\sqrt{((avgSquaredUpdate + \epsilon) /
+                       (avgSquaredGrad_out + \epsilon))}$ * grad \break
+avgSquaredUpdateOut = \rho * avgSquaredUpdate + (1 - \rho) *
+                                  {(paramUpdate)}^2 \break
+paramOut = param + paramUpdate$$
 
 )DOC");
   }

paddle/operators/adagrad_op.cc

@@ -73,12 +73,16 @@ class AdagradOpMaker : public framework::OpProtoAndCheckerMaker {
 
 Adaptive Gradient Algorithm (Adagrad).
 
-moment_out = moment + grad * grad
-param_out = param - learning_rate * grad / (sqrt(moment_out) + epsilon)
+The update is done as follows:
+
+$$momentOut = moment + grad * grad \break
+paramOut = param - learningRate * grad / ($\sqrt{momentOut}$ + \epsilon) \break
+$$
 
 The original paper(http://www.jmlr.org/papers/volume12/duchi11a/duchi11a.pdf)
-does not have the epsilon attribute. It is added here for numerical stability 
-by avoiding division by zero.
+does not have the epsilon attribute. It is added here in our implementation
+as also proposed here: http://cs231n.github.io/neural-networks-3/#ada
+for numerical stability to avoid the division by zero error.
 
 )DOC");
   }

paddle/operators/adam_op.cc

@@ -51,8 +51,8 @@ class AdamOp : public framework::OperatorWithKernel {
     PADDLE_ENFORCE_EQ(framework::product(beta1_pow_dims), 1,
                       "Beta1 power accumulator should have 1 dimension");
     auto beta2_pow_dims = ctx->GetInputDim("Beta2Pow");
-    PADDLE_ENFORCE_EQ(framework::product(beta1_pow_dims), 1,
-                      "Beta1 power accumulator should have 1 dimension");
+    PADDLE_ENFORCE_EQ(framework::product(beta2_pow_dims), 1,
+                      "Beta2 power accumulator should have 1 dimension");
 
     auto param_dims = ctx->GetInputDim("Param");
     PADDLE_ENFORCE_EQ(
@@ -60,10 +60,10 @@ class AdamOp : public framework::OperatorWithKernel {
         "Param and Grad input of AdamOp should have same dimension");
     PADDLE_ENFORCE_EQ(
         param_dims, ctx->GetInputDim("Moment1"),
-        "Param and Moment input of AdamOp should have same dimension");
+        "Param and Moment1 input of AdamOp should have same dimension");
     PADDLE_ENFORCE_EQ(
         param_dims, ctx->GetInputDim("Moment2"),
-        "Param and InfNorm input of AdamOp should have same dimension");
+        "Param and Moment2 input of AdamOp should have same dimension");
 
     ctx->SetOutputDim("ParamOut", param_dims);
     ctx->SetOutputDim("Moment1Out", param_dims);
@@ -103,23 +103,20 @@ class AdamOpMaker : public framework::OpProtoAndCheckerMaker {
         .SetDefault(1.0e-8f);
 
     AddComment(R"DOC(
-Adam Updates Operator.
+Adam Optimizer.
 
 This implements the Adam optimizer from Section 2 of the Adam
-paper[1]. Adam is a first-order gradient-based optimization
-method based on adaptive estimates of lower-order moments.
+paper : https://arxiv.org/abs/1412.6980.
+Adam is a first-order gradient-based optimization method based on
+adaptive estimates of lower-order moments.
 
 Adam updates:
 
-moment1_out = beta1 * moment1 + (1 − beta1) * grad
-moment2_out = beta2 * moment2 + (1 − beta2) * grad * grad
-learning_rate_t = learning_rate_t *
-                  sqrt(1 - beta2_pow) / (1 - beta1_pow)
-param_out = param - learning_rate_t * moment1/ (sqrt(moment2) + epsilon)
-
-References:
-  [1] Adam: A Method for Stochastic Optimization
-      (https://arxiv.org/abs/1412.6980)
+$$moment_1_{out} = \beta_1 * moment_1 + (1 - \beta_1) * grad \break
+moment_2_{out} = \beta_2 * moment_2 + (1 - \beta_2) * grad * grad \break
+learningRate = learningRate *
+                  $\sqrt{(1 - \beta_2_{pow})}$ / (1 - \beta_1_{pow}) \break
+paramOut = param - learningRate * moment_1/ ($\sqrt{(moment_2)} + \epsilon)$$
 
 )DOC");
   }

paddle/operators/adamax_op.cc

@@ -99,26 +99,22 @@ class AdamaxOpMaker : public framework::OpProtoAndCheckerMaker {
                    "Constant for numerical stability")
         .SetDefault(1.0e-8f);
     AddComment(R"DOC(
-Adamax Updates Operator.
+Adamax Optimizer.
 
-This implements the Adamax optimizer from Section 7 of the Adam
-paper[1]. Adamax is a variant of the
+We implement the Adamax optimizer from Section 7 of the Adam
+paper: https://arxiv.org/abs/1412.6980. Adamax is a variant of the
 Adam algorithm based on the infinity norm.
 
 Adamax updates:
 
-moment_out = beta1 * moment + (1 - beta1) * grad
-inf_norm_out = max(beta2 * inf_norm + epsilon, abs(grad))
-learning_rate_t = learning_rate/(1 - beta1_pow)
-param_out = param - learning_rate_t * moment_out/inf_norm_out
+$$momentOut = \beta_1 * moment + (1 - \beta_1) * grad \break
+infNormOut = max(\beta_2 * infNorm + \epsilon, |grad|) \break
+learningRate = learningRate /(1 - \beta_1_{pow}) \break
+paramOut = param - learningRate * momentPut / infNormOut$$
 
 The original paper does not have an epsilon attribute.
-However, it is added here for numerical stability
-by preventing divide by 0.
-
-References:
-  [1] Adam: A Method for Stochastic Optimization
-      (https://arxiv.org/abs/1412.6980)
+However, it is added here for numerical stability to prevent the
+division by 0 error.
 
 )DOC");
   }

paddle/operators/auc_op.cc

@@ -23,11 +23,11 @@ class AucOp : public framework::OperatorWithKernel {
 
  protected:
   void InferShape(framework::InferShapeContext *ctx) const override {
-    PADDLE_ENFORCE(ctx->HasInput("Out"), "Input of Out must be initialized.");
+    PADDLE_ENFORCE(ctx->HasInput("Out"), "Input of Out should not be null.");
     PADDLE_ENFORCE(ctx->HasInput("Indices"),
-                   "Input of Indices must be initialized.");
+                   "Input of Indices should not be null.");
     PADDLE_ENFORCE(ctx->HasInput("Label"),
-                   "Input of Label must be initialized.");
+                   "Input of Label should not be null.");
     auto inference_height = ctx->GetInputDim("Out")[0];
     auto label_height = ctx->GetInputDim("Label")[0];
 
@@ -52,20 +52,20 @@ class AucOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("Out",
              "A floating point 2D tensor, values are in the range [0, 1]."
-             "Each row is descend sorted. This input should be the"
+             "Each row is sorted in descending order. This input should be the"
              "output of topk."
              "Typically, this tensor indicates the probability of each label");
     AddInput("Indices",
              "An int 2D tensor, indicating the indices of original"
-             "tensor before sort. Typically, this tensor indicates which label"
-             "the probability stands for.");
+             "tensor before sorting. Typically, this tensor indicates which "
+             "label the probability stands for.");
     AddInput("Label",
              "A 2D int tensor indicating the label of the training data."
              "The height is batch size and width is always 1.");
     // TODO(typhoonzero): support weight input
     AddOutput("AUC",
               "A scalar representing the "
-              "current area-under-curve.");
+              "current area-under-the-curve.");
 
     AddAttr<std::string>("curve", "Curve type, can be 'ROC' or 'PR'.")
         .SetDefault("ROC");
@@ -74,19 +74,18 @@ class AucOpMaker : public framework::OpProtoAndCheckerMaker {
                  " roc curve.")
         .SetDefault(200);
 
-    AddComment(
-        R"DOC(Computes the AUC according forward output and label.
-Best to use for binary classification evaluations.
+    AddComment(R"DOC(
+Area Under The Curve (AUC) Operator.
 
+This implementation computes the AUC according to forward output and label.
+It is used very widely in binary classification evaluation. As a note:
 If input label contains values other than 0 and 1, it will be cast
-to bool.
-
-You can find the definations here: 
+to bool. You can find the relevant definitions here:
 https://en.wikipedia.org/wiki/Receiver_operating_characteristic#Area_under_the_curve
 
-Possible curves are:
-- ROC: Receiver operating characteristic
-- PR: Precision Recall
+There are two types of possible curves:
+1. ROC: Receiver operating characteristic
+2. PR: Precision Recall
 )DOC");
   }
 };

paddle/operators/batch_norm_op.cc

@@ -51,6 +51,10 @@ class BatchNormOp : public framework::OperatorWithKernel {
     PADDLE_ENFORCE(ctx->HasOutput("SavedMean"), "");
     PADDLE_ENFORCE(ctx->HasOutput("SavedVariance"), "");
 
+    const float epsilon = ctx->Attrs().Get<float>("epsilon");
+    PADDLE_ENFORCE_GE(epsilon, 0.0, "epsilon should be larger than 0");
+    PADDLE_ENFORCE_LE(epsilon, 0.001, "epsilon should not be too large");
+
     // make sure Mean/MeanOut and Variance/VarianceOut share memory in Python
     PADDLE_ENFORCE_EQ(ctx->Inputs("Mean")[0], ctx->Outputs("MeanOut")[0],
                       "Mean and MeanOut should share the same memory");
@@ -66,7 +70,7 @@ class BatchNormOp : public framework::OperatorWithKernel {
                                              : x_dims[x_dims.size() - 1]);
 
     PADDLE_ENFORCE(x_dims.size() >= 3 && x_dims.size() <= 5,
-                   "Input x must have 3 to 5 dimensions.");
+                   "Input X must have 3 to 5 dimensions.");
 
     PADDLE_ENFORCE_EQ(ctx->GetInputDim("Scale").size(), 1UL);
     PADDLE_ENFORCE_EQ(ctx->GetInputDim("Scale")[0], C);
@@ -93,16 +97,16 @@ class BatchNormOpMaker : public framework::OpProtoAndCheckerMaker {
     AddInput("X", "The input tensor");
     AddInput("Scale",
              "Scale is a 1-dimensional tensor of size C "
-             "to be applied to the output");
+             "that is applied to the output");
     AddInput("Bias",
              "Bias is a 1-dimensional tensor of size C "
-             "to be applied to the output");
+             "that is applied to the output");
     AddInput("Mean",
-             "The global mean (for training) or the "
+             "The global mean (for training) or "
              "estimated mean (for testing)");
     AddInput("Variance",
              "The global variance (for training) "
-             "or the estimated Variance (for testing)");
+             "or estimated Variance (for testing)");
     AddOutput("Y", "result after normalization");
     AddOutput("MeanOut",
               "Share memory with Mean. "
@@ -119,10 +123,14 @@ class BatchNormOpMaker : public framework::OpProtoAndCheckerMaker {
               "will apply to output when training")
         .AsIntermediate();
     AddComment(R"DOC(
-https://arxiv.org/pdf/1502.03167.pdf
+Batch Normalization.
 
-NHWC `[batch, in_height, in_width, in_channels]`
-NCHW `[batch, in_channels, in_height, in_width]`
+Batch Norm has been implemented as discussed in the paper:
+https://arxiv.org/pdf/1502.03167.pdf
+Can be used as a normalizer function for conv2d and fully_connected operations.
+The required data format for this layer is one of the following:
+1. NHWC `[batch, in_height, in_width, in_channels]`
+2. NCHW `[batch, in_channels, in_height, in_width]`
 
 )DOC");
   }
@@ -297,7 +305,6 @@ class BatchNormGradOp : public framework::OperatorWithKernel {
 
   framework::DataType IndicateDataType(
       const framework::ExecutionContext &ctx) const override {
-    VLOG(3) << "IndicateDataType " << this->Type();
     const auto *var = ctx.InputVar(framework::GradVarName("Y"));
     if (var == nullptr) {
       PADDLE_THROW("can't find Y@GRAD");

paddle/operators/cast_op.cc

@@ -23,13 +23,17 @@ class CastOpProtoMaker : public framework::OpProtoAndCheckerMaker {
   CastOpProtoMaker(framework::OpProto *proto,
                    framework::OpAttrChecker *op_checker)
       : OpProtoAndCheckerMaker(proto, op_checker) {
-    AddInput("X", "the input tensor of cast op");
-    AddOutput("Out", "the output tensor of cast op");
-    AddComment(R"DOC(Cast operator.
-cast the input tensor to other data type.
-)DOC");
+    AddInput("X", "The input tensor of cast op");
+    AddOutput("Out", "The output tensor of cast op");
     AddAttr<int>("out_data_type", "output data type");
     AddAttr<int>("in_data_type", "input data type");
+    AddComment(R"DOC(
+Cast Operator.
+
+This Operator casts the input tensor to another data type and
+returns tha Output Tensor.
+
+)DOC");
   }
 };
 

paddle/operators/clip_op.cc

@@ -49,8 +49,11 @@ class ClipOpMaker : public framework::OpProtoAndCheckerMaker {
     AddAttr<AttrType>(
         "max", "(float)Maximum value, above which element is replaced by max");
     AddComment(R"DOC(
-Clip operator limits the given input within an interval. The interval is
+Clip Operator.
+
+The clip operator limits the value of given input within an interval. The interval is
 specified with arguments 'min' and 'max'.
+
 )DOC");
   }
 };

paddle/operators/concat_op.cc

@@ -56,20 +56,24 @@ class ConcatOpMaker : public framework::OpProtoAndCheckerMaker {
  public:
   ConcatOpMaker(framework::OpProto *proto, framework::OpAttrChecker *op_checker)
       : OpProtoAndCheckerMaker(proto, op_checker) {
-    AddInput("X", "the input tensors of concat operator.").AsDuplicable();
-    AddOutput("Out", "the output tensor of concat operator.");
-    AddComment(R"DOC(
-            Join the input tensors along with the axis.
-            Examples:
-              Input[0] = [[1,2],[3,4]]
-              Input[1] = [[5,6]]
-              axis = 0
-              Output = [[1,2],
-                        [3,4],
-                        [5,6]]
-        )DOC");
-    AddAttr<int>("axis", "The axis which the inputs will be joined with.")
+    AddInput("X", "Input tensors of concat operator.").AsDuplicable();
+    AddOutput("Out", "Output tensor of concat operator.");
+    AddAttr<int>("axis",
+                 "The axis along which the input tensors will be concatenated.")
         .SetDefault(0);
+    AddComment(R"DOC(
+Concat Operator.
+
+Concatenate the input tensors along dimension axis.
+Examples:
+  Input[0] = [[1,2],[3,4]]
+  Input[1] = [[5,6]]
+  axis = 0
+  Output = [[1,2],
+            [3,4],
+            [5,6]]
+
+)DOC");
   }
 };
 

paddle/operators/cond_op.cc

@@ -216,11 +216,12 @@ class CondOpProtoAndCheckerMaker : public framework::OpProtoAndCheckerMaker {
     AddOutput("IndexTensors", "Index Tensors contains indices for true/false");
 
     AddComment(R"DOC(
-Sample dependent Cond Operator:
-Given Cond[i] as a 1/0 vector to indicate true/false
-The equation is:
-Out[i] = subnet_t[i], if Cond[i] == true
-Out[i] = subnet_t[i], if Cond[i] == false
+Sample Dependent Conditional Operator.
+
+Given Cond[i] as a 1/0 vector to indicate true/false:
+Out[i] = subnet_true[i], if Cond[i] == true
+Out[i] = subnet_false[i], if Cond[i] == false
+
 )DOC");
   }
 };

paddle/operators/conv2d_op.cc

@@ -56,17 +56,18 @@ Conv2DOpMaker::Conv2DOpMaker(framework::OpProto* proto,
   AddInput(
       "Input",
       "The input tensor of convolution operator. "
-      "The format of input tensor is NCHW. Where N is batch size, C is the "
-      "number of channels, H and W is the height and width of image.");
+      "The format of input tensor is NCHW, where N is batch size, C is the "
+      "number of channels, H is the height of the image, "
+      "and W is the width of the image.");
   AddInput("Filter",
-           "The filter tensor of convolution operator."
+           "The filter tensor of convolution operator. "
            "The format of the filter tensor is MCHW, where M is the number of "
            "output image channels, C is the number of input image channels, "
-           "H and W is height and width of filter. "
-           "If the groups attribute is greater than 1, C equal the number of "
+           "H is the height of the filter, and W is the width of the filter. "
+           "If the groups attribute is greater than 1, C equals the number of "
            "input image channels divided by the groups.");
   AddOutput("Output",
-            "The output tensor of convolution operator."
+            "The output tensor of convolution operator. "
             "The format of output tensor is also NCHW.");
   AddAttr<std::vector<int>>("strides", "strides of convolution operator.")
       .SetDefault({1, 1});
@@ -74,16 +75,19 @@ Conv2DOpMaker::Conv2DOpMaker(framework::OpProto* proto,
       .SetDefault({0, 0});
   AddAttr<int>(
       "groups",
-      "group size of convolution operator. "
-      "Refer to grouped convolution in Alex Krizhevsky's paper: "
-      "when group=2, the first half of the filters are only connected to the "
-      "first half of the input channels, and the second half only connected "
-      "to the second half.")
+      "Group size of convolution operator. "
+      "According to grouped convolution in Alex Krizhevsky's Deep CNN paper: "
+      "when group=2, the first half of the filters is only connected to the "
+      "first half of the input channels, while the second half of the filters "
+      "is only connected to the second half of the input channels.")
       .SetDefault(1);
   AddComment(R"DOC(
-The convolution operation calculates the output based on the input, filter
-and strides, paddings, groups parameters. The size of each dimension of the
-parameters is checked in the infer-shape.
+Convolution Operator.
+
+The convolution operation calculates the output based on the input, filter, 
+strides, paddings, and groups parameters. The size of each dimension of the
+parameters is checked in the infer-shape method.
+
 )DOC");
 }
 

paddle/operators/conv2d_transpose_op.cc

@@ -54,15 +54,16 @@ Conv2DTransposeOpMaker::Conv2DTransposeOpMaker(
   AddInput(
       "Input",
       "(Tensor) The input tensor of convolution transpose operator. "
-      "The format of input tensor is NCHW. Where N is batch size, C is the "
-      "number of input channels, H and W is the height and width of image.");
+      "The format of input tensor is NCHW, where N is batch size, C is the "
+      "number of input channels, H is the height of the image, and "
+      "W is the width of the image.");
   AddInput("Filter",
            "(Tensor) The filter tensor of convolution transpose operator."
            "The format of the filter tensor is CMHW, where C is the number of "
            "output image channels, M is the number of input image channels, "
-           "H and W is height and width of filter. "
+           "H is the height of the filter, and W is the width of the filter. "
            "We enforce groups number == 1 and padding == 0 in "
-           "convolution transpose Scenario.");
+           "the convolution transpose scenario.");
   AddOutput("Output",
             "(Tensor) The output tensor of convolution transpose operator."
             "The format of output tensor is also NCHW.");
@@ -73,9 +74,12 @@ Conv2DTransposeOpMaker::Conv2DTransposeOpMaker(
                             "paddings of convolution transpose operator.")
       .SetDefault({0, 0});
   AddComment(R"DOC(
-The convolution transpose operation calculates the output based on the input, filter
-and strides, paddings, groups parameters. The size of each dimension of the
-parameters is checked in the infer-shape.
+Convolution Transpose Operator.
+
+The convolution transpose operation calculates the output based on the input, 
+filter, strides, paddings, and groups parameters. The size of each dimension 
+of the parameters is checked in the infer-shape method.
+
 )DOC");
 }
 

paddle/operators/conv_cudnn_op.cc

@@ -29,7 +29,7 @@ class CudnnConvOpMaker : public Conv2DOpMaker {
                  "workspace is a section of GPU memory which will be "
                  "allocated/freed each time the operator runs, larger "
                  "workspace size can increase performance but also requires "
-                 "better hardward. This size should be carefully setted.")
+                 "better hardware. This size should be chosen carefully.")
         .SetDefault(4096);
   }
 };

paddle/operators/conv_shift_op.cc

@@ -96,14 +96,13 @@ as used in the Neural Turing Machine: https://arxiv.org/abs/1410.5401
 
 The equation is:
 
-  \f[
-      Out[i] = \sum_{j=-(N-1)/2}^{(N-1)/2} X_{i+j} * Y_{j}
-  \f]
+$$Out[i] = \sum_{j=-(N-1)/2}^{(N-1)/2} X_{i+j} * Y_{j}$$
 
-where X's index is computed modulo M, and b's index is computed modulo N.
+where X's index is computed modulo M, and Y's index is computed modulo N.
+
+Both inputs X and Y can carry LoD (Level of Details) information.
+However, the output only shares the LoD information with input X.
 
