Merge pull request #5084 from lcy-seso/crf

Add the LinearChainCrf operator.

paddle/framework/operator.cc

@@ -37,32 +37,32 @@ ExecutionContext::GetEigenDevice<platform::GPUPlace, Eigen::GpuDevice>() const {
 std::string OperatorBase::Input(const std::string& name) const {
   auto& ins = Inputs(name);
   PADDLE_ENFORCE_LE(ins.size(), 1UL,
-                    "Op %s input %s should contain only one variable", type_,
-                    name);
+                    "Operator %s's input %s should contain only one variable.",
+                    type_, name);
   return ins.empty() ? kEmptyVarName : ins[0];
 }
 
 const std::vector<std::string>& OperatorBase::Inputs(
     const std::string& name) const {
   auto it = inputs_.find(name);
-  PADDLE_ENFORCE(it != inputs_.end(), "Op %s do not have input %s", type_,
-                 name);
+  PADDLE_ENFORCE(it != inputs_.end(), "Operator %s does not have the input %s.",
+                 type_, name);
   return it->second;
 }
 
 std::string OperatorBase::Output(const std::string& name) const {
   auto& outs = Outputs(name);
   PADDLE_ENFORCE_LE(outs.size(), 1UL,
-                    "Op %s output %s should contain only one variable", type_,
-                    name);
+                    "Operator %s's output %s should contain only one variable.",
+                    type_, name);
   return outs.empty() ? kEmptyVarName : outs[0];
 }
 
 const std::vector<std::string>& OperatorBase::Outputs(
     const std::string& name) const {
   auto it = outputs_.find(name);
-  PADDLE_ENFORCE(it != outputs_.end(), "Op %s does not have output called %s",
-                 type_, name);
+  PADDLE_ENFORCE(it != outputs_.end(),
+                 "Operator %s does not have an output called %s.", type_, name);
   return it->second;
 }
 

paddle/framework/operator.h

@@ -427,7 +427,8 @@ class OperatorWithKernel : public OperatorBase {
             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 same.", Type());
+                           "DataType of Paddle Op %s must be the same.",
+                           Type());
             data_type = tmp;
           }
         }

paddle/framework/tensor.h

@@ -118,10 +118,12 @@ class Tensor {
                              const platform::DeviceContext& ctx);
 
   /**
-   * @brief   Return the slice of the tensor.
+   * @brief  Return a sub-tensor of the given tensor.
    *
-   * @param[in] begin_idx   The begin index of the slice.
-   * @param[in] end_idx     The end index of the slice.
+   * @param[in] begin_idx   The index of the start row(inclusive) to slice.
+   *                        The index number begins from 0.
+   * @param[in] end_idx     The index of the end row(exclusive) to slice.
+   *                        The index number begins from 0.
    */
   inline Tensor Slice(const int& begin_idx, const int& end_idx) const;
 

paddle/framework/tensor_impl.h

@@ -112,9 +112,10 @@ inline void* Tensor::mutable_data(platform::Place place, std::type_index type) {
   if (holder_ != nullptr) {
     holder_->set_type(type);
   }
-  PADDLE_ENFORCE_GT(numel(), 0,
-                    "Tensor's numel must be larger than zero to call "
-                    "Tensor::mutable_data. Call Tensor::set_dim first.");
+  PADDLE_ENFORCE_GT(
+      numel(), 0,
+      "When calling this method, the Tensor's numel must be larger than zero. "
+      "Please check Tensor::Resize has been called first.");
   int64_t size = numel() * SizeOfType(type);
   /* some versions of boost::variant don't have operator!= */
   if (holder_ == nullptr || !(holder_->place() == place) ||
@@ -229,10 +230,12 @@ inline void Tensor::CopyFromVector(const std::vector<T>& src,
 
 inline Tensor Tensor::Slice(const int& begin_idx, const int& end_idx) const {
   check_memory_size();
-  PADDLE_ENFORCE_GE(begin_idx, 0, "Slice begin index is less than zero.");
-  PADDLE_ENFORCE_LE(end_idx, dims_[0], "Slice end index is out of bound.");
-  PADDLE_ENFORCE_LT(begin_idx, end_idx,
-                    "Begin index must be less than end index.");
+  PADDLE_ENFORCE_GE(begin_idx, 0,
+                    "The start row index must be greater than 0.");
+  PADDLE_ENFORCE_LE(end_idx, dims_[0], "The end row index is out of bound.");
+  PADDLE_ENFORCE_LT(
+      begin_idx, end_idx,
+      "The start row index must be lesser than the end row index.");
 
   if (dims_[0] == 1) {
     return *this;

paddle/gserver/layers/CRFLayer.cpp

@@ -101,8 +101,10 @@ void CRFLayer::backward(const UpdateCallback& callback) {
                               : real(1.0f);
     instanceWeight *= coeff_;
 