-Both of the input `X` and `Y` can carry LoD (Level of Details) information.
-However, the output only shares the LoD information with input `X`.
 )DOC");
   }
 };

paddle/operators/cos_sim_op.cc

@@ -79,15 +79,16 @@ class CosSimOpMaker : public framework::OpProtoAndCheckerMaker {
     AddComment(R"DOC(
 Cosine Similarity Operator.
 
-The equation is: Out = X^T * Y / (sqrt(X^T * X) * sqrt(Y^T * Y)).
+$Out = X^T * Y / (\sqrt{X^T * X} * \sqrt{Y^T * Y})$
 
-The input `X` and `Y` must have the same shape, except that the 1st dimension
-of input `Y` could be just 1 (different from input `X`), which will be
-broadcasted to match the shape of input `X` before computing their cosine
+The input X and Y must have the same shape, except that the 1st dimension
+of input Y could be just 1 (different from input X), which will be
+broadcasted to match the shape of input X before computing their cosine
 similarity.
 
-Both the input `X` and `Y` can carry the LoD (Level of Details) information,
-or not. But the output only shares the LoD with input `X`.
+Both the input X and Y can carry the LoD (Level of Details) information,
+or not. But the output only shares the LoD information with input X.
+
 )DOC");
   }
 };

paddle/operators/crf_decoding_op.cc

+/* Copyright (c) 2016 PaddlePaddle Authors. All Rights Reserve.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License. */
+
+#include "paddle/operators/crf_decoding_op.h"
+
+namespace paddle {
+namespace operators {
+class CRFDecodingOpMaker : public framework::OpProtoAndCheckerMaker {
+ public:
+  CRFDecodingOpMaker(framework::OpProto* proto,
+                     framework::OpAttrChecker* op_checker)
+      : OpProtoAndCheckerMaker(proto, op_checker) {
+    AddInput("Emission",
+             "(LoDTensor, default: LoDTensor<float>). A LoDTensor with shape "
+             "[N x D] where N is the size of the mini-batch and D is the total "
+             "tag number. This input is the unscaled emission weight matrix of "
+             "the linear_chain_crf operator.");
+    AddInput(
+        "Transition",
+        "(Tensor, default: Tensor<float>). A Tensor with shape [(D + 2) x D]. "
+        "This input is the transition weights learned by the linear_chain_crf "
+        "operator, denoted as w. The 1st row of w are transition weights for "
+        "the start mask. The 2nd row of w are transition weights for the end "
+        "mask. Transition weights between other tags begin from the 3rd row of "
+        "w. See more details in comments of the linear_chain_crf operator.");
+    AddInput(
+        "Label",
+        "(LoDTensor,  LoDTensor<int>). The ground truth with shape "
+        "[N x 1]. This input is optional. See more details in the operator's "
+        "comments.")
+        .AsDispensable();
+    AddOutput("ViterbiPath",
+              "(LoDTensor, LoDTensor<int>). The decoding results. What to "
+              "return changes depending on whether the Input(Label) (the groud "
+              "truth) is given. See more details in the operator's comment.");
+    AddComment(R"DOC(
+The crf_decoding operator reads the emission feature weights and the transition
+freature weights learned by the linear_chain_crf operator. It implements the
+Viterbi algorithm which is a dynamic programming algorithm for finding the most
+likely sequence of hidden states, called the Viterbi path, that results in a
+sequence of observed tags.
+
+The output of this operator changes according to whether Input(Label) is given:
+
+1. Input(Label) is given:
+
+This happens in training. This operator is used to co-work with the chunk_eval
+operator.
+
+When Input(Label) is given, the crf_decoding operator returns a row vector
+with shape [N x 1] whose values are fixed to be 0, indicating an incorrect
+prediction, or 1 indicating a tag is correctly predicted. Such an ouput is the
+input to chunk_eval operator.
+
+2. Input(Label) is not given:
+
+This is the standard decoding process.
+
+The crf_decoding operator returns a row vecotr with shape [N x 1] whose values
+range from 0 to maximum tag number - 1. Each element indicates an index of a
+predicted tag.
+)DOC");
+  }
+};
+
+class CRFDecodingOp : public framework::OperatorWithKernel {
+ public:
+  using framework::OperatorWithKernel::OperatorWithKernel;
+
+  void InferShape(framework::InferShapeContext* ctx) const override {
+    PADDLE_ENFORCE(ctx->HasInput("Emission"),
+                   "Input(Emission) should be not null.");
+    PADDLE_ENFORCE(ctx->HasInput("Transition"),
+                   "Input(Transition) should be not null.");
+
+    PADDLE_ENFORCE(ctx->HasOutput("ViterbiPath"),
+                   "Output(ViterbiPath) should be not null.");
+
+    auto emission_dims = ctx->GetInputDim("Emission");
+    PADDLE_ENFORCE_EQ(emission_dims.size(), 2UL,
+                      "The Input(Emission) should be a 2-D tensor.");
+    PADDLE_ENFORCE(emission_dims[0], "An empty mini-batch is not allowed.");
+
+    auto transition_dims = ctx->GetInputDim("Transition");
+    PADDLE_ENFORCE_EQ(transition_dims.size(), 2UL,
+                      "The Input(Transition) should be a 2-D tensor.");
+    PADDLE_ENFORCE_EQ(
+        transition_dims[0] - 2, transition_dims[1],
+        "An invalid dimension for the Input(Transition), which should "
+        "be a 2-D tensor with shape [(D + 2) x D].");
+    PADDLE_ENFORCE_EQ(
+        emission_dims[1], transition_dims[1],
+        "The 2nd dimension of the Input(Emission) and the Input(Transition) "
+        "should be equal to the tag number.");
+
+    if (ctx->HasInput("Label")) {
+      auto label_dims = ctx->GetInputDim("Label");
+      PADDLE_ENFORCE(label_dims.size() == 2UL && label_dims[1] == 1UL,
+                     "The Input(Label) should be a 2-D tensor with the 2nd "
+                     "dimensions fixed to 1.");
+      PADDLE_ENFORCE_EQ(
+          emission_dims[0], label_dims[0],
+          "The height of Input(Emission) and the height of Input(Label) "
+          "should be the same.");
+    }
+
+    ctx->ShareLoD("Emission", /*->*/ "ViterbiPath");
+    ctx->SetOutputDim("ViterbiPath", {emission_dims[0], 1});
+  }
+
+ protected:
+  framework::DataType IndicateDataType(
+      const framework::ExecutionContext& ctx) const override {
+    return framework::ToDataType(ctx.Input<LoDTensor>("Emission")->type());
+  }
+};
+}  // namespace operators
+}  // namespace paddle
+
+namespace ops = paddle::operators;
+REGISTER_OP_WITHOUT_GRADIENT(crf_decoding, ops::CRFDecodingOp,
+                             ops::CRFDecodingOpMaker);
+REGISTER_OP_CPU_KERNEL(
+    crf_decoding, ops::CRFDecodingOpKernel<paddle::platform::CPUPlace, float>,
+    ops::CRFDecodingOpKernel<paddle::platform::CPUPlace, double>);

paddle/operators/crf_decoding_op.h

+/* Copyright (c) 2016 PaddlePaddle Authors. All Rights Reserve.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License. */
+
+#pragma once
+#include "paddle/framework/eigen.h"
+#include "paddle/framework/op_registry.h"
+#include "paddle/operators/math/math_function.h"
+
+namespace paddle {
+namespace operators {
+
+using framework::LoDTensor;
+using framework::LoD;
+using framework::Tensor;
+
+template <typename Place, typename T>
+class CRFDecodingOpKernel : public framework::OpKernel<T> {
+ public:
+  void Compute(const framework::ExecutionContext& ctx) const override {
+    PADDLE_ENFORCE(platform::is_cpu_place(ctx.GetPlace()),
+                   "The crf_decoding operator can only run on CPU.");
+
+    auto* emission_weights = ctx.Input<LoDTensor>("Emission");
+    auto* transition_weights = ctx.Input<Tensor>("Transition");
+    auto* label = ctx.Input<LoDTensor>("Label");
+    auto* decoded_path = ctx.Output<Tensor>("ViterbiPath");
+
+    PADDLE_ENFORCE_EQ(emission_weights->NumLevels(), 1UL,
+                      "The Input(Emission) should be a sequence.");
+    auto lod = emission_weights->lod();
+    PADDLE_ENFORCE(lod.size(), "Input(Emission) must be a sequence.");
+    const size_t level = 0;
+    const size_t seq_num = lod[level].size() - 1;
+
+    int* path = decoded_path->mutable_data<int>(platform::CPUPlace());
+    math::SetConstant<platform::CPUPlace, int>()(ctx.device_context(),
+                                                 decoded_path, 0);
+    for (size_t i = 0; i < seq_num; ++i) {
+      int start_pos = static_cast<int>(lod[level][i]);
+      int end_pos = static_cast<int>(lod[level][i + 1]);
+      Tensor decoded_path_one_seq = decoded_path->Slice(start_pos, end_pos);
+      Decode(emission_weights->Slice(start_pos, end_pos), *transition_weights,
+             &decoded_path_one_seq);
+    }
+
+    if (label) {
+      PADDLE_ENFORCE_EQ(label->NumLevels(), 1UL,
+                        "The Input(Label) should be a sequence.");
+      const int* label_value = label->data<int>();
+      size_t batch_size = emission_weights->dims()[0];
+      for (size_t i = 0; i < batch_size; ++i) {
+        path[i] = label_value[i] == path[i] ? 1 : 0;
+      }
+    }
+  }
+
+ private:
+  void Decode(const Tensor& emission_weights, const Tensor& transition_weights,
+              Tensor* decoded_path) const {
+    auto emission_dims = emission_weights.dims();
+    const size_t seq_len = emission_dims[0];
+    const size_t tag_num = emission_dims[1];
+
+    const size_t state_trans_base_idx = 2;
+
+    const T* x = emission_weights.data<T>();
+    const T* w = transition_weights.data<T>();
+    int* path = decoded_path->data<int>();
+
+    // alpha is a memo table. An element alpha(k, v) records the score of the
+    // best sequence of tags from position 1 to position k with v being the end
+    // tag.
+    Tensor alpha;
+    T* alpha_value = alpha.mutable_data<T>(emission_dims, platform::CPUPlace());
+    Tensor track;
+    int* track_value =
+        track.mutable_data<int>(emission_dims, platform::CPUPlace());
+
+    for (size_t i = 0; i < tag_num; ++i) alpha_value[i] = w[i] + x[i];
+
+    for (size_t k = 1; k < seq_len; ++k) {
+      for (size_t i = 0; i < tag_num; ++i) {
+        T max_score = -std::numeric_limits<T>::max();
+        int max_j = 0;
+        for (size_t j = 0; j < tag_num; ++j) {
+          T score = alpha_value[(k - 1) * tag_num + j] +
+                    w[(j + state_trans_base_idx) * tag_num + i];
+          if (score > max_score) {
+            max_score = score;
+            max_j = j;
+          }
+        }
+
+        alpha_value[k * tag_num + i] = max_score + x[k * tag_num + i];
+        track_value[k * tag_num + i] = max_j;
+      }
+    }
+
+    T max_score = -std::numeric_limits<T>::max();
+    int max_i = 0;
+    for (size_t i = 0; i < tag_num; ++i) {
+      T score = alpha_value[(seq_len - 1) * tag_num + i] + w[tag_num + i];
+      if (score > max_score) {
+        max_score = score;
+        max_i = i;
+      }
+    }
+    path[seq_len - 1] = max_i;
+    for (int k = seq_len - 1; k >= 1; --k) {
+      path[k - 1] = max_i = track_value[k * tag_num + max_i];
+    }
+  }
+};
+
+}  // namespace operators
+}  // namespace paddle

paddle/operators/crop_op.cc

@@ -56,34 +56,35 @@ class CropOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X",
              "The input of pad op. "
-             "The input should be a k-D tensor(k > 0 and k < 7)");
+             "The input should be a k-D tensor(k > 0 and k < 7).");
     AddInput("Y",
-             "The input used as reference for cropping"
-             " with the same dimension as X. ")
+             "The input used as reference for cropping, "
+             "which is of the same dimensions as X.")
         .AsDispensable();
     AddOutput("Out",
-              "The output of crop op "
-              "with the same dimension as X.");
+              "The output of crop op, "
+              "which is of the same dimensions as X.");
     AddAttr<std::vector<int>>("offsets",
-                              "A list<int> describing offsets to be cropped."
-                              "The size of offsets list should be as same as "
-                              "dimension size of  input X.");
+                              "A list<int> describing offsets to be cropped. "
+                              "The size of offsets list should be the same as "
+                              "the dimension size of input X.");
     AddAttr<std::vector<int>>("shape",
-                              "A list<int> describing the shape of output."
-                              "The size of shape list should be as same as "
-                              "dimension size of  input X.")
+                              "A list<int> describing the shape of output. "
+                              "The size of shape list should be the same as "
+                              "the dimension size of input X.")
         .SetDefault(std::vector<int>());
     AddComment(R"DOC(
 Crop Operator.
+
 Crop input into output, as specified by offsets and shape.
 
 There are two ways to set shape:
-1. referenc input: crop input X as shape as reference input.
+1. reference input: crop input X into the same shape as reference input.
                     The dimension of reference input should
-                    be as same as input X.
-2. shape list: crop input X by shape described by a list<int>.
-               The size of shape list should be as same as
-               dimension size of  input X.
+                    be the same as the dimension of input X.
+2. shape list: crop input X into the shape described by a list<int>.
+               The size of shape list should be the same as
+               the dimension size of input X.
 
 The input should be a k-D tensor(k > 0 and k < 7). As an example:
 
@@ -91,20 +92,20 @@ Given:
 
     X = [[0, 1, 2, 0, 0]
          [0, 3, 4, 0, 0]
-         [0, 0, 0, 0, 0]]
+         [0, 0, 0, 0, 0]],
 
 and
 
-    offsets = [0, 1]
+    offsets = [0, 1],
 
 and
 
-    shape = [2, 2]
+    shape = [2, 2],
 
-then we get
+we get:
 
     Out = [[1, 2],
-           [3, 4]]
+           [3, 4]].
 
 )DOC");
   }

paddle/operators/cross_entropy_op.cc

@@ -49,7 +49,7 @@ class CrossEntropyOp : public framework::OperatorWithKernel {
   }
 
  protected:
-  // Explicitly set that data type of the output of the cross_entropy operator
+  // Explicitly set that the data type of computation kernel of cross_entropy
   // is determined by its input "X".
   framework::DataType IndicateDataType(
       const framework::ExecutionContext& ctx) const override {
@@ -96,7 +96,8 @@ class CrossEntropyGradientOp : public framework::OperatorWithKernel {
   }
 
  protected:
-  // CrossEntropy's data type just determined by "X"
+  // Explicitly set that the data type of computation kernel of cross_entropy
+  // is determined by its input "X".
   framework::DataType IndicateDataType(
       const framework::ExecutionContext& ctx) const override {
     return framework::ToDataType(ctx.Input<Tensor>("X")->type());
@@ -117,9 +118,9 @@ class CrossEntropyOpMaker : public framework::OpProtoAndCheckerMaker {
         "Label",
         "(Tensor, default Tensor<int>), the ground truth which is "
         "a 2-D tensor. "
-        "When soft_label is set to false, `Label` is a Tensor<int> with shape "
+        "When soft_label is set to false, Label is a Tensor<int> with shape "
         "[N x 1]. "
-        "When soft_label is set to true, `Label` is a Tensor<float/double> "
+        "When soft_label is set to true, Label is a Tensor<float/double> "
         "with shape [N x K].");
     AddOutput("Y",
               "(Tensor, default Tensor<float>), a 2-D tensor "
@@ -137,13 +138,13 @@ computation.
 1) One-hot cross-entropy:
     soft_label = false, Label[i, 0] indicates the class index for sample i:
 
-                Y[i] = -log(X[i, Label[i]])
+                $Y[i] = -\log(X[i, Label[i]])$
 
 2) Soft-label cross-entropy:
     soft_label = true, Label[i, j] indicates the soft label of class j
     for sample i:
 
-                Y[i] = \sum_j{-Label[i, j] * log(X[i, j])}
+                $Y[i] = \sum_j{-Label[i, j] * log(X[i, j])}$
 
    Please make sure that in this case the summuation of each row of Label
    equals one.
@@ -153,8 +154,9 @@ computation.
      non-zero element (equals 1), soft-label cross-entropy degenerates to a
      one-hot cross-entropy with one-hot label representation.
 
-Both the input `X` and `Label` can carry the LoD (Level of Details) information,
-or not. But the output only shares the LoD with input `X`.
+Both the input X and Label can carry the LoD (Level of Details) information,
+or not. But the output only shares the LoD information with input X.
+
 )DOC");
   }
 };

paddle/operators/decayed_adagrad_op.cc

@@ -75,11 +75,18 @@ class DecayedAdagradOpMaker : public framework::OpProtoAndCheckerMaker {
                    "Constant for numerical stability")
         .SetDefault(1.0e-6f);
     AddComment(R"DOC(
+Decayed Adagrad Optimizer.
 
-Decayed Adagrad
+The update is done as follows:
 
-moment_out = decay * moment + (1 - decay) * grad * grad
-param_out = param - learning_rate * grad / (sqrt(moment_out) + epsilon)
+$$
+moment\_out = decay * moment + (1 - decay) * grad * grad \\
+param\_out = param - \frac{learning\_rate * grad}{\sqrt{moment\_out} + epsilon}
+$$
+
+The original paper(http://www.jmlr.org/papers/volume12/duchi11a/duchi11a.pdf)
+does not have an epsilon attribute. It is added here for numerical
+stability to avoid the division by zero error.
 
 )DOC");
   }

paddle/operators/dropout_op.cc

@@ -43,22 +43,24 @@ class DropoutOpMaker : public framework::OpProtoAndCheckerMaker {
   DropoutOpMaker(framework::OpProto* proto,
                  framework::OpAttrChecker* op_checker)
       : OpProtoAndCheckerMaker(proto, op_checker) {
-    AddAttr<float>("dropout_prob", "Probability of setting units to zero.")
-        .SetDefault(.5f);
-    AddAttr<bool>("is_training", "Whether in training phase.").SetDefault(true);
-    AddAttr<int>("seed", "Dropout random seed.").SetDefault(0);
     AddInput("X", "The input of dropout op.");
     AddOutput("Out", "The output of dropout op.");
     AddOutput("Mask", "The random sampled dropout mask.").AsIntermediate();
 
+    AddAttr<float>("dropout_prob", "Probability of setting units to zero.")
+        .SetDefault(.5f);
+    AddAttr<bool>("is_training", "True if in training phase.").SetDefault(true);
+    AddAttr<int>("seed", "Dropout random seed.").SetDefault(0);
+
     AddComment(R"DOC(
 Dropout Operator.
 
-'Dropout' refers to randomly dropping out units in a nerual network. It is a
+Dropout refers to randomly dropping out units in a nerual network. It is a
 regularization technique for reducing overfitting by preventing neuron
 co-adaption during training. The dropout operator randomly set (according to
 the given dropout probability) the outputs of some units to zero, while others
-being set to their inputs.
+are set equal to their corresponding inputs.
+
 )DOC");
   }
 };

paddle/operators/dynamic_recurrent_op.cc

@@ -386,12 +386,13 @@ class DynamicRecurrentOpProtoAndCheckerMaker
         RNNAlgorithm::kArgNames[RNNAlgorithm::ComputeMode::kForward];
     // inputs and outputs stored in proto
     AddInput(name.inlinks,
-             "the inputs that need to be segmented for each step.")
+             "The inputs that need to be segmented for each step.")
         .AsDuplicable();
-    AddInput(name.initial_states, "variables to initialize states.")
+    AddInput(name.initial_states, "Variables to initialize the states.")
         .AsDuplicable();
 
-    AddOutput(name.outlinks, "the outputs that need to concated for all steps.")
+    AddOutput(name.outlinks,
+              "The outputs that need to be concatenated for all steps.")
         .AsDuplicable();
     AddOutput(name.step_scopes, "step scopes");
 
@@ -399,7 +400,12 @@ class DynamicRecurrentOpProtoAndCheckerMaker
     AddAttr<std::vector<std::string>>(name.ex_states, "names of ex_states");
     AddAttr<std::vector<std::string>>(name.states, "names of states");
 
-    AddComment("This is a RNN operator for varience-length sequences.");
+    AddComment(R"DOC(
+Dynamic Recurrent Operator.
+
+This is a RNN operator for varience-length sequences.
+
+)DOC");
   }
 };
 

paddle/operators/elementwise_add_op.cc

@@ -22,7 +22,7 @@ class ElementwiseAddOpMaker : public ElementwiseOpMaker {
   ElementwiseAddOpMaker(framework::OpProto* proto,
                         framework::OpAttrChecker* op_checker)
       : ElementwiseOpMaker(proto, op_checker) {
-    SetComment("add", "Out = X + Y");
+    SetComment("Add", "$Out = X + Y$");
     AddComment(comment_);
   }
 };

paddle/operators/elementwise_div_op.cc

@@ -22,7 +22,7 @@ class ElementwiseDivOpMaker : public ElementwiseOpMaker {
   ElementwiseDivOpMaker(framework::OpProto* proto,
                         framework::OpAttrChecker* op_checker)
       : ElementwiseOpMaker(proto, op_checker) {
-    SetComment("Div", "Out = X / Y");
+    SetComment("Div", "$Out = X / Y$");
     AddComment(comment_);
   }
 };

paddle/operators/elementwise_mul_op.cc

@@ -23,7 +23,7 @@ class ElementwiseMulOpMaker : public ElementwiseOpMaker {
   ElementwiseMulOpMaker(framework::OpProto* proto,
                         framework::OpAttrChecker* op_checker)
       : ElementwiseOpMaker(proto, op_checker) {
-    SetComment("Mul", "Out = X ⊙ Y");
+    SetComment("Mul", "$Out = X \\odot\\ Y$");
     AddComment(comment_);
   }
 };

paddle/operators/elementwise_op.h

@@ -46,37 +46,42 @@ class ElementwiseOpMaker : public framework::OpProtoAndCheckerMaker {
   ElementwiseOpMaker(framework::OpProto* proto,
                      framework::OpAttrChecker* op_checker)
       : OpProtoAndCheckerMaker(proto, op_checker) {
-    AddInput("X", R"DOC(
-The first input of elementwise op, it's a tensor of any dimensions.
-)DOC");
-    AddInput("Y", R"DOC(
-The sencond input of elementwise op, it's a tensor and it's dimensions
-must be small or equal to X's dimensions.
-)DOC");
+    AddInput("X", "(Tensor) The first input tensor of elementwise op");
+    AddInput("Y", "(Tensor) The second input tensor of elementwise op");
+    AddOutput("Out", "The output of elementwise op");
     AddAttr<int>("axis",
-                 R"DOC(
-When the shape(Y) does not equal the shape(X),Y will be broadcasted
-to match the shape of X and axis should be dimension index Y in X
-        )DOC")
+                 "(int, default -1) The starting dimension index "
+                 "for broadcasting Y onto X")
         .SetDefault(-1)
         .EqualGreaterThan(-1);
-
-    AddOutput("Out", "The output of elementwise op");
     comment_ = R"DOC(
-Limited elementwise {name} operator.The equation is: Out = {equation}.
-1. The shape of Y should be same with X or
-2. Y's shape is a subset of X.
-   Y will be broadcasted to match the shape of X and axis should be dimension index Y in X.
-
-   example:
-      shape(X) = (2, 3, 4, 5), shape(Y) = (,)
-      shape(X) = (2, 3, 4, 5), shape(Y) = (5,)
-      shape(X) = (2, 3, 4, 5), shape(Y) = (4, 5)
-      shape(X) = (2, 3, 4, 5), shape(Y) = (3, 4), with axis=1
-      shape(X) = (2, 3, 4, 5), shape(Y) = (2), with axis=0
+Limited Elementwise {name} Operator.
+
+The equation is:
+
+{equation}
+
+X is a tensor of any dimension and the dimensions of tensor Y must be smaller than
+or equal to the dimensions of X. 
+
+There are two cases for this operator:
+1. The shape of Y is same with X;
+2. The shape of Y is a subset of X.
+
+For case 2:
+Y will be broadcasted to match the shape of X and axis should be 
+the starting dimension index for broadcasting Y onto X.
+
+example:
+  shape(X) = (2, 3, 4, 5), shape(Y) = (,)
+  shape(X) = (2, 3, 4, 5), shape(Y) = (5,)
+  shape(X) = (2, 3, 4, 5), shape(Y) = (4, 5)
+  shape(X) = (2, 3, 4, 5), shape(Y) = (3, 4), with axis=1
+  shape(X) = (2, 3, 4, 5), shape(Y) = (2), with axis=0
 
 Both the input X and Y can carry the LoD (Level of Details) information,
-or not. But the output only shares the LoD with input X.
+or not. But the output only shares the LoD information with input X.
+
 )DOC";
     AddComment(comment_);
   }

paddle/operators/elementwise_sub_op.cc

@@ -22,7 +22,7 @@ class ElementwiseSubOpMaker : public ElementwiseOpMaker {
   ElementwiseSubOpMaker(framework::OpProto* proto,
                         framework::OpAttrChecker* op_checker)
       : ElementwiseOpMaker(proto, op_checker) {
-    SetComment("Sub", "Out = X - Y");
+    SetComment("Sub", "$Out = X - Y$");
     AddComment(comment_);
   }
 };

paddle/operators/feed_op.cc

@@ -59,8 +59,13 @@ class FeedOpInfoMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "The input of feed op");
     AddOutput("Out", "The output of feed op");
-    AddComment("feed op, it should not be configured by users directly");
-    AddAttr<int>("col", "column of feed");
+    AddAttr<int>("col", "(int) The column of feed");
+    AddComment(R"DOC(
+Feed Operator.
+
+It should not be configured by users directly.
+
+)DOC");
   }
 };
 

paddle/operators/fetch_op.cc

@@ -66,8 +66,13 @@ class FetchOpInfoMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "The input of fetch op");
     AddOutput("Out", "The output of fetch op");
-    AddComment("fetch op, it should not be configured by users directly");
-    AddAttr<int>("col", "column of fetch");
+    AddAttr<int>("col", "(int) The column of fetch");
+    AddComment(R"DOC(
+Fetch Operator.
+
+It should not be configured by users directly.
+
+)DOC");
   }
 };
 }  // namespace operators

paddle/operators/fill_constant_batch_size_like_op.cc

@@ -70,11 +70,16 @@ class FillConstantBatchSizeLikeOpMaker
               "with the specified value");
     AddAttr<std::vector<int>>("shape", "(vector<int>) The shape of the output");
     AddAttr<int>("dim_idx",
-                 "(int, default 0) the index of batch size dimension")
+                 "(int, default 0) The index of batch size dimension")
         .SetDefault(0);
     AddAttr<float>("value", "(float, default 0) The value to be filled")
         .SetDefault(0.0f);
-    AddComment(R"DOC(Fill up a variable with specified constant value.)DOC");
+    AddComment(R"DOC(
+FillConstantBatchSizeLike Operator.
+
+Fill up a variable with specified constant value.
+
+)DOC");
   }
 };
 }  // namespace operators

paddle/operators/fill_constant_op.cc

@@ -54,7 +54,12 @@ class FillConstantOpMaker : public framework::OpProtoAndCheckerMaker {
     AddOutput("Out",
               "(Tensor) Tensor of specified shape will be filled "
               "with the specified value");
-    AddComment(R"DOC(Fill up a variable with specified constant value.)DOC");
+    AddComment(R"DOC(
+FillConstantBatchSizeLike Operator.
+
+Fill up a variable with specified constant value.
+
+)DOC");
   }
 };
 }  // namespace operators

paddle/operators/fill_zeros_like_op.cc

@@ -37,11 +37,13 @@ class FillZerosLikeOpMaker : public framework::OpProtoAndCheckerMaker {
                        framework::OpAttrChecker *op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "The input of fill-zeros-like op.");
-    AddOutput("Y", "The varibale will be filled up with zeros.");
+    AddOutput("Y", "The variable will be filled up with zeros.");
     AddComment(R"DOC(
-Fill up a vriable with zeros.
+FillZerosLike Operator.
+
+Fill up a variable with zeros.
+The output will have the same size as the input.
 
-The output will have the same size with input.
 )DOC");
   }
 };

paddle/operators/gather_op.cc

@@ -67,11 +67,28 @@ class GatherOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "The source input of gather op");
     AddInput("Index", "The index input of gather op");
-    AddOutput("Out", "The output of add op");
+    AddOutput("Out", "The output of gather op");
     AddComment(R"DOC(
-Gather Operator by selecting from the first axis,
+Gather Operator.
+
+$Out = X[Index]$
+
+Out is obtained by gathering entries of the outer-most dimension 
+of X indexed by Index and concatenate them together.
+
+Example:
+
+X = [[1, 2],
+     [3, 4],
+     [5, 6]]
+
+Index = [[1, 2]]
+
+Then:
+
+Out = [[3, 4],
+       [5, 6]]
 
-Out = X[Index]
 )DOC");
   }
 };

paddle/operators/gaussian_random_op.cc

@@ -68,21 +68,35 @@ class GaussianRandomOpMaker : public framework::OpProtoAndCheckerMaker {
   GaussianRandomOpMaker(framework::OpProto* proto,
                         framework::OpAttrChecker* op_checker)
       : framework::OpProtoAndCheckerMaker(proto, op_checker) {
-    AddOutput("Out", "output matrix of random op");
-    AddComment(R"DOC(
-GaussianRandom operator.
-Use to initialize tensor with gaussian random generator.
-)DOC");
+    AddOutput("Out", "Output matrix of gaussian random op");
 
-    AddAttr<std::vector<int>>("shape", "The dimension of random tensor.");
-    AddAttr<float>("mean", "mean of random tensor.").SetDefault(.0f);
-    AddAttr<float>("std", "std of random tensor.").SetDefault(1.0f);
+    AddAttr<std::vector<int>>("shape",
+                              "(vector<int>) "
+                              "The dimension of random tensor.");
+    AddAttr<float>("mean",
+                   "(float, default 0.0) "
+                   "mean of random tensor.")
+        .SetDefault(.0f);
+    AddAttr<float>("std",
+                   "(float, default 1.0) "
+                   "std of random tensor.")
+        .SetDefault(1.0f);
     AddAttr<int>("seed",
+                 "(int, default 0) "
                  "Random seed of generator."
-                 "0 means use system wide seed")
+                 "0 means use system wide seed.")
         .SetDefault(0);
-    AddAttr<int>("data_type", "output data type")
+    AddAttr<int>("data_type",
+                 "(int, default 5(FP32)) "
+                 "Output data type.")
         .SetDefault(framework::DataType::FP32);
+
+    AddComment(R"DOC(
+GaussianRandom Operator.
+
+Used to initialize tensors with gaussian random generator.
+
+)DOC");
   }
 };
 

paddle/operators/gru_unit_op.cc

@@ -80,19 +80,21 @@ class GRUUnitOpMaker : public framework::OpProtoAndCheckerMaker {
     AddInput("HiddenPrev",
              "(Tensor) Matrix with shape [batch_size, frame_size] for the "
              "states of previous time step.");
-    AddInput("Weight",
-             "(Tensor) Weight matrix with shape [frame_size, frame_size * 3]. "
-             "The elements continuous in memory can be divided into two parts. "
-             "The first part are weights of the update gate and reset gate "
-             "with shape [frame_size, frame_size * 2], and the second part are "
-             "weights of output candidate with shape [frame_size, frame_size]");
-    AddInput("Bias",
-             "(Tensor) Bias vector with shape [1, frame_size * 3] concating "
-             "bias of the update gate, reset gate and output candidate.")
+    AddInput(
+        "Weight",
+        "(Tensor) Weight matrix with shape [frame_size, frame_size * 3]. "
+        "The elements continuous in memory can be divided into two parts. "
+        "The first part are weights of the update gate and reset gate "
+        "with shape [frame_size, frame_size * 2], and the second part are "
+        "weights of output candidate with shape [frame_size, frame_size].");
+    AddInput(
+        "Bias",
+        "(Tensor) Bias vector with shape [1, frame_size * 3] concatenating "
+        "bias of the update gate, reset gate and output candidate.")
         .AsDispensable();
     AddOutput("Gate",
               "(Tensor) Matrix with shape [batch_size, frame_size * 3] for the "
-              "output of update gate, reset gate and output candidate")
+              "output of update gate, reset gate and output candidate.")
         .AsIntermediate();
     AddOutput("ResetHiddenPrev",
               "(Tensor) Matrix with shape [batch_size, frame_size] for the "
@@ -112,16 +114,19 @@ class GRUUnitOpMaker : public framework::OpProtoAndCheckerMaker {
         .SetDefault(sigmoid)
         .InEnum({identity, sigmoid, tanh, relu});
     AddComment(R"DOC(
-GRUUnitOp implements part calculations of the GRU unit as following:
+GRUUnit Operator.
 
-\f[
-update \ gate: u_t = actGate(xu_t + W_u * hidden_prev + bias_u) \\
-reset \ gate: r_t = actGate(xr_t + W_r * hidden_prev + bias_r)  \\
-output \ candidate: {h}_t = actNode(xc_t + W_c * dot(r_t, hidden_prev) + bias_c) \\
-output: h_t = dot((1-u_t), {h}_t) + dot(u_t, hidden_prev)
-\f]
+This operator implements partial calculations of the GRU unit as follows:
+
+$$
+update \ gate: u_t = actGate(xu_t + W_u * hidden_{prev} + bias_u) \\
+reset \ gate: r_t = actGate(xr_t + W_r * hidden_{prev} + bias_r)  \\
+output \ candidate: {h}_t = actNode({xc}_t + W_c * dot(r_t, hidden_{prev}) + bias_c) \\
+output: h_t = dot((1-u_t), {h}_t) + dot(u_t, hidden_{prev})
+$$
 
 The rest of GRU unit can be completed by using FCOp's output as the input of GRUUnitOp.
+
 )DOC");
   }
 };

paddle/operators/huber_loss_op.cc

@@ -59,10 +59,12 @@ class HuberLossOpMaker : public framework::OpProtoAndCheckerMaker {
               "The shape is same as Input(X) and will be reused in backward.")
         .AsIntermediate();
     AddOutput("Out",
-              "The output tensor with shape [batch_size, 1] which represents "
-              "the huber loss.");
+              "The output tensor with shape [batch_size, 1] "
+              "which represents the huber loss.");
     AddAttr<AttrType>("delta", "Hyper parameter in huber loss.");
     AddComment(R"DOC(
+HuberLoss Operator.
+
 Huber loss is a loss function used in robust regression. We define X as the
 input value and Y as the target value. Huber loss can evaluate the fitness of
 X to Y. Different from MSE loss, Huber loss is more robust for outliers. The

paddle/operators/increment_op.cc

@@ -39,14 +39,18 @@ class IncrementOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "(Tensor) The input tensor of increment operator");
     AddOutput("Out", "(Tensor) The output tensor of increment operator.");
-    AddComment(R"DOC(Increment operator
-
-The equation is: Out = X + step
-)DOC");
     AddAttr<AttrType>("step",
+                      "(float, default 1.0) "
                       "The step size by which the "
                       "input tensor will be incremented.")
         .SetDefault(1.0);
+    AddComment(R"DOC(
+Increment Operator.
+
+The equation is: 
+$$Out = X + step$$
+
+)DOC");
   }
 };
 

paddle/operators/l1_norm_op.cc

@@ -57,7 +57,7 @@ L1 Norm Operator.
 
 Computes the L1 norm of a tensor.
 
-Out = sum (abs(X))
+$$Out = \sum{|X|}$$
 
 )DOC");
   }

paddle/operators/linear_chain_crf_op.cc

@@ -22,52 +22,55 @@ class LinearChainCRFOpMaker : public framework::OpProtoAndCheckerMaker {
   LinearChainCRFOpMaker(framework::OpProto* proto,
                         framework::OpAttrChecker* op_checker)
       : OpProtoAndCheckerMaker(proto, op_checker) {
-    AddInput(
-        "Emission",
-        "(LoDTensor, default: LoDTensor<float>). "
-        "The unscaled emission weight matrix for the linear chain CRF. "
-        "This input is a LoDTensor with shape [N x D] where N is the size of "
-        "the mini-batch and D is the total tag number.");
-    AddInput(
-        "Transition",
-        "(Tensor, default: Tensor<float>). A Tensor with shape [(D + 2) x D]. "
-        "The learnable parameter for the linear_chain_crf operator. "
-        "See more details in the operator's comments.");
-    AddInput(
-        "Label",
-        "(LoDTensor, default: LoDTensor<int>). The ground truth which is a 2-D "
-        "LoDTensor with shape [N x 1], where N is the total element number in "
-        "a mini-batch.");
+    AddInput("Emission",
+             "(LoDTensor, default LoDTensor<float>) "
+             "A 2-D LoDTensor with shape [N x D], where N is the size of the "
+             "mini-batch and D is the total tag number. The unscaled emission "
+             "weight matrix for the linear chain CRF. ");
+    AddInput("Transition",
+             "(Tensor, default Tensor<float>) A 2-D Tensor with shape "
+             "[(D + 2) x D]. The learnable parameter for the linear_chain_crf "
+             "operator. See more details in the operator's comments.");
+    AddInput("Label",
+             "(LoDTensor, default LoDTensor<int>) A LoDTensor with shape "
+             "[N x 1], where N is the total element number in a mini-batch. "
+             "The ground truth.");
     AddOutput(
         "Alpha",
-        "Tensor, default: Tensor<float>. The forward vectors for the entire "
-        "batch. A two dimensional tensor with shape [N x D], "
-        "denoted as \f$\alpha\f$. \f$\alpha$\f is a memo table used to "
-        "calculate the normalization factor in CRF. \f$\alpha[k, v]$\f stores "
-        "the unnormalized probabilites of all possible unfinished sequences of "
-        "tags that end at position \f$k$\f with tag \f$v$\f. For each \f$k$\f, "
+        "(Tensor, default Tensor<float>) A 2-D Tensor with shape [N x D]. "
+        "The forward vectors for the entire batch. Denote it as \f$\alpha\f$. "
+        "\f$\alpha$\f is a memo table used to calculate the normalization "
+        "factor in CRF. \f$\alpha[k, v]$\f stores the unnormalized "
+        "probabilites of all possible unfinished sequences of tags that end at "
+        "position \f$k$\f with tag \f$v$\f. For each \f$k$\f, "
         "\f$\alpha[k, v]$\f is a vector of length \f$D$\f with a component for "
         "each tag value \f$v$\f. This vector is called a forward vecotr and "
         "will also be used in backward computations.")
         .AsIntermediate();
-    AddOutput("EmissionExps",
-              "The exponentials of Input(Emission). This is an intermediate "
-              "computational result in forward computation, and will be reused "
-              "in backward computation.")
+    AddOutput(
+        "EmissionExps",
+        "(Tensor, default Tensor<float>) A 2-D Tensor with shape [N x D]. "
+        "The exponentials of Input(Emission). This is an intermediate "
+        "computational result in forward computation, and will be reused in "
+        "backward computation.")
         .AsIntermediate();
-    AddOutput("TransitionExps",
-              "The exponentials of Input(Transition). This is an intermediate "
-              "computational result in forward computation, and will be reused "
-              "in backward computation.")
+    AddOutput(
+        "TransitionExps",
+        "(Tensor, default Tensor<float>) A 2-D Tensor with shape "
+        "[(D + 2) x D]. The exponentials of Input(Transition). This is an "
+        "intermediate computational result in forward computation, and "
+        "will be reused in backward computation.")
         .AsIntermediate();
     AddOutput(
         "LogLikelihood",
-        "(Tensor, default: Tensor<float>). The logarithm of the conditional "
+        "(Tensor, default Tensor<float>) The logarithm of the conditional "
         "likelihood of each training sample in a mini-batch. This is a 2-D "
         "tensor with shape [S x 1], where S is the sequence number in a "
         "mini-batch. Note: S is equal to the sequence number in a mini-batch. "
         "The output is no longer a LoDTensor.");
     AddComment(R"DOC(
+LinearChainCRF Operator.
+
 Conditional Random Field defines an undirected probabilistic graph with nodes
 denoting random variables and edges denoting dependencies between these
 variables. CRF learns the conditional probability \f$P(Y|X)\f$, where
@@ -81,29 +84,28 @@ and output must be linear sequences. Thus, the graph of such a CRF is a simple
 chain or a line, which results in the linear chain CRF.
 