+    if (output.grad) {
       MatrixPtr grad = output.grad->subRowMatrix(starts[i], starts[i + 1]);
       grad->add(*crfs_[i].getXGrad(), real(1.0f), instanceWeight);
+    }
     if (needWGrad) {
       weight_->getWGrad()->add(
           *crfs_[i].getWGrad(), real(1.0f), instanceWeight);

paddle/gserver/layers/LinearChainCRF.cpp

@@ -102,7 +102,6 @@ real LinearChainCRF::forward(real* x, int* s, int length) {
 }
 
 void LinearChainCRF::backward(real* x, int* s, int length, bool needWGrad) {
-  MatrixPtr matX = Matrix::create(x, length, numClasses_);
   Matrix::resizeOrCreate(matGrad_, length, numClasses_);
   Matrix::resizeOrCreate(beta_, length, numClasses_);
   real* b = b_->getData();

paddle/operators/cross_entropy_op.cc

@@ -28,8 +28,9 @@ class CrossEntropyOp : public framework::OperatorWithKernel {
 
     auto x_dims = ctx->GetInputDim("X");
     auto label_dims = ctx->GetInputDim("Label");
-    PADDLE_ENFORCE_EQ(x_dims.size(), 2, "Input(X)'s rank should be 2.");
-    PADDLE_ENFORCE_EQ(label_dims.size(), 2, "Input(Label)'s rank should be 2.");
+    PADDLE_ENFORCE_EQ(x_dims.size(), 2UL, "Input(X)'s rank should be 2.");
+    PADDLE_ENFORCE_EQ(label_dims.size(), 2UL,
+                      "Input(Label)'s rank should be 2.");
     PADDLE_ENFORCE_EQ(x_dims[0], label_dims[0],
                       "The 1st dimension of Input(X) and Input(Label) should "
                       "be equal.");
@@ -38,8 +39,8 @@ class CrossEntropyOp : public framework::OperatorWithKernel {
                         "If Attr(soft_label) == true, the 2nd dimension of "
                         "Input(X) and Input(Label) should be equal.");
     } else {
-      PADDLE_ENFORCE_EQ(label_dims[1], 1,
-                        "If Attr(soft_label) == false, the 2nd dimension of "
+      PADDLE_ENFORCE_EQ(label_dims[1], 1UL,
+                        "If Attr(softLabel) == false, the 2nd dimension of "
                         "Input(Label) should be 1.");
     }
 
@@ -48,7 +49,8 @@ class CrossEntropyOp : public framework::OperatorWithKernel {
   }
 
  protected:
-  // CrossEntropy's data type just determined by "X"
+  // Explicitly set that data type of the output of the cross_entropy operator
+  // is determined by its input "X".
   framework::DataType IndicateDataType(
       const framework::ExecutionContext& ctx) const override {
     return framework::ToDataType(ctx.Input<Tensor>("X")->type());