 This operator implements the Forward-Backward algorithm for the linear chain
-CRF. Please see http://www.cs.columbia.edu/~mcollins/fb.pdf and
-http://cseweb.ucsd.edu/~elkan/250Bwinter2012/loglinearCRFs.pdf for reference.
+CRF. Please refer to http://www.cs.columbia.edu/~mcollins/fb.pdf and
+http://cseweb.ucsd.edu/~elkan/250Bwinter2012/loglinearCRFs.pdf for details.
 
 Equation:
-
-- Denote Input(Emission) to this operator as \f$x\f$ here.
-- The first D values of Input(Transition) to this operator are for starting
+1. Denote Input(Emission) to this operator as \f$x\f$ here.
+2. The first D values of Input(Transition) to this operator are for starting
 weights, denoted as \f$a\f$ here.
-- The next D values of Input(Transition) of this operator are for ending
+3. The next D values of Input(Transition) of this operator are for ending
 weights, denoted as \f$b\f$ here.
-- The remaning values of Input(Transition) are for transition weights,
+4. The remaning values of Input(Transition) are for transition weights,
 denoted as \f$w\f$ here.
-- Denote Input(Label) as \f$s\f$ here.
+5. Denote Input(Label) as \f$s\f$ here.
 
 The probability of a sequence \f$s\f$ of length \f$L\f$ is defined as:
-\f$P(s) = (1/Z) exp(a_{s_1} + b_{s_L}
+\f$P(s) = (1/Z) \exp(a_{s_1} + b_{s_L}
                  + \sum_{l=1}^L x_{s_l}
                  + \sum_{l=2}^L w_{s_{l-1},s_l})\f$
 where \f$Z\f$ is a normalization value so that the sum of \f$P(s)\f$ over
 all possible sequences is \f$1\f$, and \f$x\f$ is the emission feature weight
 to the linear chain CRF.
 
-Finaly, the linear chain CRF operator outputs the logarithm of the conditional
+Finally, the linear chain CRF operator outputs the logarithm of the conditional
 likelihood of each training sample in a mini-batch.
 
 NOTE:
@@ -179,8 +181,8 @@ class LinearChainCRFOp : public framework::OperatorWithKernel {
   }
 
  protected:
-  // Explicitly set that the data type of output of the linear_chain_crf
-  // operator is determined by its input "Emission".
+  // Explicitly set that the data type of computation kernel of linear_chain_crf
+  // is determined by its input "Emission".
   framework::DataType IndicateDataType(
       const framework::ExecutionContext& ctx) const override {
     return framework::ToDataType(ctx.Input<LoDTensor>("Emission")->type());

paddle/operators/linear_chain_crf_op.h

@@ -134,7 +134,7 @@ class LinearChainCRFOpKernel : public framework::OpKernel<T> {
 
     Tensor emission_row_max;
     emission_row_max.mutable_data<T>(
-        framework::make_ddim({static_cast<int>(batch_size), 1}),
+        framework::make_ddim({static_cast<int64_t>(batch_size), 1}),
         platform::CPUPlace());
 
     auto place = ctx.GetEigenDevice<platform::CPUPlace>();
@@ -273,7 +273,7 @@ class LinearChainCRFOpKernel : public framework::OpKernel<T> {
 
     const int* lbl = label.data<int>();
     PADDLE_ENFORCE_LT(
-        *std::max_element(lbl, lbl + seq_length), tag_num,
+        static_cast<size_t>(*std::max_element(lbl, lbl + seq_length)), tag_num,
         "An invalid tag label that execesses the largest tag number.");
 
     // Calculate the nominator part, which depends on the label sequence.

paddle/operators/load_op.cc

@@ -115,14 +115,18 @@ class LoadOpProtoMaker : public framework::OpProtoAndCheckerMaker {
   LoadOpProtoMaker(framework::OpProto *proto,
                    framework::OpAttrChecker *op_checker)
       : OpProtoAndCheckerMaker(proto, op_checker) {
-    AddOutput("Out", "The tensor need to be loaded");
-    AddComment(R"DOC(Load Operator
-Load operator will load a tensor variable from disk file.
-)DOC");
+    AddOutput("Out", "(Tensor) The tensor need to be loaded");
     AddAttr<std::string>("file_path",
+                         "(string) "
                          "Variable will be loaded from \"file_path\".")
         .AddCustomChecker(
             [](const std::string &path) { return !path.empty(); });
+    AddComment(R"DOC(
+Load Operator.
+
+Load operator will load a tensor variable from disk file.
+
+)DOC");
   }
 };
 }  // namespace operators

paddle/operators/lod_rank_table_op.cc

+/* Copyright (c) 2016 PaddlePaddle Authors. All Rights Reserved.
+
+   Licensed under the Apache License, Version 2.0 (the "License");
+   you may not use this file except in compliance with the License.
+   You may obtain a copy of the License at
+
+   http://www.apache.org/licenses/LICENSE-2.0
+
+   Unless required by applicable law or agreed to in writing, software
+   distributed under the License is distributed on an "AS IS" BASIS,
+   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+   See the License for the specific language governing permissions and
+   limitations under the License. */
+#include "paddle/framework/lod_rank_table.h"
+#include "paddle/framework/op_registry.h"
+namespace paddle {
+namespace operators {
+
+class LoDRankTableOp : public framework::OperatorBase {
+ public:
+  LoDRankTableOp(const std::string &type,
+                 const framework::VariableNameMap &inputs,
+                 const framework::VariableNameMap &outputs,
+                 const framework::AttributeMap &attrs)
+      : OperatorBase(type, inputs, outputs, attrs) {}
+  void Run(const framework::Scope &scope,
+           const platform::DeviceContext &dev_ctx) const override {
+    auto x = scope.FindVar(Input("X"))->Get<framework::LoDTensor>();
+    auto *out =
+        scope.FindVar(Output("Out"))->GetMutable<framework::LoDRankTable>();
+    out->Reset(x.lod(), static_cast<size_t>(Attr<int>("level")));
+  }
+};
+
+class LoDRankTableOpProtoMaker : public framework::OpProtoAndCheckerMaker {
+ public:
+  LoDRankTableOpProtoMaker(framework::OpProto *proto,
+                           framework::OpAttrChecker *op_checker)
+      : OpProtoAndCheckerMaker(proto, op_checker) {
+    AddInput("X",
+             "(LoDTensor) input lod tensor, must contain lod information.");
+    AddOutput("Out", "(LoDRankTable) The rank table of specific level.");
+    AddAttr<int>("level", "(int) the specific lod level to rank.")
+        .SetDefault(0)
+        .EqualGreaterThan(0);
+    AddComment(R"DOC(Create LoDRanTable by LoDTensor
+
+LoD Rank Table stores the `level` of `lod` which is ordered by sequence
+length in descending order. It is useful when implement dynamic RNN and is
+shared by dynamic RNN memory, dynamic RNN slice input and dynamic RNN slice
+output operators.
+)DOC");
+  }
+};
+
+class LoDRankTableInferShape : public framework::InferShapeBase {
+ public:
+  void operator()(framework::InferShapeContext *context) const override {
+    PADDLE_ENFORCE(context->HasInput("X"), "LoDRankTable must has input X");
+  }
+};
+
+class LoDRankTableInferVarType : public framework::VarTypeInference {
+ public:
+  void operator()(const framework::OpDescBind &op_desc,
+                  framework::BlockDescBind *block) const override {
+    for (auto &o : op_desc.Output("Out")) {
+      block->Var(o)->SetType(framework::VarDesc::LOD_RANK_TABLE);
+    }
+  }
+};
+
+}  // namespace operators
+}  // namespace paddle
+
+REGISTER_OPERATOR(lod_rank_table, paddle::operators::LoDRankTableOp,
+                  paddle::operators::LoDRankTableOpProtoMaker,
+                  paddle::operators::LoDRankTableInferShape,
+                  paddle::operators::LoDRankTableInferVarType,
+                  paddle::framework::EmptyGradOpMaker);

paddle/operators/lookup_table_op.cc

@@ -53,21 +53,27 @@ class LookupTableOpMaker : public framework::OpProtoAndCheckerMaker {
                      framework::OpAttrChecker* op_checker)
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("W",
-             "An input represents embedding tensors,"
-             " which is a learnable parameter.");
+             "An input represents embedding tensors, "
+             "which is a learnable parameter.");
     AddInput("Ids",
-             "An input with type int32 or int64"
-             "contains the ids to be looked up in W."
-             "Ids must be a column vector with rank = 2."
-             "The 2nd dimension size must be 1");
-    AddOutput("Out", "The lookup results, which have the same type with W.");
-    AddAttr<bool>("is_sparse", "Sparse update").SetDefault(false);
+             "An input with type int32 or int64 "
+             "contains the ids to be looked up in W. "
+             "Ids must be a column vector with rank = 2. "
+             "The 2nd dimension size must be 1.");
+    AddOutput("Out", "The lookup results, which have the same type as W.");
+    AddAttr<bool>("is_sparse",
+                  "(boolean, default false) "
+                  "Sparse update")
+        .SetDefault(false);
     AddComment(R"DOC(
+Lookup Table Operator.
+
 This operator is used to perform lookups on the parameter W,
 then concatenated into a dense tensor.
 
-The input `Ids` can carry the LoD (Level of Details) information,
-or not. And the output only shares the LoD with input `Ids`.
+The input Ids can carry the LoD (Level of Details) information,
+or not. And the output only shares the LoD information with input Ids.
+
 )DOC");
   }
 };

paddle/operators/lrn_op.cc

@@ -45,72 +45,70 @@ class LRNOpMaker : public framework::OpProtoAndCheckerMaker {
  public:
   LRNOpMaker(framework::OpProto* proto, framework::OpAttrChecker* op_checker)
       : OpProtoAndCheckerMaker(proto, op_checker) {
-    AddInput("X", R"DOC(
- (Tensor) The input of LRN operator. It must be a 4D tenor with NCHW format.
- )DOC");
-
+    AddInput("X",
+             "(Tensor) The input of LRN operator. "
+             "It must be a 4D tenor with NCHW format.");
     AddOutput("Out",
               "(Tensor) The output of LRN operator, which is also the 4D "
               "tensor with NCHW format.");
-    AddOutput("MidOut", R"Doc(
-(Tensor)Middle result of lrn op.It's computed in forward process 
-and also used in backward process.
-    )Doc");
-
-    AddAttr<int>("n", R"DOC(
-(int, default 5)n is “adjacent” kernel maps at the same spatial position.
-        )DOC")
+    AddOutput("MidOut",
+              "(Tensor) Middle result of LRN operator. It's computed in "
+              "forward process and also used in backward process.");
+
+    AddAttr<int>("n",
+                 "(int default 5) "
+                 "n is the \"adjacent\" kernel that maps "
+                 "at the same spatial position.")
         .SetDefault(5)
         .GreaterThan(0);
 
-    AddAttr<T>("k", R"DOC(
-(float, default 2.0)k is the bias.
-        )DOC")
+    AddAttr<T>("k",
+               "(float, default 2.0) "
+               "k is the bias.")
         .SetDefault(2.0)
         .GreaterThan(0.0);
 
-    AddAttr<T>("alpha", R"DOC(
-(float, default 0.0001)alpha is the scale number.
-        )DOC")
+    AddAttr<T>("alpha",
+               "(float, default 0.0001) "
+               "alpha is the scale number.")
         .SetDefault(0.0001)
         .GreaterThan(0.0);
 
-    AddAttr<T>("beta", R"DOC(
-(float, default 0.75)beta is the power number.
-        )DOC")
+    AddAttr<T>("beta",
+               "(float, default 0.75) "
+               "beta is the power number.")
         .SetDefault(0.75)
         .GreaterThan(0.0);
 
     AddComment(R"DOC(
- Local Response Normalization.
-
- This Function comes from the paper
- "ImageNet Classification with Deep Convolutional Neural Networks".
+Local Response Normalization Operator.
 
- The original formula is:
+This operator comes from the paper
+"ImageNet Classification with Deep Convolutional Neural Networks".
 
-                                Input(i, x, y)
- Output(i, x, y) = ----------------------------------------------
-                                 -- upper
-                    (k + alpha * >  (Input(j, x, y))^2) ^ (beta)
-                                 -- j = lower
+The original formula is:
 
- upper is `min(C, c + n/2)`
- lower if `max(0, c - n/2)`
+$$
+Output(i, x, y) = Input(i, x, y) / \left(
+k + \alpha \sum\limits^{\min(C, c + n/2)}_{j = \max(0, c - n/2)}
+(Input(j, x, y))^2
+\right)^{\beta}
+$$
 
- Function implementation:
+Function implementation:
 
- inputs and outpus is NCHW format, while input.shape.ndims() is equal 4.
- And the meaning of each dimension(0-3) is respectively batch size,
- feature maps, rows and columns.
+Inputs and outpus are in NCHW format, while input.shape.ndims() equals 4.
+And dimensions 0 ~ 3 represent batch size, feature maps, rows,
+and columns, respectively.
 
- Input and Output in the above formula is for each map(i) of one image, and
- Input(i, x, y), Output(i, x, y) represents an element in an image.
+Input and Output in the formula above is for each map(i) of one image, and
+Input(i, x, y), Output(i, x, y) represents an element in an image.
 
- C is the number of feature maps of one image, and n is a hyper-parameters
- is configured when Function is initialized. The sum in the denominator
- is the sum of the same position in the neighboring maps.
-    )DOC");
+C is the number of feature maps of one image. n is a hyper-parameter
+configured when operator is initialized. The sum in the denominator
+is the sum of the same positions in the neighboring maps.
+    
+)DOC");
   }
 };
 

paddle/operators/lstm_op.cc

@@ -103,7 +103,7 @@ class LSTMOpMaker : public framework::OpProtoAndCheckerMaker {
     AddInput("H0",
              "(Tensor, optional) the initial hidden state is an optional "
              "input. This is a tensor with shape (N x D), where N is the "
-             "batch size, D is the hidden size.")
+             "batch size and D is the hidden size.")
         .AsDispensable();
     AddInput("C0",
              "(Tensor, optional) the initial cell state is an optional "
@@ -134,85 +134,82 @@ class LSTMOpMaker : public framework::OpProtoAndCheckerMaker {
     AddOutput("BatchGate",
               "(LoDTensor) This LoDTensor contains input gate, forget gate "
               "and output gate after the nonlinear computation. This "
-              "LoDTensor has the same shape with the reorganized input, which "
+              "LoDTensor has the same shape as the reorganized input, which "
               "is also be called batch input. The LoD size is 2. The first "
               "LoD is the batch offsets and the second LoD contains the "
               "indexes, which denote the position of reorganized sequence "
               "in the raw input.")
         .AsIntermediate();
     AddOutput("BatchCellPreAct",
-              "(LoDTensor) This LoDTensor is got in the forward and used "
+              "(LoDTensor) This LoDTensor is obtained in the forward and used "
               "in the backward.")
         .AsIntermediate();
     AddAttr<bool>("usePeepholes",
-                  "(bool, defalut: True) "
+                  "(bool, default True) "
                   "whether to enable diagonal/peephole connections.")
         .SetDefault(true);
     AddAttr<bool>("isReverse",
-                  "(bool, defalut: False) "
+                  "(bool, default False) "
                   "whether to compute reversed LSTM.")
         .SetDefault(false);
     AddAttr<std::string>(
         "gateActivation",
-        "(string, default: sigmoid)"
+        "(string, default sigmoid)"
         "The activation for input gate, forget gate and output "
         "gate, `sigmoid` by default.")
         .SetDefault("sigmoid");
     AddAttr<std::string>("cellActivation",
-                         "(string, default: tanh)"
+                         "(string, default tanh)"
                          "The activation for cell output, `tanh` by defalut.")
         .SetDefault("tanh");
     AddAttr<std::string>("candidateActivation",
-                         "(string, default: tanh)"
+                         "(string, default tanh)"
                          "The activation for candidate hidden state, "
                          "`tanh` by default.")
         .SetDefault("tanh");
-    AddComment(R"DOC(Long-Short Term Memory (LSTM) Operator
+    AddComment(R"DOC(
+Long-Short Term Memory (LSTM) Operator.
 
-The defalut implementation is diagonal/peephole connection [1], the formula is
-as follows
+The defalut implementation is diagonal/peephole connection 
+(https://arxiv.org/pdf/1402.1128.pdf), the formula is as follows:
 
-    i_t = \sigma(W_{ix}x_{t} + W_{ih}h_{t-1} + W_{ic}c_{t-1} + b_i)
+$$
+i_t = \sigma(W_{ix}x_{t} + W_{ih}h_{t-1} + W_{ic}c_{t-1} + b_i) \\
 
-    f_t = \sigma(W_{fx}x_{t} + W_{fh}h_{t-1} + W_{fc}c_{t-1} + b_f)
+f_t = \sigma(W_{fx}x_{t} + W_{fh}h_{t-1} + W_{fc}c_{t-1} + b_f) \\
 
-    \tilde{c_t} = act_g(W_{cx}x_t + W_{ch}h_{t-1} + b_c)
+\tilde{c_t} = act_g(W_{cx}x_t + W_{ch}h_{t-1} + b_c) \\
 
-    o_t = \sigma(W_{ox}x_{t} + W_{oh}h_{t-1} + W_{oc}c_t + b_o)
+o_t = \sigma(W_{ox}x_{t} + W_{oh}h_{t-1} + W_{oc}c_t + b_o) \\
 
-    c_t = f_t ⊙ c_{t-1} + i_t ⊙ \tilde{c_t}
+c_t = f_t \odot c_{t-1} + i_t \odot \tilde{c_t} \\
 
-    h_t = o_t ⊙ act_h(c_t)
+h_t = o_t \odot act_h(c_t)
+$$
 
 where the W terms denote weight matrices (e.g. \f$W_{xi}\f$ is the matrix
 of weights from the input gate to the input), \f$W_{ic}, W_{fc}, W_{oc}\f$
-are diagonal weight matrices for peephole connections. In our implenmention,
-We use vectors to reprenset these diagonal weight matrices. The b terms
+are diagonal weight matrices for peephole connections. In our implementation,
+we use vectors to reprenset these diagonal weight matrices. The b terms
 denote bias vectors (\f$b_i\f$ is the input gate bias vector), \f$\sigma\f$
-is the non-line actications, such as logistic sigmoid function, and
-\f$i, f, o\f$ and \f$c\f$ are respectively the input gate, forget gate,
-output gate and cell activation vectors, all of which are the same size as
+is the non-line activations, such as logistic sigmoid function, and
+\f$i, f, o\f$ and \f$c\f$ are the input gate, forget gate, output gate,
+and cell activation vectors, respectively, all of which have the same size as
 the cell output activation vector \f$h\f$.
 
-The ⊙ is the element-wise product of the vectors, \f$act_g\f$ and \f$act_h\f$
-are the cell input and cell output activation functions, `tanh` is usually
+The \f$\odot\f$ is the element-wise product of the vectors. \f$act_g\f$ and \f$act_h\f$
+are the cell input and cell output activation functions and `tanh` is usually
 used for them. \f$\tilde{c_t}\f$ is also called candidate hidden state,
 which is computed based on the current input and the previous hidden state.
 
-Set `usePeepholes` False to disable peephole connection [2]. The formula
+Set usePeepholes False to disable peephole connection 
+(http://www.bioinf.jku.at/publications/older/2604.pdf). The formula
 is omitted here.
 
-@note These \f$W_{xi}x_{t}, W_{xf}x_{t}, W_{xc}x_{t}, W_{xo}x_{t}\f$
-operations on the input x_{t} were NOT included in this operator.
+Note that these \f$W_{xi}x_{t}, W_{xf}x_{t}, W_{xc}x_{t}, W_{xo}x_{t}\f$
+operations on the input \f$x_{t}\f$ are NOT included in this operator.
 Users can choose to use fully-connect operator before LSTM operator.
 
-[1] Hasim Sak, Andrew Senior, and Francoise Beaufays. Long short-term memory
-recurrent neural network architectures for large scale acoustic modeling.
-INTERSPEECH, 2014.
-
-[2] S. Hochreiter and J. Schmidhuber. Long Short-Term Memory.
-Neural Computation, 9(8):1735-1780, 1997.
-
 )DOC");
   }
 };

paddle/operators/lstm_unit_op.cc

@@ -57,17 +57,22 @@ class LstmUnitOpMaker : public framework::OpProtoAndCheckerMaker {
         "The cell state tensor of last time-step in the Lstm Unit operator.");
     AddOutput("C", "The cell tensor of Lstm Unit operator.");
     AddOutput("H", "The hidden state tensor of Lstm Unit operator.");
-
-    AddComment(R"DOC(Lstm-Unit Operator
+    AddAttr<float>("forget_bias",
+                   "(float, default 0.0) "
+                   "The forget bias of Lstm Unit.")
+        .SetDefault(0.0);
+    AddComment(R"DOC(
+Lstm Unit Operator
 
 Equation:
-  i, f, o, j = split(X)
-  C = C_prev * sigm(f + forget_bias) + sigm(i) * tanh(j)
-  H = C * sigm(o)
+
+$$
+i, f, o, j = split(X) \\
+C = C_{prev} * sigm(f + forget\_bias) + sigm(i) * tanh(j) \\
+H = C * sigm(o)
+$$
 
 )DOC");
-    AddAttr<float>("forget_bias", "The forget bias of Lstm Unit.")
-        .SetDefault(0.0);
   }
 };
 

paddle/operators/margin_rank_loss_op.cc

@@ -55,8 +55,6 @@ class MarginRankLossOpMaker : public framework::OpProtoAndCheckerMaker {
              "(2-D tensor with shape [batch_size x 1]) "
              "The label indicating X1 ranked higher than X2 or not, "
              "can only be +1 or -1.");
-    AddAttr<T>("margin", "(scalar, default 0) Margin for MarginRankLossOp.")
-        .SetDefault(static_cast<T>(0));
     AddOutput("Activated",
               "(2-D tensor with shape [batch_size x 1]) Intermediate tensor "
               "to indicate whether each element of Output(Out) is activated.")
@@ -64,23 +62,26 @@ class MarginRankLossOpMaker : public framework::OpProtoAndCheckerMaker {
     AddOutput("Out",
               "(2-D tensor with shape [batch_size x 1]) "
               "The output loss of MarginRankLoss operator.");
+    AddAttr<T>("margin", "(scalar, default 0) Margin for MarginRankLossOp.")
+        .SetDefault(static_cast<T>(0));
     AddComment(R"DOC(
+MarginRankLoss Operator.
 
-MarginRankLoss operator measures the loss given a pair of training sample
+This operator measures the loss given a pair of training sample
 {`X1`, `X2`} and the `Label` with attribute `margin`, where `Label = +1` 
-indicating X1 is ranked higher than `X2`, otherwise `Label = -1`. The loss 
-turns out
+indicating X1 is ranked higher than `X2` and `Label = -1` otherwise. The loss 
+is calculated as:
 
-loss(X1, X2, Label) = max(0, -Label * (X1 - X2) + margin).
+$loss(X1, X2, Label) = \max(0, -Label * (X1 - X2) + margin)$
 
-The attribute `margin` involved here helps make the predictions more robust.
+The attribute `margin` here helps make the predictions more robust.
 Denote the item ranked higher as the positive sample, otherwise the negative 
 sample. If the score of the two samples satisfies 
 
-positive sample - negative sample < margin,
+$positive sample - negative sample < margin$
 
-the pair of samples will contribute to the final loss, which will backpropogate 
-and train the ranking model to enlarge the difference of the two score.
+the pair of samples will contribute to the final loss, which will backpropagate 
+and train the ranking model to enlarge the difference between the two scores.
 
 For batch input with size `batch_size`, `X1`, `X2` and `Label`
 all have the same shape [batch_size x 1].

paddle/operators/matmul_op.cc

@@ -144,7 +144,10 @@ class MatMulOpMaker : public framework::OpProtoAndCheckerMaker {
         )DOC")
         .SetDefault(false);
     AddComment(R"DOC(
-The MatMul operator is used to perform (batched) matrix multiplication
+MatMul Operator.
+
+
+This operator is used to perform (batched) matrix multiplication
 over the last two dimensions of the input tensors `X` and `Y`.
 
 If a transpose flag is specified, the last two dimensions of the
@@ -166,7 +169,8 @@ The differences are:
 - We add `transpose_X` and `transpose_Y` flags.
 
 Both the input `X` and `Y` can carry the LoD (Level of Details) information,
-or not. But the output only shares the LoD with input `X`.
+or not. But the output only shares the LoD information with input `X`.
+
 )DOC");
   }
 };

paddle/operators/mean_op.cc

@@ -36,7 +36,11 @@ class MeanOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "The input of mean op");
     AddOutput("Out", "The output of mean op");
-    AddComment(R"DOC( Mean Operator
+    AddComment(R"DOC(
+Mean Operator.
+
+Out is a scalar which is the mean of all elements in X. 
+
 )DOC");
   }
 };

paddle/operators/minus_op.cc

@@ -52,14 +52,16 @@ class MinusOpMaker : public framework::OpProtoAndCheckerMaker {
     AddInput("Y", "The right tensor of minus operator.");
     AddOutput("Out", "The output tensor of minus operator.");
 
-    AddComment(R"DOC(Minus Operator
+    AddComment(R"DOC(
+Minus Operator.
 
 Equation:
 
-    Out = X - Y
+    $Out = X - Y$
 
 Both the input `X` and `Y` can carry the LoD (Level of Details) information,
-or not. But the output only shares the LoD with input `X`.
+or not. But the output only shares the LoD information with input `X`.
+
 )DOC");
   }
 };

paddle/operators/modified_huber_loss_op.cc

@@ -43,27 +43,35 @@ class ModifiedHuberLossOpMaker : public framework::OpProtoAndCheckerMaker {
                            framework::OpAttrChecker* op_checker)
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X",
-             "The input tensor of modified huber loss op."
+             "The input tensor of modified huber loss op. "
              "X is 2-D tensor with shape [batch_size, 1].");
     AddInput("Y",
-             "The target labels of modified huber loss op."
-             "The shape of Y is same as X. Values of Y must be 0 or 1.");
+             "The target labels of modified huber loss op. "
+             "The shape of Y is the same as X. Values of Y must be 0 or 1.");
     AddOutput("IntermediateVal",
               "Variable to save intermediate result which will be reused in "
               "backward processing.")
         .AsIntermediate();
     AddOutput("Out", "Classification loss for X.");
     AddComment(R"DOC(
-Modified huber loss is used in binary classification problem. The shape of
-input X and target Y are both [N, 1] and so is the shape of output loss.
-Since target Y is not differentiable, cacluating gradient for Y is illegal.
-The formulation of modified huber loss is:
-
-L(y, f(x)) = max(0, 1 - yf(x))^2  for yf(x) >= -1,
-             -4yf(x)              otherwise.
-
-Make sure the values of target label Y are in {0, 1} here. The operator will
+Modified Huber Loss Operator.
+
+This operator is used in binary classification problem. The shape of
+input X and target Y are both [N, 1] and so is the shape of the output loss.
+Since target Y is not differentiable, calculating gradient for Y is illegal.
+The formula of modified huber loss is:
+
+$$
+L(y, f(x)) = 
+\begin{cases}
+(\max(0, 1 - yf(x)))^2,  \text{if} \  yf(x) >= -1    \\
+             -4yf(x),    \quad \text{otherwise}
+\end{cases}
+$$
+
+Make sure the values of target label Y are in {0, 1} here. This operator will
 scale values of Y to {-1, +1} when computing losses and gradients.
+
 )DOC");
   }
 };

paddle/operators/momentum_op.cc

@@ -75,17 +75,23 @@ class MomentumOpMaker : public framework::OpProtoAndCheckerMaker {
     AddOutput("VelocityOut", "(Tensor) Output updated velocity");
 
     AddAttr<float>("mu", "(float) Momentum coefficient");
-    AddAttr<bool>("useNesterov", "(bool) Use Nesterov Momentum")
+    AddAttr<bool>("useNesterov",
+                  "(bool, default false) "
+                  "Use Nesterov Momentum")
         .SetDefault(false);
     AddComment(R"DOC(
-
-Momentum Algorithm with a flag for Nestrov Moemntum (momentum).
-
-velocity = mu * velocity + gradient
-if (use_nesterov):
-  param = param - gradient * learning_rate + mu * velocity * learning_rate
-else:
-  param = param - learning_rate * velocity
+Momentum Optimizer.
+
+This optimizer has a flag for Nestrov Momentum.
+The update equations are as follows:
+
+$$
+velocity = mu * velocity + gradient \\
+if (use\_nesterov):   \\
+  param = param - gradient * learning\_rate + mu * velocity * learning\_rate \\
+else:   \\
+  param = param - learning\_rate * velocity. \\
+$$
 
 )DOC");
   }

paddle/operators/mul_op.cc

@@ -78,6 +78,7 @@ class MulOpMaker : public framework::OpProtoAndCheckerMaker {
     AddOutput("Out", "The output of mul op");
     AddAttr<int>(
         "x_num_col_dims",
+        "(int, default 1) "
         R"DOC(mul_op can take tensors with more than two dimensions as input `X`,
             in that case, tensors will be reshaped to a matrix. The matrix's first
             dimension(column length) will be the product of tensor's last
@@ -88,20 +89,24 @@ class MulOpMaker : public framework::OpProtoAndCheckerMaker {
         .EqualGreaterThan(1);
     AddAttr<int>(
         "y_num_col_dims",
+        "(int, default 1) "
         R"DOC(mul_op can take tensors with more than two dimensions as input `Y`,
              in that case, tensors will be reshaped to a matrix. Just like input `X`.
         )DOC")
         .SetDefault(1)
         .EqualGreaterThan(1);
     AddComment(R"DOC(
-Mul operator is used to perform matrix multiplication for input X and Y.
+Mul Operator. 
+
+This operator is used to perform matrix multiplication for input X and Y.
 
 The equation is:
 
-    Out = X * Y
+    $$Out = X * Y$$
 
 Both the input `X` and `Y` can carry the LoD (Level of Details) information,
-or not. But the output only shares the LoD with input `X`.
+or not. But the output only shares the LoD information with input `X`.
+
 )DOC");
   }
 };

paddle/operators/multiplex_op.cc

@@ -66,7 +66,8 @@ class MultiplexOpMaker : public framework::OpProtoAndCheckerMaker {
     AddInput("X", "The candidate tensors of multiplex operator.")
         .AsDuplicable();
     AddOutput("Out", "The output tensor of multiplex operator.");
-    AddComment(R"DOC(Multiplex operator
+    AddComment(R"DOC(
+Multiplex Operator.
 
 Multiplex multiple tensors according to the index provided by the index tensor.
 
@@ -77,10 +78,11 @@ the (Ids[i])-th tensor.
 
 For i-th row of the output tensor:
 
-y[i] = x_{k}[i]
+$$y[i] = x_{k}[i]$$
 
-where y is the output tensor. `x_{k}` is the k-th input tensor
+where `y` is the output tensor, `x_{k}` is the k-th input tensor,
 and `k = Ids[i]`.
+
 )DOC");
   }
 };

paddle/operators/name_convention.md

@@ -4,10 +4,10 @@ To make the operator document itself more clear, we recommend operator names obe
 
 ### OpProtoMaker names
 
-When defining an operator in Paddle, a corresponding [OpProtoMaker](https://github.com/PaddlePaddle/Paddle/blob/develop/paddle/framework/operator.h#L170) (TODO: OpProtoMaker Doc)need to be defined. All the Input/Output and Attributes will write into the [OpProto](https://github.com/PaddlePaddle/Paddle/blob/develop/paddle/framework/framework.proto#L61) , and will be used in client language to create operator. 
+When defining an operator in Paddle, a corresponding [OpProtoMaker](https://github.com/PaddlePaddle/Paddle/blob/develop/paddle/framework/operator.h#L170) (TODO: OpProtoMaker Doc)need to be defined. All the Input/Output and Attributes will write into the [OpProto](https://github.com/PaddlePaddle/Paddle/blob/develop/paddle/framework/framework.proto#L61) , and will be used in client language to create operator.
 
 - Input/Output.
-  - Input/Output names follow the **CamelCase**. e.g. `X`, `Y`, `Matrix`, `LastAxisInMatrix`. Input/Output much more like Variables, we prefer to meaningful English words. 
+  - Input/Output names follow the **CamelCase**. e.g. `X`, `Y`, `Matrix`, `LastAxisInMatrix`. Input/Output much more like Variables, we prefer to meaningful English words.
   - If an operator's Input/Output are tensors in math, not match to any meaningful words, input name should starts from `X`. e.g. `X`, `Y`, and output name should starts from `Out`. e.g. `Out`. This rule intends making operators which have few inputs/outputs unified.
 
 - Attribute.
@@ -15,7 +15,7 @@ When defining an operator in Paddle, a corresponding [OpProtoMaker](https://gith
 
 - Comments.
   - Input/Output/Attr comment follow the format of **(type,default value) usage**, corresponding to which type it can be and how it will be used in the operator. e.g.  Attribute in Accumulator`"gamma" `,`(float, default 1.0) Accumulation multiplier`.
-  - Operator comment format of` R"DOC(your comment here)DOC"`. You should explain the input/output of the operator first. If there is math calculation in this operator, you should write the equation in the comment. e.g. `Out = X + Y`. 
+  - Operator comment format of` R"DOC(your comment here)DOC"`. You should explain the input/output of the operator first. If there is math calculation in this operator, you should write the equation in the comment. e.g. `Out = X + Y`.
 
 - Order.
   - Follow the order of Input/Output, then Attribute, then Comments. See the example in best practice.
@@ -24,7 +24,7 @@ When defining an operator in Paddle, a corresponding [OpProtoMaker](https://gith
 
 Here we give some examples to show how these rules will be used.
 
-- The operator has one input, one output. e.g.`relu`, inputs: `X`, outputs: `Out`. 
+- The operator has one input, one output. e.g.`relu`, inputs: `X`, outputs: `Out`.
 
 - The operator has two input, one output. e.g. `rowwise_add`, inputs : `X`, `Y`, outputs : `Out`.
 
@@ -38,23 +38,27 @@ public:
   AccumulateOpMaker(framework::OpProto *proto,
                             framework::OpAttrChecker *op_checker)
     : OpProtoAndCheckerMaker(proto, op_checker) {
-    AddInput("X", "(Tensor) The input tensor that has to be accumulated to the output tensor. 
-    If the output size is not the same as input size, 
+    AddInput("X", "(Tensor) The input tensor that has to be accumulated to the output tensor.
+    If the output size is not the same as input size,
     the output tensor is first reshaped and initialized to zero, and only then, accumulation is done.");
     AddOutput("Out", "(Tensor) Accumulated output tensor");
     AddAttr<float>("gamma", "(float, default 1.0) Accumulation multiplier").SetDefault(1.0f);
     AddComment(R"DOC(
-Accumulate operator accumulates the input tensor to the output tensor. If the
+Accumulate Operator.
+
+This operator accumulates the input tensor to the output tensor. If the
 output tensor already has the right size, we add to it; otherwise, we first
 initialize the output tensor to all zeros, and then do accumulation. Any
 further calls to the operator, given that no one else fiddles with the output
 in the interim, will do simple accumulations.
-Accumulation is done as shown:
+
+Accumulation is done as follows:
 
 Out = 1*X + gamma*Out
 
 where X is the input tensor, Out is the output tensor and gamma is the multiplier
 argument.
+
 )DOC");
   }
 };

paddle/operators/nccl_op.cc

@@ -48,12 +48,17 @@ class NCCLInitOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddOutput("Communicator",
               "Create Communicator for communicating between gpus");
-    AddAttr<std::vector<int>>("gpus", "gpu id lists");
-    AddAttr<int>("data_type", "output data type")
+    AddAttr<std::vector<int>>("gpus", "(vector<int>) GPU id lists");
+    AddAttr<int>("data_type",
+                 "(int, default 5 (FP32)) "
+                 "Output data type")
         .SetDefault(framework::DataType::FP32);
     AddComment(R"DOC(
-               create communicator.
-        )DOC");
+NCCLInit Operator.
+
+Create communicator.
+
+)DOC");
   }
 };
 
@@ -143,11 +148,15 @@ class NCCLAllReduceOpMaker : public framework::OpProtoAndCheckerMaker {
     AddInput("Communicator", "Communicator for communicating between gpus");
     AddOutput("Out", "The output of AllReduce op");
     AddAttr<std::string>("reduction",
+                         "(string, default 'ncclSum') "
                          "{'ncclMin', 'ncclMax', 'ncclProd', 'ncclSum'}.")
         .SetDefault("ncclSum");
     AddComment(R"DOC(
-            AllReduce the input tensors.
-        )DOC");
+NCCLAllReduce Operator.
+
+AllReduce the input tensors.
+
+)DOC");
   }
 };
 
@@ -161,14 +170,20 @@ class NCCLReduceOpMaker : public framework::OpProtoAndCheckerMaker {
     AddInput("Communicator", "Communicator for communicating between gpus");
     AddOutput("Out", "The output of Reduce op");
     AddAttr<std::string>("reduction",
+                         "(string, default 'ncclSum') "
                          "{'ncclMin', 'ncclMax', 'ncclProd', 'ncclSum'}.")
         .SetDefault("ncclSum");
     AddAttr<int>("root",
-                 "root gpu of the parameter. if not "
-                 "set(platform::kInvalidGPUId). hashed by name.")
+                 "(int, default kInvalidGPUId) "
+                 "Root gpu of the parameter. If not, "
+                 "set(platform::kInvalidGPUId). Hashed by name.")
         .SetDefault(platform::kInvalidGPUId);
     AddComment(R"DOC(
-            Reduce the tensors)DOC");
+NCCLReduce Operator.
+
+Reduce the tensors.
+
+)DOC");
   }
 };
 