paddle/operators/linear_chain_crf_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/linear_chain_crf_op.h"
+
+namespace paddle {
+namespace operators {
+
+class LinearChainCRFOpMaker : public framework::OpProtoAndCheckerMaker {
+ public:
+  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.");
+    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, "
+        "\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.")
+        .AsIntermediate();
+    AddOutput("TransitionExps",
+              "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 "
+        "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(
+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
+\f$X = (x_1, x_2, ... , x_n)\f$ are structured inputs and
+\f$Y = (y_1, y_2, ... , y_n)\f$ are labels for the inputs.
+
+Linear chain CRF is a special case of CRF that is useful for sequence labeling
+task. Sequence labeling tasks do not assume a lot of conditional
+independences among inputs. The only constraint they impose is that the input
+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.
+
+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
+weights, denoted as \f$a\f$ here.
+- 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,
+denoted as \f$w\f$ here.
+- 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$P(s) = (1/Z) exp(a_{s_1} + b_{s_L}
+                 + \sum_{l=1}^L x_{s_l}
+                 + \sum_{l=2}^L w_{s_{l-1},s_l})\f$
+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
+likelihood of each training sample in a mini-batch.
+
+NOTE:
+1. The feature function for a CRF is made up of the emission features and the
+transition features. The emission feature weights are NOT computed in
+this operator. They MUST be computed first before this operator is called.
+
+2. Because this operator performs global normalization over all possible
+sequences internally, it expects UNSCALED emission feature weights.
+Please do not call this op with the emission feature being output of any
+nonlinear activation.
+
+3. The 2nd dimension of Input(Emission) MUST be equal to the tag number.
+
+)DOC");
+  }
+};
+
+class LinearChainCRFOp : 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->HasInput("Label"), "Input(Label) should be not null.");
+
+    PADDLE_ENFORCE(ctx->HasOutput("Alpha"),
+                   "Output(Alpha) should be not null.");
+    PADDLE_ENFORCE(ctx->HasOutput("EmissionExps"),
+                   "Output(EmissionExps) should be not null.");
+    PADDLE_ENFORCE(ctx->HasOutput("TransitionExps"),
+                   "Output(TransitionExps) should be not null.");
+    PADDLE_ENFORCE(ctx->HasOutput("LogLikelihood"),
+                   "Output(LogLikelihood) 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.");
+
+    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->SetOutputDim("Alpha", emission_dims);
+    ctx->SetOutputDim("EmissionExps", emission_dims);
+    ctx->SetOutputDim("TransitionExps", transition_dims);
+    // TODO(caoying) This is tricky. The 1st dimension of Output(LogLikelihood)
+    // is the sequence number in a mini-batch. The dimension set here should be
+    // resized to its correct size in the function Compute. Fix this once we can
+    // get LoD information in the InferShape interface.
+    ctx->SetOutputDim("LogLikelihood", {emission_dims[0], 1});
+  }
+
+ protected:
+  // Explicitly set that the data type of output of the linear_chain_crf
+  // operator is determined by its input "Emission".
+  framework::DataType IndicateDataType(
+      const framework::ExecutionContext& ctx) const override {
+    return framework::ToDataType(ctx.Input<LoDTensor>("Emission")->type());
+  }
+};
+
+class LinearChainCRFGradOp : public framework::OperatorWithKernel {
+ public:
+  using framework::OperatorWithKernel::OperatorWithKernel;
+
+  void InferShape(framework::InferShapeContext* ctx) const override {
+    PADDLE_ENFORCE(ctx->HasInput("EmissionExps"),
+                   "Input(EmissionExps) should be not null.");
+    PADDLE_ENFORCE(ctx->HasInput("TransitionExps"),
+                   "Input(TransitionExps) should be not null.");
+    PADDLE_ENFORCE(ctx->HasInput(framework::GradVarName("LogLikelihood")),
+                   "Input(LogLikelihood@GRAD) shoudl be not null.");
+
+    auto emission_exps_dims = ctx->GetInputDim("EmissionExps");
+    PADDLE_ENFORCE_EQ(emission_exps_dims.size(), 2UL,
+                      "The Input(EmissionExps) should be a 2-D tensor.");
+    PADDLE_ENFORCE(emission_exps_dims[0],
+                   "An empty mini-batch is not allowed.");
+
+    auto transition_exps_dims = ctx->GetInputDim("TransitionExps");
+    PADDLE_ENFORCE_EQ(transition_exps_dims.size(), 2UL,
+                      "The Input(TransitionExps) should be a 2-D tensor.");
+    PADDLE_ENFORCE_EQ(
+        transition_exps_dims[0] - 2, transition_exps_dims[1],
+        "An invalid dimension for the Input(TransitionExps), which should "
+        "be a 2-D tensor with shape [(D + 2) x D].");
+    PADDLE_ENFORCE_EQ(
+        emission_exps_dims[1], transition_exps_dims[1],
+        "The 2nd dimension of the Input(EmissionExps) and the "
+        "Input(TransitionExps) should be equal to the tag number.");
+
+    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_exps_dims[0], label_dims[0],
+        "The height of Input(EmissionExps) and the height of Input(Label) "
+        "should be the same.");
+
+    if (ctx->HasOutput(framework::GradVarName("Emission"))) {
+      ctx->SetOutputDim(framework::GradVarName("Emission"), emission_exps_dims);
+    }
+    if (ctx->HasOutput(framework::GradVarName("Transition"))) {
+      ctx->SetOutputDim(framework::GradVarName("Transition"),
+                        transition_exps_dims);
+    }
+  }
+
+ protected:
+  // Explicitly set that the data type of output of the linear_chain_crf_grad
+  // operator is determined by its input: gradients of LogLikelihood.
+  framework::DataType IndicateDataType(
+      const framework::ExecutionContext& ctx) const override {
+    return framework::ToDataType(
+        ctx.Input<LoDTensor>(framework::GradVarName("LogLikelihood"))->type());
+  }
+};
+
+}  // namespace operators
+}  // namespace paddle
+
+namespace ops = paddle::operators;
+REGISTER_OP(linear_chain_crf, ops::LinearChainCRFOp, ops::LinearChainCRFOpMaker,
+            linear_chain_crf_grad, ops::LinearChainCRFGradOp);
+REGISTER_OP_CPU_KERNEL(
+    linear_chain_crf,
+    ops::LinearChainCRFOpKernel<paddle::platform::CPUPlace, float>,
+    ops::LinearChainCRFOpKernel<paddle::platform::CPUPlace, double>);
+REGISTER_OP_CPU_KERNEL(
+    linear_chain_crf_grad,
+    ops::LinearChainCRFGradOpKernel<paddle::platform::CPUPlace, float>,
+    ops::LinearChainCRFGradOpKernel<paddle::platform::CPUPlace, double>);