@@ -182,12 +197,16 @@ class NCCLBcastOpMaker : public framework::OpProtoAndCheckerMaker {
     AddInput("Communicator", "Communicator for communicating between gpus");
     AddOutput("Out", "The output of Bcast");
     AddAttr<int>("root",
-                 "root gpu of the parameter. if not "
-                 "set(platform::kInvalidGPUId). hashed by name.")
+                 "(int, default kInvalidGPUId) "
+                 "Root gpu of the parameter. If not, "
+                 "set(platform::kInvalidGPUId). Hashed by name.")
         .SetDefault(platform::kInvalidGPUId);
     AddComment(R"DOC(
-            Bcast the tensors.
-        )DOC");
+NCCLBcast Operator.
+
+Bcast the tensors.
+
+)DOC");
   }
 };
 

paddle/operators/pad_op.cc

@@ -54,41 +54,44 @@ class PadOpMaker : public framework::OpProtoAndCheckerMaker {
              "The input of pad op. "
              "The input should be a k-D tensor(k > 0 and k < 7)");
     AddOutput("Out",
-              "The output of pad op."
+              "The output of pad op. "
               "A tensor with the same shape as X.");
+    AddAttr<std::vector<int>>(
+        "paddings",
+        "(vector<int>) "
+        "A list<int> to describe the padding rules for each dimension. "
+        "For 2-D image tensor, paddings=[0, 1, 2, 3] means "
+        "padding 0 row to top, 1 row to bottom, 2 columns to left "
+        "and 3 columns to right. Size of paddings should be equal to "
+        "2 * dimension size of the input tensor.");
+    AddAttr<float>("pad_value",
+                   "(float, default 0.0) "
+                   "The value to fill the padded areas.")
+        .SetDefault(0.0f);
     AddComment(R"DOC(
-Pad input into output, as specified by paddings and pad_value. The input should be a k-D tensor(k > 0 and k < 7). As an example:
+Pad Operator.
+
+Pad input into output, as specified by paddings and pad_value. 
+The input should be a k-D tensor(k > 0 and k < 7). As an example:
 
 Given:
 
 X = [[1, 2],
-   [3, 4]]
-
-and
+     [3, 4]],
 
-paddings = [0, 1, 1, 2]
+paddings = [0, 1, 1, 2],
 
 and
 
-pad_value = 0
+pad_value = 0,
 
-then we get
+we have:
 
 Out = [[0, 1, 2, 0, 0]
        [0, 3, 4, 0, 0]
        [0, 0, 0, 0, 0]]
+
 )DOC");
-    AddAttr<std::vector<int>>(
-        "paddings",
-        "A list<int> to describes padding rules for each dimension."
-        " For 2-D image tensor, paddings=[0, 1, 2, 3] means"
-        " padding 0 row to top, 1 row to bottom, 2 columns to left"
-        " and 3 columns to right.Size of paddings should be equal to"
-        " 2 * dimension size of input tensor.");
-    AddAttr<float>("pad_value",
-                   "(float) default to 0; "
-                   "The value to fill padded areas.")
-        .SetDefault(0.0f);
   }
 };
 

paddle/operators/pool_op.cc

@@ -73,125 +73,138 @@ Pool2dOpMaker::Pool2dOpMaker(framework::OpProto *proto,
   AddInput(
       "X",
       "(Tensor) The input tensor of pooling operator. "
-      "The format of input tensor is NCHW. Where N is batch size, C is the "
-      "number of channels, H and W is the height and width of feature.");
+      "The format of input tensor is NCHW, where N is batch size, C is the "
+      "number of channels, H is the height of the feature, "
+      "and W is the width of the feature.");
   AddOutput("Out",
-            "(Tensor) The output tensor of pooling operator."
-            "The format of output tensor is also NCHW."
-            "Where N is batch size, C is "
-            "the number of channels, H and W is the height and "
-            "width of feature.");
+            "(Tensor) The output tensor of pooling operator. "
+            "The format of output tensor is also NCHW, "
+            "where N is batch size, C is the number of channels, "
+            "H is the height of the feature, "
+            "and W is the width of the feature.");
 
   AddAttr<std::string>("poolingType",
                        "(string), pooling type, can be \"max\" for max-pooling "
                        "and \"avg\" for average-pooling.")
       .InEnum({"max", "avg"});
   AddAttr<std::vector<int>>("ksize",
-                            "(vector ), the pooling window size(height, width) "
-                            "of pooling operator."
+                            "(vector<int>) The pooling window "
+                            "size(height, width) of the pooling operator. "
                             "If globalPooling = true, ksize and paddings will "
                             "be ignored.");  // TODO(Chengduo): Add checker.
                                              // (Currently,
   // TypedAttrChecker don't support vector type.)
   AddAttr<bool>("globalPooling",
-                "(bool default: false), whether to use the global pooling."
+                "(bool, default false) Whether to use the global pooling. "
                 "If globalPooling = true, ksize and paddings will be ignored.")
       .SetDefault(false);
-  AddAttr<std::vector<int>>(
-      "strides",
-      "(vector, default:{1, 1}), strides(height, width) of pooling operator.")
+  AddAttr<std::vector<int>>("strides",
+                            "(vector<int>, default {1, 1}), strides(height, "
+                            "width) of pooling operator.")
       .SetDefault({1, 1});  // TODO(Chengduo): Add checker. (Currently,
   // TypedAttrChecker don't support vector type.)
   AddAttr<std::vector<int>>(
       "paddings",
-      "(vector defalut:{0,0}), paddings(height, width) of pooling operator."
+      "(vector<int>, defalut {0,0}), paddings(height, width) of pooling "
+      "operator."
       "If globalPooling = true, paddings and ksize will be ignored.")
       .SetDefault({0, 0});  // TODO(Chengduo): Add checker. (Currently,
   // TypedAttrChecker don't support vector type.)
 
   AddComment(R"DOC(
+Pool2d Operator.
+
 The pooling2d operation calculates the output based on
 the input, poolingType and ksize, strides, paddings parameters.
-Input(X) and output(Out) are in NCHW format. Where N is batch size, C is the
-number of channels, H and W is the height and width of feature.
+Input(X) and output(Out) are in NCHW format, where N is batch size, C is the
+number of channels, H is the height of the feature, and W is the width of the feature.
 Parameters(ksize, strides, paddings) are two elements.
 These two elements represent height and width, respectively.
 The input(X) size and output(Out) size may be different.
 
 Example:
   Input:
-       X shape: (N, C, H_in, W_in)
+       X shape: $(N, C, H_{in}, W_{in})$
   Output:
-       Out shape: (N, C, H_out, W_out)
-  where
-       H_out = (H_in - ksize[0] + 2 * paddings[0]) / strides[0] + 1;
-       W_out = (W_in - ksize[1] + 2 * paddings[1]) / strides[1] + 1;
+       Out shape: $(N, C, H_{out}, W_{out})$
+  where 
+       $$ 
+       H_{out} = (H_{in} - ksize[0] + 2 * paddings[0]) / strides[0] + 1 \\
+       W_{out} = (W_{in} - ksize[1] + 2 * paddings[1]) / strides[1] + 1
+       $$
+
 )DOC");
 }
 
 Pool3dOpMaker::Pool3dOpMaker(framework::OpProto *proto,
                              framework::OpAttrChecker *op_checker)
     : OpProtoAndCheckerMaker(proto, op_checker) {
-  AddInput(
-      "X",
-      "(Tensor) The input tensor of pooling operator. "
-      "The format of input tensor is NCDHW. Where N is batch size, C is "
-      "the number of channels, D, H and W is the depth, height and width of "
-      "feature.");
+  AddInput("X",
+           "(Tensor) The input tensor of pooling operator. "
+           "The format of input tensor is NCDHW, where N is batch size, C is "
+           "the number of channels, and D, H and W is the depth, height and "
+           "width of "
+           "the feature, respectively.");
   AddOutput("Out",
             "(Tensor) The output tensor of pooling operator."
-            "The format of output tensor is also NCDHW."
-            "Where N is batch size, C is "
-            "the number of channels, D, H and W is the depth, height and "
-            "width of feature.");
+            "The format of output tensor is also NCDHW, "
+            "where N is batch size, C is "
+            "the number of channels, and D, H and W is the depth, height and "
+            "width of the feature, respectively.");
 
   AddAttr<std::string>("poolingType",
-                       "(string), pooling type, can be \"max\" for max-pooling "
+                       "(string) Pooling type, can be \"max\" for max-pooling "
                        "and \"avg\" for average-pooling.")
       .InEnum({"max", "avg"});
-  AddAttr<std::vector<int>>("ksize",
-                            "(vector ), the pooling window size(depth, height, "
-                            "width) of pooling "
-                            "operator."
-                            "If globalPooling = true, ksize and paddings wille "
-                            "be ignored.");  // TODO(Chengduo): Add checker.
-                                             // (Currently,
+  AddAttr<std::vector<int>>(
+      "ksize",
+      "(vector<int>) The pooling window size(depth, height, "
+      "width) of pooling operator. "
+      "If globalPooling = true, ksize and paddings will "
+      "be ignored.");  // TODO(Chengduo): Add checker.
+                       // (Currently,
   // TypedAttrChecker don't support vector type.)
   AddAttr<bool>("globalPooling",
-                "(bool default: false), whether to use the global pooling."
+                "(bool, default false) Whether to use the global pooling. "
                 "If globalPooling = true, ksize and paddings wille be ignored.")
       .SetDefault(false);
-  AddAttr<std::vector<int>>("strides",
-                            "(vector, default:{1,1,1}), strides(depth, height, "
-                            "width) of pooling operator.")
+  AddAttr<std::vector<int>>(
+      "strides",
+      "(vector<int>, default {1,1,1}) Strides(depth, height, "
+      "width) of the pooling operator.")
       .SetDefault({1, 1, 1});  // TODO(Chengduo): Add checker. (Currently,
                                // TypedAttrChecker don't support vector type.)
   AddAttr<std::vector<int>>(
       "paddings",
-      "(vector defalut:{0,0,0}), paddings(depth, height, "
-      "width) of pooling operator."
-      "If globalPooling = true, ksize and paddings wille be ignored.")
+      "(vector<int>, defalut {0,0,0}), paddings(depth, height, "
+      "width) of pooling operator. "
+      "If globalPooling = true, ksize and paddings will be ignored.")
       .SetDefault({0, 0, 0});  // TODO(Chengduo): Add checker. (Currently,
                                // TypedAttrChecker don't support vector type.)
 
   AddComment(R"DOC(
+Pool3d Operator.
+
 The pooling3d operation calculates the output based on
-the input, poolingType and ksize, strides, paddings parameters.
-Input(X) and output(Out) are in NCDHW format. Where N is batch
-size, C is the number of channels, D, H and W is the depth, height and
-width of feature. Parameters(ksize, strides, paddings) are three elements.
-These three elements represent depth, height and width, respectively.
-The input(X) size and output(Out) size may be different.
+the input, poolingType, ksize, strides, and paddings parameters.
+Input(X) and output(Out) are in NCDHW format, where N is batch
+size, C is the number of channels, and D, H and W are the depth, height and
+width of the feature, respectively. Parameters(ksize, strides, paddings) 
+are three elements. These three elements represent depth, height and 
+width, respectively. The input(X) size and output(Out) size may be different.
 
 Example:
   Input:
-       X shape: (N, C, D_in, H_in, W_in)
+       X shape: $(N, C, D_{in}, H_{in}, W_{in})$
   Output:
-       Out shape: (N, C, D_out, H_out, W_out)
+       Out shape: $(N, C, D_{out}, H_{out}, W_{out})$
   where
-       D_out = (D_in - ksize[0] + 2 * paddings[0]) / strides[0] + 1;
-       H_out = (H_in - ksize[1] + 2 * paddings[1]) / strides[1] + 1;
-       W_out = (W_in - ksize[2] + 2 * paddings[2]) / strides[2] + 1;
+       $$
+       D_{out} = (D_{in} - ksize[0] + 2 * paddings[0]) / strides[0] + 1 \\
+       H_{out} = (H_{in} - ksize[1] + 2 * paddings[1]) / strides[1] + 1 \\
+       W_{out} = (W_{in} - ksize[2] + 2 * paddings[2]) / strides[2] + 1
+       $$
+
 )DOC");
 }
 }  // namespace operators

paddle/operators/pool_with_index_op.cc

@@ -89,64 +89,73 @@ class MaxPool2dWithIndexOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput(
         "X",
-        "(Tensor), the input tensor of pooling operator. "
-        "The format of input tensor is NCHW. Where N is batch size, C is the "
-        "number of channels, H and W is the height and width of image.");
+        "(Tensor) The input tensor of pooling operator. "
+        "The format of input tensor is NCHW, where N is batch size, C is the "
+        "number of channels, H is the height of the image, "
+        "and W is the width of the image.");
     AddOutput("Out",
-              "(Tensor), the output tensor of pooling operator."
-              "The format of output tensor is also NCHW."
-              "Where N is batch size, C is "
-              "the number of channels, H and W is the height and "
-              "width of image.");
+              "(Tensor) The output tensor of pooling operator. "
+              "The format of output tensor is also NCHW, "
+              "where N is batch size, C is "
+              "the number of channels, H is the height of the image "
+              "and W is the width of the image.");
     AddOutput("Mask",
-              "(Tensor), the Mask tensor of pooling operator."
-              "The format of output tensor is also NCHW."
-              "Where N is batch size, C is the number of channels, H and W "
-              "is the height and width of image."
-              "The value in it is the index in current feature map");
+              "(Tensor) The Mask tensor of pooling operator."
+              "The format of output tensor is also NCHW, "
+              "where N is batch size, C is the number of channels, "
+              "H is the height of the image, "
+              "and W is the width of the image. "
+              "It represents the index in the current feature map.");
 
     AddAttr<std::vector<int>>("ksize",
-                              "(vector ), the pooling window size(height, "
-                              "width) of pooling operator."
+                              "(vector<int>) The pooling window size(height, "
+                              "width) of pooling operator. "
                               "If globalPooling = true, ksize and paddings "
                               "will be ignored.");  // TODO(Chengduo): Add
                                                     // checker. (Currently,
     // TypedAttrChecker don't support vector type.)
     AddAttr<bool>(
         "globalPooling",
-        "(bool default: false), whether to use the global pooling."
+        "(bool, default false) Whether to use the global pooling. "
         "If globalPooling = true, ksize and paddings will be ignored.")
         .SetDefault(false);
-    AddAttr<std::vector<int>>(
-        "strides",
-        "(vector, default:{1, 1}), strides(height, width) of pooling operator.")
+    AddAttr<std::vector<int>>("strides",
+                              "(vector<int>, default {1, 1}), strides(height, "
+                              "width) of pooling operator.")
         .SetDefault({1, 1});  // TODO(Chengduo): Add checker. (Currently,
     // TypedAttrChecker don't support vector type.)
     AddAttr<std::vector<int>>(
         "paddings",
-        "(vector defalut:{0, 0}), paddings(height, width) of pooling operator."
+        "(vector<int>, defalut {0, 0}), paddings(height, width) of pooling "
+        "operator. "
         "If globalPooling = true, paddings and will be ignored.")
         .SetDefault({0, 0});  // TODO(Chengduo): Add checker. (Currently,
     // TypedAttrChecker don't support vector type.)
 
     AddComment(R"DOC(
+MaxPool2d Operator.
+
 The maxPooling2d with index operation calculates the output and the mask
-based on the input and ksize, strides, paddings parameters. Input(X) and
-output(Out, Mask) are in NCHW format. Where N is batch size, C is the
-number of channels, H and W is the height and width of feature.
+based on the input, ksize, strides, and paddings parameters. Input(X) and
+output(Out, Mask) are in NCHW format, where N is batch size, C is the
+number of channels, H is the height of the feature, 
+and W is the width of the feature.
 Parameters(ksize, strides, paddings) are two elements.
 These two elements represent height and width, respectively.
 The input(X) size and output(Out, Mask) size may be different.
 
 Example:
   Input:
-       X shape: (N, C, H_in, W_in)
+       X shape: $(N, C, H_{in}, W_{in})$
   Output:
-       Out shape: (N, C, H_out, W_out)
-       Mask shape: (N, C, H_out, W_out)
+       Out shape: $(N, C, H_{out}, W_{out})$
+       Mask shape: $(N, C, H_{out}, W_{out})$
   where
-       H_out = (H_in - ksize[0] + 2 * paddings[0]) / strides[0] + 1;
-       W_out = (W_in - ksize[1] + 2 * paddings[1]) / strides[1] + 1;
+       $$
+       H_{out} = (H_{in} - ksize[0] + 2 * paddings[0]) / strides[0] + 1 \\
+       W_{out} = (W_{in} - ksize[1] + 2 * paddings[1]) / strides[1] + 1
+       $$
+
 )DOC");
   }
 };
@@ -156,70 +165,76 @@ class MaxPool3dWithIndexOpMaker : public framework::OpProtoAndCheckerMaker {
   MaxPool3dWithIndexOpMaker(framework::OpProto *proto,
                             framework::OpAttrChecker *op_checker)
       : OpProtoAndCheckerMaker(proto, op_checker) {
-    AddInput(
-        "X",
-        "(Tensor), the input tensor of pooling operator. "
-        "The format of input tensor is NCDHW. Where N is batch size, C is "
-        "the number of channels, D, H and W is the depth, height and width of "
-        "image.");
+    AddInput("X",
+             "(Tensor) The input tensor of pooling operator. "
+             "The format of input tensor is NCDHW, where N is batch size, C is "
+             "the number of channels, and D, H and W are the depth, height and "
+             "width of "
+             "the image, respectively");
     AddOutput("Out",
-              "(Tensor), the output tensor of pooling operator."
-              "The format of output tensor is also NCDHW."
-              "Where N is batch size, C is "
-              "the number of channels, D, H and W is the depth, height and "
-              "width of image.");
+              "(Tensor) The output tensor of pooling operator. "
+              "The format of output tensor is also NCDHW, "
+              "where N is the batch size, C is the number of channels, "
+              "and D, H and W are the depth, height and "
+              "width of the image, respectively.");
     AddOutput("Mask",
-              "(Tensor), the Mask tensor of pooling operator."
-              "The format of output tensor is also NCDHW."
-              "Where N is batch size, C is the number of channels, D, H and W "
-              "is the depth, height and width of image."
-              "The value in it is the index in current feature map");
+              "(Tensor) The Mask tensor of pooling operator. "
+              "The format of output tensor is also NCDHW, "
+              "where N is the batch size, C is the number of channels, and "
+              "D, H and W are the depth, height and width "
+              "of the image, respectively. "
+              "It represents the index in the current feature map.");
 
     AddAttr<std::vector<int>>("ksize",
-                              "(vector), the pooling window size(depth, "
-                              "height, width) of pooling "
-                              "operator."
+                              "(vector<int>) The pooling window size(depth, "
+                              "height, width) of pooling operator. "
                               "If globalPooling = true, ksize and paddings "
                               "will be ignored.");  // TODO(Chengduo): Add
                                                     // checker. (Currently,
     // TypedAttrChecker don't support vector type.)
     AddAttr<bool>(
         "globalPooling",
-        "(bool default: false), whether to use the global pooling."
+        "(bool, default false) Whether to use the global pooling. "
         "If globalPooling = true, ksize and paddings will be ignored.")
         .SetDefault(false);
     AddAttr<std::vector<int>>("strides",
-                              "(vector, default:{1,1,1}), strides(depth, "
+                              "(vector<int>, default {1,1,1}), strides(depth, "
                               "height, width) of pooling operator.")
         .SetDefault({1, 1, 1});  // TODO(Chengduo): Add checker. (Currently,
     // TypedAttrChecker don't support vector type.)
     AddAttr<std::vector<int>>(
         "paddings",
-        "(vector defalut:{0,0,0}), paddings(depth, "
-        "height, width) of pooling operator."
+        "(vector, defalut {0,0,0}), paddings(depth, "
+        "height, width) of pooling operator. "
         "If globalPooling = true, paddings and ksize will be ignored.")
         .SetDefault({0, 0, 0});  // TODO(Chengduo): Add checker. (Currently,
     // TypedAttrChecker don't support vector type.)
 
     AddComment(R"DOC(
+MaxPool3d Operator.
+
 The maxpooling3d with index operation calculates the output and the mask
 based on the input and ksize, strides, paddings parameters.
-Input(X) and output(Out, Mask) are in NCDHW format. Where N is batch
-size, C is the number of channels, D, H and W is the depth, height and
-width of feature. Parameters(ksize, strides, paddings) are three elements.
+Input(X) and output(Out, Mask) are in NCDHW format, where N is batch
+size, C is the number of channels, and D, H and W are the depth, height and
+width of the feature, respectively. 
+Parameters(ksize, strides, paddings) are three elements.
 These three elements represent depth, height and width, respectively.
 The input(X) size and output(Out, Mask) size may be different.
 