paddle/operators/linear_chain_crf_op.cu

+/* 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/linear_chain_crf_op.h"
+
+namespace ops = paddle::operators;
+
+REGISTER_OP_GPU_KERNEL(
+    linear_chain_crf,
+    ops::LinearChainCRFOpKernel<paddle::platform::GPUPlace, float>,
+    ops::LinearChainCRFOpKernel<paddle::platform::GPUPlace, double>);
+REGISTER_OP_GPU_KERNEL(
+    linear_chain_crf_grad,
+    ops::LinearChainCRFGradOpKernel<paddle::platform::GPUPlace, float>,
+    ops::LinearChainCRFGradOpKernel<paddle::platform::GPUPlace, double>);

paddle/operators/softmax_with_cross_entropy_op.cc

@@ -32,9 +32,9 @@ class SoftmaxWithCrossEntropyOpMaker
     AddInput("Label",
              "(Tensor, default: Tensor<int>), The ground truth which is a 2-D "
              "tensor. "
-             "If softLable is set to 0, Label is a Tensor<int> with shape [N x "
-             "1]. "
-             "If softLable is set to 1, Label is a Tensor<float/double> "
+             "If softLabel is set to false, Label is a Tensor<int> with shape "
+             "[N x 1]."
+             "If softLabel is set to true, Label is a Tensor<float/double> "
              "with shape [N x K].");
     AddOutput(
         "Softmax",
@@ -60,19 +60,23 @@ Because this operators performs a softmax on logits internally, it expects
 unscaled logits. Please do not call this op with the output of softmax operator,
 which will produce incorrect results.
 
-This operators expects mutually exclusive hard labels, each sample in a batch
-is in exactly one class with probabilities 1. Each sample in the batch with one
-and only one label.
+When the attribute softLabel is set false, this operators expects mutually
+exclusive hard labels, each sample in a batch is in exactly one class with
+probabilities 1. Each sample in the batch with one and only one label.
 
 Equation:
 
 1) hard label (one-hot label)
 
-Loss_j = -\text{Logit}_{Label_j} + \log\left(\sum_{i=0}^{K}\exp(\text{Logit}_i)\right), j = 1, ..., K
+Loss_j = \f$ -\text{Logit}_{Label_j} +
+\log\left(\sum_{i=0}^{K}\exp(\text{Logit}_i)\right),
+j = 1, ..., K $\f
 
 2) soft label (a distribution over all classes)
 
-Loss_j = -\sum_{i=0}^{K}\text{Label}_i\left(\text{Logit}_i-\log\left(\sum_{i=0}^{K}\exp(\text{Logit}_i)\right)\right), j = 1,...,K
+Loss_j = \f$ -\sum_{i=0}^{K}\text{Label}_i\left(\text{Logit}_i -
+\log\left(\sum_{i=0}^{K}\exp(\text{Logit}_i)\right)\right),
+j = 1,...,K $\f
 