 Example:
   Input:
-       X shape: (N, C, D_in, H_in, W_in)
+       X shape: $(N, C, D_{in}, H_{in}, W_{in})$
   Output:
-       Out shape: (N, C, D_out, H_out, W_out)
-       Mask shape: (N, C, D_out, H_out, W_out)
+       Out shape: $(N, C, D_{out}, H_{out}, W_{out})$
+       Mask shape: $(N, C, D_{out}, H_{out}, W_{out})$
   where
-       D_out = (D_in - ksize[0] + 2 * paddings[0]) / strides[0] + 1;
-       H_out = (H_in - ksize[1] + 2 * paddings[1]) / strides[1] + 1;
-       W_out = (W_in - ksize[2] + 2 * paddings[2]) / strides[2] + 1;
+       $$
+       D_{out} = (D_{in} - ksize[0] + 2 * paddings[0]) / strides[0] + 1 \\
+       H_{out} = (H_{in} - ksize[1] + 2 * paddings[1]) / strides[1] + 1 \\
+       W_{out} = (W_{in} - ksize[2] + 2 * paddings[2]) / strides[2] + 1
+       $$
+
 )DOC");
   }
 };

paddle/operators/precision_recall_op.cc

@@ -92,76 +92,78 @@ class PrecisionRecallOpMaker : public framework::OpProtoAndCheckerMaker {
                          framework::OpAttrChecker *op_checker)
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("MaxProbs",
-             "(Tensor, default Tensor<float>), a 2-D tensor with shape N x 1, "
+             "(Tensor, default Tensor<float>) A 2-D tensor with shape N x 1, "
              "where N is the batch size. Each row contains the max probability "
              "of an instance which computed by the previous top_k (k=1) "
              "operator.");
     AddInput("Indices",
-             "(Tensor, default Tensor<int>), a 2-D tensor with shape N x 1, "
+             "(Tensor, default Tensor<int>) A 2-D tensor with shape N x 1, "
              "where N is the batch size. Each row contains the corresponding "
              "index which computed by the previous top_k (k=1) operator.");
     AddInput("Labels",
-             "(Tensor, default Tensor<int>), a 2-D tensor with shape N x 1, "
+             "(Tensor, default Tensor<int>) A 2-D tensor with shape N x 1, "
              "where N is the batch size. Each element is a label and the "
              "value should be in [0, class_number - 1].");
     AddInput("Weights",
-             "(Tensor, default Tensor<float>), a 2-D tensor with shape N x 1, "
+             "(Tensor, default Tensor<float>) A 2-D tensor with shape N x 1, "
              "where N is the batch size. This input is optional. If provided, "
              "weight of instance would be considered when computing metrics.")
         .AsDispensable();
     AddInput("StatesInfo",
-             "(Tensor, default Tensor<int>), a 2-D tensor with shape D x 4, "
+             "(Tensor, default Tensor<int>) A 2-D tensor with shape D x 4, "
              "where D is the number of classes. This input is optional. If "
              "provided, current state will be accumulated to this state and "
-             "the accumulation state will be as the output state.")
+             "the accumulation state will be the output state.")
         .AsDispensable();
     AddOutput("BatchMetrics",
-              "(Tensor, default Tensor<float>), a 1-D tensor with shape {6}."
-              "This output tensor contains metrics for current batch data."
+              "(Tensor, default Tensor<float>) A 1-D tensor with shape {6}. "
+              "This output tensor contains metrics for current batch data. "
               "The layout is [macro average precision, macro average recall, "
               "macro f1 score, micro average precision, micro average recall, "
-              "micro f1 score]");
+              "micro f1 score].");
     AddOutput("AccumMetrics",
-              "(Tensor, default Tensor<float>), a 1-D tensor with shape {6}."
-              "This output tensor contains metrics for accumulated data."
+              "(Tensor, default Tensor<float>) A 1-D tensor with shape {6}. "
+              "This output tensor contains metrics for accumulated data. "
               "The layout is [macro average precision, macro average recall, "
               "macro f1 score, micro average precision, micro average recall, "
-              "micro f1 score]");
+              "micro f1 score].");
     AddOutput("AccumStatesInfo",
-              "(Tensor, default Tensor<float>), a 2-D tensor with shape D x 4, "
+              "(Tensor, default Tensor<float>) A 2-D tensor with shape D x 4, "
               "where D is equal to class number. This output tensor contains "
               "accumulated state variables used to compute metrics. The layout "
               "for each class is [true positives, false positives, "
               "true negatives, false negatives].");
-    AddAttr<int>("class_number", "Number of classes to be evaluated.");
+    AddAttr<int>("class_number", "(int) Number of classes to be evaluated.");
     AddComment(R"DOC(
-When given 'Input(Indices)' and 'Input(Labels)', this operator can be used
+Precision Recall Operator.
+
+When given Input(Indices) and Input(Labels), this operator can be used
 to compute various metrics including:
-  - macro average precision
-  - macro average recall
-  - macro f1 score
-  - micro average precision
-  - micro average recall
-  - micro f1 score
+1. macro average precision
+2. macro average recall
+3. macro f1 score
+4. micro average precision
+5. micro average recall
+6. micro f1 score
 
 To compute the above metrics, we need to do statistics for true positives,
-false positives and false negatives. Here count of true negatives is not
+false positives and false negatives. Here the count of true negatives is not
 necessary, but counting it may provide potential usage and the cost is
-trivial, so the operator also provides count of true negatives.
+trivial, so the operator also provides the count of true negatives.
 
 We define state as a 2-D tensor with shape [class_number, 4]. Each row of a
 state contains statistic variables for corresponding class. Layout of each row
 is: TP(true positives), FP(false positives), TN(true negatives),
-FN(false negatives). If 'Input(Weights)' provided, TP, FP, TN, FN will be
-calculated by given weight instead of instance count.
+FN(false negatives). If Input(Weights) is provided, TP, FP, TN, FN will be
+calculated by given weight instead of the instance count.
 
 This operator also supports metrics computing for cross-batch situation. To
-achieve this, 'Input(StatesInfo)' should be provided. State of current batch
-data will be accumulated to 'Input(StatesInfo)' and 'Output(AccumStatesInfo)'
+achieve this, Input(StatesInfo) should be provided. State of current batch
+data will be accumulated to Input(StatesInfo) and Output(AccumStatesInfo)
 is the accumulation state.
 
-'Output(BatchMetrics)' is metrics of current batch data while
-'Output(AccumStatesInfo)' is metrics of accumulation data.
+Output(BatchMetrics) is metrics of current batch data while
+Output(AccumStatesInfo) is metrics of accumulation data.
 
 )DOC");
   }

paddle/operators/prelu_op.cc

@@ -41,17 +41,24 @@ class PReluOpMaker : public framework::OpProtoAndCheckerMaker {
   PReluOpMaker(framework::OpProto *proto, framework::OpAttrChecker *op_checker)
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "The input tensor of prelu operator.");
-    AddInput("Alpha", "The alpha weight of PRelu operator.");
-    AddOutput("Out", "The output tensor of PRelu operator.");
-    AddComment(R"DOC(PRelu operator
+    AddInput("Alpha", "The alpha weight of prelu operator.");
+    AddOutput("Out", "The output tensor of prelu operator.");
+    AddComment(R"DOC(
+PRelu Operator.
 
 The equation is:
 
-  f(x) = alpha * x , for x < 0
-  f(x) = x         , for x >= 0
+$$
+f(x) =
+\begin{cases}
+\alpha * x, \quad  \text{if} \ x < 0 \\
+x,         \qquad  \text{if} \ x >= 0
+\end{cases}
+$$
 
 The input `X` can carry the LoD (Level of Details) information,
-or not. And the output shares the LoD with input `X`.
+or not. And the output shares the LoD information with input `X`.
+
 )DOC");
   }
 };

paddle/operators/proximal_adagrad_op.cc

@@ -83,22 +83,26 @@ class ProximalAdagradOpMaker : public framework::OpProtoAndCheckerMaker {
                    "L1 regularization strength.")
         .SetDefault(0.0f);
     AddAttr<float>("l2",
-                   "(float, default 0.0)"
+                   "(float, default 0.0) "
                    "L2 regularization strength.")
         .SetDefault(0.0f);
     AddComment(R"DOC(
+Proximal Adagrad Optimizer.
 
-Optimizer that implements the proximal adagrad algorithm.
+Optimizer that implements the proximal adagrad algorithm:
 
-moment = moment + grad * grad
-prox_param = param - learning_rate * grad * (1 / sqrt(moment))
-param = sign(prox_param) / (1 + learning_rate * l2) *
-        max { |prox_param| - learning_rate * l1 , 0 }
+$$
+moment = moment + grad * grad \\
+prox\_param = param - learning\_rate * grad * (1 / \sqrt{moment}) \\
+param = sign(prox\_param) / (1 + learning\_rate * l2) *
+        \max(|prox\_param| - learning\_rate * l1 , 0)
+$$
 
 The paper that proposed Proximal GD: 
 (http://papers.nips.cc/paper/3793-efficient-learning-using-forward-backward-splitting.pdf)
 Here, we use the adagrad learning rate as specified here: 
 (http://www.jmlr.org/papers/volume12/duchi11a/duchi11a.pdf)
+
 )DOC");
   }
 };

paddle/operators/proximal_gd_op.cc

@@ -67,19 +67,23 @@ class ProximalGDOpMaker : public framework::OpProtoAndCheckerMaker {
                    "L1 regularization strength.")
         .SetDefault(0.0f);
     AddAttr<float>("l2",
-                   "(float, default 0.0)"
+                   "(float, default 0.0) "
                    "L2 regularization strength.")
         .SetDefault(0.0f);
     AddComment(R"DOC(
+ProximalGD Operator.
 
-Optimizer that implements the proximal gradient descent algorithm.
+Optimizer that implements the proximal gradient descent algorithm:
 
-prox_param = param - learning_rate * grad
-param = sign(prox_param) / (1 + learning_rate * l2) *
-        max { |prox_param| - learning_rate * l1 , 0 }
+$$
+prox\_param = param - learning\_rate * grad \\
+param = sign(prox\_param) / (1 + learning\_rate * l2) *
+        \max(|prox\_param| - learning\_rate * l1, 0)
+$$        
 
 The paper that proposed Proximal Gradient Descent:
 (http://papers.nips.cc/paper/3793-efficient-learning-using-forward-backward-splitting.pdf)
+
 )DOC");
   }
 };

paddle/operators/rank_loss_op.cc

@@ -26,9 +26,9 @@ class RankLossOp : public framework::OperatorWithKernel {
 
   void InferShape(framework::InferShapeContext *ctx) const override {
     // input check
-    PADDLE_ENFORCE(ctx->HasInput("Label"), "Input(Label) shouldn't be null");
-    PADDLE_ENFORCE(ctx->HasInput("Left"), "Input(Left) shouldn't be null");
-    PADDLE_ENFORCE(ctx->HasInput("Right"), "Input(Right) shouldn't be null");
+    PADDLE_ENFORCE(ctx->HasInput("Label"), "Input(Label) shouldn't be null.");
+    PADDLE_ENFORCE(ctx->HasInput("Left"), "Input(Left) shouldn't be null.");
+    PADDLE_ENFORCE(ctx->HasInput("Right"), "Input(Right) shouldn't be null.");
 
     auto label_dims = ctx->GetInputDim("Label");
     auto left_dims = ctx->GetInputDim("Left");
@@ -50,32 +50,32 @@ class RankLossOpMaker : public framework::OpProtoAndCheckerMaker {
     AddInput("Label",
              "The label indicating A ranked higher than B or not, row vector.");
     AddInput("Left", "The output of RankNet for doc A, vector.");
-    AddInput("Right", "The output of RankNet for doc B, vetor");
+    AddInput("Right", "The output of RankNet for doc B, vetor.");
     AddOutput("Out", "The output loss of RankLoss operator, vector.");
-    AddComment(R"DOC(RankLoss operator
+    AddComment(R"DOC(
+RankLoss Operator.
 
-Rank loss operator for RankNet[1]. RankNet is a pairwise ranking model with
+RankLoss operator for RankNet
+(http://icml.cc/2015/wp-content/uploads/2015/06/icml_ranking.pdf). 
+RankNet is a pairwise ranking model with
 one training sample consisting of a pair of doc A and B, and the label P
 indicating that A is ranked higher than B or not:
 
 P = {0, 1} or {0, 0.5, 1}, where 0.5 means no information about the rank of
 the input pair.
 
-The RankLoss operator contains three inputs: Left (o_i), Right (o_j) and Label
-(P_{i,j}), which represent the output of RankNet for two docs and the label
-respectively, and yields the rank loss C_{i,j} by following the expression
+The RankLoss operator takes three inputs: Left (o_i), Right (o_j) and Label
+(P_{i,j}), which represent the output of RankNet for the two docs and the label, 
+respectively, and yields the rank loss C_{i,j} using the following equation:
 
-\f[
+\f$$
   C_{i,j} = -\tilde{P_{ij}} * o_{i,j} + log(1 + e^{o_{i,j}}) \\
   o_{i,j} =  o_i - o_j  \\
   \tilde{P_{i,j}} = \left \{0, 0.5, 1 \right \} \ or \ \left \{0, 1 \right \}
-\f]
+\f$$
 
 The operator can take inputs of one sample or in batch.
 
-[1]. Chris Burges, Tal Shaked, Erin Renshaw, et al. Learning to
-     Rank using Gradient Descent.
-     http://icml.cc/2015/wp-content/uploads/2015/06/icml_ranking.pdf
 )DOC");
   }
 };

paddle/operators/recurrent_op.cc

@@ -509,14 +509,14 @@ class RecurrentOpProtoMaker : public framework::OpProtoAndCheckerMaker {
     AddInput(kInitialStates, "rnn initial states").AsDuplicable();
     AddInput(kParameters,
              "Parameters are used by step block as its input. However, the "
-             "inputs is not a sequence tensor. Every time step, each operator "
-             "in step block just use the parameter directly")
+             "input is not a sequence tensor. Every time step, each operator "
+             "in step block just use the parameter directly.")
         .AsDuplicable();
     AddOutput(kOutputs,
-              "The output sequence of RNN. The sequence length must be same")
+              "The output sequence of RNN. The sequence length must be same.")
         .AsDuplicable();
     AddOutput(kStepScopes,
-              "StepScopes contains all local variables in each time step.");
+              "StepScopes contain all local variables in each time step.");
     AddAttr<std::vector<std::string>>(kExStates,
                                       string::Sprintf(
                                           R"DOC(The ex-state variable names.
@@ -556,10 +556,12 @@ if reverse is True
       o          o          o         o
 )DOC").SetDefault(false);
     AddAttr<bool>(kIsTrain, "").SetDefault(true);
-    AddComment(R"DOC(Static Length Recurrent Operator
+    AddComment(R"DOC(
+Static Length Recurrent Operator.
+
+The static length recurrent operator can only operate on fixed size sequence
+data, i.e. in each mini-batch, the sequence length of all inputs are the same.
 
-The static length recurrent operator can only operate on fix sized sequence
-data, i.e. in each mini-batch, the sequence length of all inputs are same.
 )DOC");
   }
 };

paddle/operators/reduce_op.cc

@@ -80,24 +80,27 @@ class ReduceOpMaker : public framework::OpProtoAndCheckerMaker {
  public:
   ReduceOpMaker(framework::OpProto *proto, framework::OpAttrChecker *op_checker)
       : OpProtoAndCheckerMaker(proto, op_checker) {
-    AddInput(
-        "X",
-        "(Tensor) The input tensor. Tensors with rank at most 6 are supported");
+    AddInput("X",
+             "(Tensor) The input tensor. Tensors with rank at most 6 are "
+             "supported.");
     AddOutput("Out", "(Tensor) The result tensor.");
     AddAttr<int>(
         "dim",
-        "(int, default 1) The dimension to reduce. "
+        "(int, default 0) The dimension to reduce. "
         "Must be in the range [-rank(input), rank(input)). "
         "If `dim < 0`, the dim to reduce is `rank + dim`. "
-        "Noting that reducing on the first dim will make the LoD info lost.")
+        "Note that reducing on the first dim will make the LoD info lost.")
         .SetDefault(0);
     AddAttr<bool>("keep_dim",
                   "(bool, default false) "
                   "If true, retain the reduced dimension with length 1.")
         .SetDefault(false);
     comment_ = R"DOC(
-{ReduceOP} operator computes the {reduce} of input tensor along the given dimension. 
-The result tensor has 1 fewer dimension than the input unless `keep_dim` is true.
+{ReduceOp} Operator.
+
+This operator computes the {reduce} of input tensor along the given dimension. 
+The result tensor has 1 fewer dimension than the input unless keep_dim is true.
+
 )DOC";
     AddComment(comment_);
   }

paddle/operators/reshape_op.cc

@@ -71,8 +71,11 @@ class ReshapeOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "The input tensor of reshape operator.");
     AddOutput("Out", "The output tensor of reshape operator.");
-    AddAttr<std::vector<int>>("shape", "Target shape of reshape operator.");
-    AddComment(R"DOC(Reshape operator
+    AddAttr<std::vector<int>>("shape",
+                              "(vector<int>) "
+                              "Target shape of reshape operator.");
+    AddComment(R"DOC(
+Reshape Operator.
 
 Reshape Input(X) into the shape specified by Attr(shape).
 
@@ -81,7 +84,7 @@ Given a 2-D tensor X with 2 rows and 2 columns
 
     [[1, 2], [3, 4]]
 
-with target shape = [1, 4], the reshape operator will transform
+and target shape = [1, 4], the reshape operator will transform
 the tensor X into a 1-D tensor:
 
     [1, 2, 3, 4]

paddle/operators/rmsprop_op.cc

@@ -68,22 +68,22 @@ class RmspropOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("Param",
              "(Tensor, default Tensor<float>) "
-             "Input parameter value that has to be updated");
+             "Input parameter value that has to be updated.");
     AddInput("MeanSquare",
              "(Tensor, default Tensor<float>)"
-             " The mean square value that gets updated");
+             " The mean square value that gets updated.");
     AddInput("LearningRate",
              "(Tensor, default Tensor<float>) "
-             "The learning rate should be a tensor of size 1");
+             "The learning rate should be a tensor of size 1.");
     AddInput("Grad",
              "(Tensor, default Tensor<float>) "
-             "Input gradient of the parameter");
+             "Input gradient of the parameter.");
     AddInput("Moment",
-             "(Tensor, default Tensor<float>) The moment that gets updated");
+             "(Tensor, default Tensor<float>) The moment that gets updated.");
 
-    AddOutput("ParamOut", "(Tensor) Output updated parameter value");
-    AddOutput("MomentOut", "(Tensor) Output updated moment");
-    AddOutput("MeanSquareOut", "(Tensor) Output Mean squared updated value");
+    AddOutput("ParamOut", "(Tensor) Output updated parameter value.");
+    AddOutput("MomentOut", "(Tensor) Output updated moment.");
+    AddOutput("MeanSquareOut", "(Tensor) Output Mean squared updated value.");
 
     AddAttr<float>("epsilon",
                    "(float, default 1e-10) Constant "
@@ -93,18 +93,19 @@ class RmspropOpMaker : public framework::OpProtoAndCheckerMaker {
                    "(float, default 0.9) "
                    "Discounting factor for coming gradient.")
         .SetDefault(0.9f);
-    AddAttr<float>("momentum", "(float, default 0.0) Constant value")
+    AddAttr<float>("momentum", "(float, default 0.0) Constant value.")
         .SetDefault(0.0f);
     AddComment(R"DOC(
+Rmsprop Optimizer. 
 
-RMSprop
-
-MeanSquareOut = decay * MeanSquare + (1 - decay) * Grad * Grad
+$$
+MeanSquareOut = decay * MeanSquare + (1 - decay) * Grad * Grad \\
 MomentOut = momentum * Moment +
-            LearningRate * Grad / sqrt(MeanSquareOut + epsilon)
+            \frac{LearningRate * Grad}{\sqrt{MeanSquareOut + epsilon}} \\
 ParamOut = Param -  MomentOut
+$$
 
-The original slides that proposed RMSprop: Slide 29 of
+The original slides that proposed Rmsprop: Slide 29 of
 http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf)
 
 )DOC");

paddle/operators/save_op.cc

@@ -163,14 +163,19 @@ class SaveOpProtoMaker : public framework::OpProtoAndCheckerMaker {
   SaveOpProtoMaker(framework::OpProto *proto,
                    framework::OpAttrChecker *op_checker)
       : OpProtoAndCheckerMaker(proto, op_checker) {
-    AddInput("X", "The tensor need to be saved");
-    AddComment(R"DOC(Save operator
-Save operator will serialize and write a tensor variable to disk file.
+    AddInput("X", "(Tensor ) Input tensor to be saved");
+    AddComment(R"DOC(
+Save operator
+
+This operator will serialize and write a tensor variable to file on disk.
 )DOC");
-    AddAttr<bool>("overwrite", "Overwrite the output file if exist")
+    AddAttr<bool>("overwrite",
+                  "(boolean, default true)"
+                  "Overwrite the output file if exist")
         .SetDefault(true);
     AddAttr<std::string>("file_path",
-                         "Variable will be saved to \"file_path\".")
+                         "(string)"
+                         "The \"file_path\" where the variable will be saved.")
         .AddCustomChecker(
             [](const std::string &path) { return !path.empty(); });
   }

paddle/operators/scale_op.cc

@@ -40,13 +40,16 @@ class ScaleOpMaker : public framework::OpProtoAndCheckerMaker {
  public:
   ScaleOpMaker(framework::OpProto *proto, framework::OpAttrChecker *op_checker)
       : OpProtoAndCheckerMaker(proto, op_checker) {
-    AddInput("X", "The input tensor of scale operator.");
-    AddOutput("Out", "The output tensor of scale operator.");
-    AddComment(R"DOC(Scale operator
+    AddInput("X", "(Tensor) Input tensor of scale operator.");
+    AddOutput("Out", "(Tensor) Output tensor of scale operator.");
+    AddComment(R"DOC(
+Scale operator
 
-The equation is: Out = scale*X
+$$Out = scale*X$$
 )DOC");
-    AddAttr<AttrType>("scale", "The scaling factor of the scale operator.")
+    AddAttr<AttrType>("scale",
+                      "(float, default 0)"
+                      "The scaling factor of the scale operator.")
         .SetDefault(1.0);
   }
 };

paddle/operators/seq_expand_op.cc

@@ -53,8 +53,10 @@ class SeqExpandOpMaker : public framework::OpProtoAndCheckerMaker {
               "(LodTensor)The output of seq_expand op."
               "The lod of output will be as same as input(Y)'s lod.");
     AddComment(R"DOC(
-Expand input(X) according to LOD of input(Y).
+Seq Expand Operator.
 
+This operator expands input(X) according to LOD of input(Y).
+Following are cases to better explain how this works:
 Case 1:
 
 Given 2-level a LoDTensor input(X)

paddle/operators/sequence_concat_op.cc

@@ -47,19 +47,19 @@ class SequenceConcatOpMaker : public framework::OpProtoAndCheckerMaker {
                         framework::OpAttrChecker* op_checker)
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X",
-             "(A vector of LoDTensor), the input is a vector of LoDTensor, "
+             "(vector<LoDTensor>) Input is a vector of LoDTensor, "
              "each of which is a variable-length sequence or nested sequence.")
         .AsDuplicable();
     AddOutput("Out",
-              "(A LoDTensor), the variable-length output of "
+              "(LoDTensor), Variable-length output of "
               "sequence_concat Op.");
     AddAttr<int>("axis",
-                 "(int, default 0)"
-                 "The axis which the inputs will be joined with. "
+                 "(int, default 0) "
+                 "The axis along which the inputs will be joined. "
                  "If axis is 0, the inputs will be joined with LoD index.")
         .SetDefault(0);
     AddAttr<int>("level",
-                 "(int, default 0)"
+                 "(int, default 0) "
                  "The level at which the inputs will be joined. "
                  "If the level is 0, the inputs will be joined at the nested "
                  "sequence level. "
@@ -68,34 +68,38 @@ class SequenceConcatOpMaker : public framework::OpProtoAndCheckerMaker {
                  "The level should be less than the level number of inputs.")
         .SetDefault(0);
     AddComment(R"DOC(
-    The sequence_concat operator concatenates multiple LoDTensors.
-    It only supports sequence (LoD Tensor with level number is 1)
-    or a nested sequence (LoD tensor with level number is 2) as its input.
-    - Case1:
-      If the axis is other than 0(here, axis is 1 and level is 1),
-      each input should have the same LoD information and the LoD
-      information of the output keeps the same as the input.
-
-      LoD(x0) = {{0,2,4}, {0,1,2,3,4}}; Dims(x0) = (4,3,4)
-      LoD(x1) = {{0,2,4}, {0,1,2,3,4}}; Dims(x1) = (4,4,4)
-      LoD(Out) = {{0,2,4}, {0,1,2,3,4}}; Dims(Out) = (4,7,4)
-
-    - Case2:
-      If the axis is 0(here, leve is 0), the inputs are concatenated along
-      time steps, the LoD information of the output need to re-compute.
-
-      LoD(x0) = {{0,2,4}, {0,1,2,3,4}}; Dims(x0) = (4,3,4)
-      LoD(x1) = {{0,3,5}, {0,1,2,3,5}}; Dims(x1) = (5,3,4)
-      LoD(Out) = {{0,5,9}, {0,1,2,3,4,5,6,7,9}}; Dims(Out) = (9,3,4)
-
-    - Case3:
-      If the axis is 0(here, level is 1).
-
-      LoD(x0) = {{0,2,4}, {0,1,2,3,4}}; Dims(x0) = (4,3,4)
-      LoD(x1) = {{0,3,5}, {0,1,3,4,5}}; Dims(x1) = (5,3,4)
-      LoD(Out) = {{0,5,9}, {0,2,5,7,9}}; Dims(Out) = (9,3,4)
-
-    NOTE: The levels of all the inputs should be the same.
+Sequence Concat Operator.
+
+The sequence_concat operator concatenates multiple LoDTensors.
+It supports a sequence (LoD Tensor with level number is 1)
+or a nested sequence (LoD tensor with level number is 2) as its input.
+The following examples explain how the operator works:
+- Case1:
+  If the axis is other than 0(here, axis is 1 and level is 1),
+  each input should have the same LoD information and the LoD
+  information of the output keeps the same as the input.
+
+    LoD(x0) = {{0,2,4}, {0,1,2,3,4}}; Dims(x0) = (4,3,4)
+    LoD(x1) = {{0,2,4}, {0,1,2,3,4}}; Dims(x1) = (4,4,4)
+    LoD(Out) = {{0,2,4}, {0,1,2,3,4}}; Dims(Out) = (4,7,4)
+
+- Case2:
+  If the axis is 0(here, leve is 0), the inputs are concatenated along
+  time steps, the LoD information of the output need to re-compute.
+
+    LoD(x0) = {{0,2,4}, {0,1,2,3,4}}; Dims(x0) = (4,3,4)
+    LoD(x1) = {{0,3,5}, {0,1,2,3,5}}; Dims(x1) = (5,3,4)
+    LoD(Out) = {{0,5,9}, {0,1,2,3,4,5,6,7,9}}; Dims(Out) = (9,3,4)
+
+- Case3:
+  If the axis is 0(here, level is 1).
+
+    LoD(x0) = {{0,2,4}, {0,1,2,3,4}}; Dims(x0) = (4,3,4)
+    LoD(x1) = {{0,3,5}, {0,1,3,4,5}}; Dims(x1) = (5,3,4)
+    LoD(Out) = {{0,5,9}, {0,2,5,7,9}}; Dims(Out) = (9,3,4)
+
+NOTE: The levels of all the inputs should be the same.
+
     )DOC");
   }
 };

paddle/operators/sequence_conv_op.cc

@@ -105,10 +105,10 @@ class SequenceConvOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput(
         "X",
-        "(LoDTensor) the input(X) is a LodTensor, which support "
+        "(LoDTensor) the input(X) is a LodTensor, which supports "
         "variable-time length input sequence. The underlying tensor in "
-        "this LoDTensor is a matrix with shape (T, N), where, T is the "
-        "total time steps in this mini-batch, N is the input_hidden_size.");
+        "this LoDTensor is a matrix with shape (T, N), where T is the "
+        "total time steps in this mini-batch and N is the input_hidden_size.");
     AddInput("PaddingData",
              "(Tensor, optional) the input(PaddingData) is an optional "
              "parameter, and it is learnable. "
@@ -157,14 +157,16 @@ class SequenceConvOpMaker : public framework::OpProtoAndCheckerMaker {
         .GreaterThan(0);
 
     AddComment(R"DOC(
-    SequenceConvOp performs convolution operation on features of
-    contextLength time-steps of each instance.
-    The convolution operation calculates the output based on the input, filter
-    and strides, paddings parameters. The size of each dimension of the
-    parameters is checked in the infer-shape. In order to ensure the equal
-    length of sequence before and after convolution, it is necessary to fill
-    the top and bottom of each sequence according to context_length,
-    context_stride and context_start.
+Sequence Conv Operator.
+
+SequenceConvOp performs convolution operation on features of contextLength
+time-steps of each instance. The convolution operation calculates the output
+based on the input, filter, strides and paddings parameters.
+The size of each dimension of the parameters is checked during infer-shape.
+In order to ensure the equal length of sequence before and after convolution,
+it is necessary to fill the top and bottom of each sequence based on
+context_length, context_stride and context_start.
+
     )DOC");
   }
 };

paddle/operators/sequence_pool_op.cc

@@ -54,33 +54,36 @@ class SequencePoolOpMaker : public framework::OpProtoAndCheckerMaker {
         .SetDefault("AVERAGE")
         .InEnum({"AVERAGE", "SUM", "SQRT", "LAST", "FIRST", "MAX"});
     AddComment(R"DOC(
-    SequencePoolOp pools features of all time-steps of each instance.
-
-    It supports six pooling pooltype:
-    - AVERAGE: Out[i] = average_{for each instance in i-th sequence}{X[i]}
-    - SUM:     Out[i] = sum_{for each instance in i-th sequence}{X[i]}
-    - SQRT:    Out[i] = sum_{for each instance in i-th sequence}{X[i]} 
-                        / sqrt(i-th sequence length)
-    - LAST:    Out[i] = last instance in i-th sequence X[i]
-    - FIRST:   Out[i] = first instance in i-th sequence X[i]
-    - MAX:     Out[i] = max_{for each instance in i-th sequence}{X[i]}
-
-    For a mini-batch of 3 variable-length sentences, containing 2, 3, and 2 time-steps:
-
-    Assume X is a [7,M,N] LoDTensor, and X->lod()[0] = [0, 2, 5, 7], 7=2+3+2.
-    Besides, for the sake of simplicity, we assume M=1 and N=1,
-    and the value of X = [[1, 3], [2, 4, 6], [5, 1]].
-
-    Thus, Out is a [3,1,1] Tensor without LoD infomation.
-    And for different pooltype, the value of Out is as follows:
-
-    - AVERAGE: [2, 4, 3], where 2=(1+3)/2, 4=(2+4+6)/3, 3=(5+1)/2
-    - SUM: [4, 12, 6], where 4=1+3, 12=2+4+6, 6=5+1
-    - SQRT: [2.82, 6.93, 4.24], where 2.82=(1+3)/sqrt(2),
+Sequence Pool Operator.
+
+The SequencePoolOp pools features of all time-steps of each instance.
+It supports six pooling types:
+1. AVERAGE: Out[i] = $$avg(X_i)$$
+2. SUM:     Out[i] = $$\sum_jX_{ij}$$
+3. SQRT:    Out[i] = $$\frac{\sum_jX_{ij}}{\sqrt{len(X_i)}}$$
+4. LAST:    Out[i] = last instance in i-th sequence X[i]
+5. FIRST:   Out[i] = first instance in i-th sequence X[i]
+6. MAX:     Out[i] = $$max(X_i)$$
+
+The following example explains how this works:
+For a mini-batch of 3 variable-length sentences,
+containing 2, 3, and 2 time-steps:
+
+Assume X is a [7,M,N] LoDTensor, and X->lod()[0] = [0, 2, 5, 7], 7=2+3+2.
+Besides, for the sake of simplicity, we assume M=1 and N=1,
+and the value of X = [[1, 3], [2, 4, 6], [5, 1]].
+
+Thus, Out is a [3,1,1] Tensor without LoD infomation.
+And for different pooltype, the value of Out is as follows:
+
+- AVERAGE: [2, 4, 3], where 2=(1+3)/2, 4=(2+4+6)/3, 3=(5+1)/2
+- SUM: [4, 12, 6], where 4=1+3, 12=2+4+6, 6=5+1
+- SQRT: [2.82, 6.93, 4.24], where 2.82=(1+3)/sqrt(2),
            6.93=(2+4+6)/sqrt(3), 4.24=(5+1)/sqrt(2)
-    - MAX: [3, 6, 5], where 3=max(1,3), 6=max(2,4,6), 5=max(5,1)
-    - LAST: [3, 6, 1], where 3=last(1,3), 6=last(2,4,6), 1=last(5,1)
-    - FIRST: [1, 2, 5], where 1=first(1,3), 2=first(2,4,6), 5=first(5,1)
+- MAX: [3, 6, 5], where 3=max(1,3), 6=max(2,4,6), 5=max(5,1)
+- LAST: [3, 6, 1], where 3=last(1,3), 6=last(2,4,6), 1=last(5,1)
+- FIRST: [1, 2, 5], where 1=first(1,3), 2=first(2,4,6), 5=first(5,1)
+
     )DOC");
   }
 };

paddle/operators/sequence_softmax_op.cc

@@ -43,20 +43,24 @@ class SequenceSoftmaxOpMaker : public framework::OpProtoAndCheckerMaker {
               "(LoDTensor) 1-D or 2-D output LoDTensor with the 2-nd dimension "
               "of length 1.");
     AddComment(R"DOC(
-SequenceSoftmaxOp computes softmax activation among all time-steps for each
+Sequence Softmax Operator.
+
+SequenceSoftmaxOp computes the softmax activation among all time-steps for each
 sequence. The dimension of each time-step should be 1. Thus, the shape of
-input Tensor can be either [N, 1] or [N], where N is the sum of all sequences'
-lengths.
+input Tensor can be either [N, 1] or [N], where N is the sum of the length
+of all sequences.
 
-Equation:
+The algorithm works as follows:
     for i-th sequence in a mini-batch:
-        Out(X[lod[i]:lod[i+1]], :) =
-            exp(X[lod[i]:lod[i+1], :]) / sum(exp(X[lod[i]:lod[i+1], :]))
+        $$Out(X[lod[i]:lod[i+1]], :) =
+            \frac{\exp(X[lod[i]:lod[i+1], :])}
+            {\sum(\exp(X[lod[i]:lod[i+1], :]))}$$
 
 For example, for a mini-batch of 3 sequences with variable-length,
 each containing 2, 3, 2 time-steps, the lod of which is [0, 2, 5, 7],
 then softmax will be computed among X[0:2, :], X[2:5, :], X[5:7, :]
 and N turns out to be 7.
+
 )DOC");
   }
 };

paddle/operators/sgd_op.cc

@@ -45,15 +45,17 @@ class SGDOpMaker : public framework::OpProtoAndCheckerMaker {
  public:
   SGDOpMaker(framework::OpProto* proto, framework::OpAttrChecker* op_checker)
       : OpProtoAndCheckerMaker(proto, op_checker) {
-    AddInput("Param", "Input parameter");
-    AddInput("LearningRate", "Learning rate of SGD");
-    AddInput("Grad", "Input gradient");
-    AddOutput("ParamOut", "output parameter");
+    AddInput("Param", "(Tensor) Input parameter");
+    AddInput("LearningRate", "(Tensor) Learning rate of SGD");
+    AddInput("Grad", "(Tensor) Input gradient");
+    AddOutput("ParamOut", "(Tensor) Output parameter");
     AddComment(R"DOC(
 
-Simplest sgd algorithm.
+SGD operator
 
-param_out = param - learning_rate * grad;
+This operator implements one step of the stochastic gradient descent algorithm.
+
+$$param_out = param - learning_rate * grad$$
 
 )DOC");
   }

paddle/operators/sigmoid_cross_entropy_with_logits_op.cc

@@ -107,26 +107,28 @@ class SigmoidCrossEntropyWithLogitsOpMaker
     AddComment(R"DOC(
 SigmoidCrossEntropyWithLogits Operator.
 
-This measures the elementwise probability error in discrete classification tasks
+This measures the element-wise probability error in classification tasks
 in which each class is independent. This can be thought of as predicting labels
-for a data-point that are not mutually exclusive. For example, a news article
-can be about politics, technology or sports at the same time or none of these.
+for a data-point, where labels are not mutually exclusive.
+For example, a news article can be about politics, technology or sports
+at the same time or none of these.
 
 The logistic loss is given as follows:
 
-       loss = -Labels * log(sigmoid(X)) - (1 - Labels) * log(1 - sigmoid(X))
+       $$loss = -Labels * \log(\sigma(X)) - (1 - Labels) * \log(1 - \sigma(X))$$
 
-We know that sigmoid(X) = (1 / (1 + exp(-X))). By substituting this we get
+We know that $$\sigma(X) = (1 / (1 + \exp(-X)))$$. By substituting this we get:
 
-       loss = X - X * Labels + log(1 + exp(-X))
+       $$loss = X - X * Labels + \log(1 + \exp(-X))$$
 
-For stability and to prevent overflow of exp(-X) when X < 0,
-we can reformulate the loss as follows:
+For stability and to prevent overflow of $$\exp(-X)$$ when X < 0,
+we reformulate the loss as follows:
 
-       loss = max(X, 0) - X * Labels + log(1 + exp(-abs(X)))
+       $$loss = \max(X, 0) - X * Labels + \log(1 + \exp(-|X|))$$
 
 Both the input `X` and `Labels` can carry the LoD (Level of Details) information.
 However the output only shares the LoD with input `X`.
+
 )DOC");
   }
 };

paddle/operators/sign_op.cc

@@ -38,9 +38,10 @@ class SignOpMaker : public framework::OpProtoAndCheckerMaker {
       : OpProtoAndCheckerMaker(proto, op_checker) {
     AddInput("X", "(Tensor) Input tensor of sign operator.");
     AddOutput("Out", "(Tensor) Output tensor of sign operator.");
-    AddComment(R"DOC(Sign operator
+    AddComment(R"DOC(
+Sign operator
 
-The equation is: Out = X.sign()
+$$Out = X.sign()$$
 )DOC");
   }
 };

paddle/operators/smooth_l1_loss_op.cc

@@ -77,14 +77,17 @@ class SmoothL1LossOpMaker : public framework::OpProtoAndCheckerMaker {
                       "A float scalar with default value 3.0.")
         .SetDefault(3.0);
     AddComment(R"DOC(
-Compute smooth l1 loss for input and target. The operator take the 1st
-dimension of input as batch size. For each instance, it will compute
-smooth l1 loss element by element first and sum all losses to one value.
-So the output shape is [batch_size, 1].
+Smooth L1 Loss Operator.
+
+This operator computes the smooth l1 loss for input and target.
+The operator takes the first dimension of input as the batch size.
+For each instance, it computes the smooth l1 loss element by element first
+and then sums all the losses. So the resulting output shape
+is [batch_size, 1].
 
 The equation is:
-loss = 0.5 * (sigma * (x-y))^2    if abs(x - y) < 1 / sigma^2
-       abs(x - y) - 0.5 / sigma^2 otherwise
+loss = $$0.5 * (\sigma * (x-y))^2$$   if $$|x - y| < 1 /({\sigma}^2)$$
+       $$\frac{|x - y| - 0.5}{{\sigma}^2}$$ otherwise
 
 )DOC");
   }