 )DOC");
   }

python/paddle/v2/framework/tests/test_linear_chain_crf_op.py

+import unittest
+import random
+import numpy as np
+
+from op_test import OpTest
+
+
+class LinearChainCrfForward(object):
+    def __init__(self, seq_start_positions, emission_weights, emission_row_max,
+                 emission_exps, transition_weights, transition_exps, labels):
+        self.tag_num = emission_weights.shape[1]
+        self.seq_num = len(seq_start_positions) - 1
+
+        self.seq_start_positions = seq_start_positions
+        self.labels = labels
+        self.x = emission_weights
+
+        self.x_row_max = emission_row_max
+        self.x_exps = emission_exps
+
+        # unnormalized logits of the transition weights for the start mark.
+        self.a = transition_weights[0, :]
+        self.a_exps = transition_exps[0, :]
+        # unnormalized logits of the transition weights for the end mark.
+        self.b = transition_weights[1, :]
+        self.b_exps = transition_exps[1, :]
+        # unnormalized logits of the transition weights for all the other tags.
+        self.w = transition_weights[2:, :]
+        self.w_exps = transition_exps[2:, :]
+
+        # The output of linear chain crf operator.
+        # alpha is a memo table in dynamic programming to caculate
+        # nomalization factor.
+        self.alpha = np.zeros(
+            (seq_start_positions[-1], self.tag_num), dtype="float64")
+        self.log_likelihood = np.zeros((self.seq_num, 1))
+
+    def _l1_norm(self, x):
+        s = np.sum(x)
+        x /= s
+        return s
+
+    def _forward_a_sequence(self, x, x_row_max, x_exps, label, alpha):
+        seq_len = x_row_max.shape[0]
+        log_likelihood = 0.
+
+        for i in range(self.tag_num):
+            alpha[0, i] = self.a_exps[i] * x_exps[0, i]
+        log_likelihood = -x_row_max[0] - np.log(self._l1_norm(alpha[0, :]))
+
+        # calculate the unnormalized logits of the normalization factor.
+        for k in range(1, seq_len):
+            for i in range(self.tag_num):
+                s = 0.
+                for j in range(self.tag_num):
+                    s += alpha[k - 1, j] * self.w_exps[j, i]
+                alpha[k, i] = x_exps[k, i] * s
+            log_likelihood -= x_row_max[k] + np.log(self._l1_norm(alpha[k, :]))
+        s = 0.
+        for i in range(self.tag_num):
+            s += alpha[-1, i] * self.b_exps[i]
+        log_likelihood -= np.log(s)
+
+        # calculate the nominator part.
+        log_likelihood += (
+            self.a[label[0]] + x[0, label[0]] + self.b[label[-1]])
+
+        for k in range(1, seq_len):
+            log_likelihood += (x[k, label[k]] + self.w[label[k - 1], label[k]])
+        return -log_likelihood
+
+    def crf_forward_compute(self):
+        for i in range(self.seq_num):
+            start = self.seq_start_positions[i]
+            end = self.seq_start_positions[i + 1]
+
+            self.log_likelihood[i] = self._forward_a_sequence(
+                self.x[start:end, :], self.x_row_max[start:end, :],
+                self.x_exps[start:end, :], self.labels[start:end, :],
+                self.alpha[start:end, :])
+        return self.alpha, self.log_likelihood
+
+
+class TestLinearChainCrfOp(OpTest):
+    def set_test_data(self):
+        # TODO(caoying) Fix the unittest by: add the boundary cases when
+        # sequence lengths are 1, 2, and 3.
+
+        SEQ_NUM = 3
+        TAG_NUM = 17
+        MAX_SEQ_LEN = 5
+
+        # the linear_chain_crf operator only supports sequence (LoD level = 1)
+        lod = [[0]]
+        for i in range(SEQ_NUM):
+            lod[-1].append(lod[-1][-1] + random.randint(1, MAX_SEQ_LEN))
+        emission = np.random.uniform(-1, 1,
+                                     [lod[-1][-1], TAG_NUM]).astype("float64")
+        emission_row_max = np.amax(emission, axis=1, keepdims=True)
+        emission_exps = np.exp(emission - emission_row_max)
+
+        transition = np.random.uniform(-0.5, 0.5,
+                                       [TAG_NUM + 2, TAG_NUM]).astype("float64")
+        transition_exps = np.exp(transition)
+
+        labels = np.random.randint(
+            low=0, high=TAG_NUM, size=(lod[-1][-1], 1), dtype="int32")
+
+        self.inputs = {
+            "Emission": (emission, lod),
+            "Transition": transition,
+            "Label": (labels, lod)
+        }
+        crf = LinearChainCrfForward(lod[0], emission, emission_row_max,
+                                    emission_exps, transition, transition_exps,
+                                    labels)
+        alpha, log_likelihood = crf.crf_forward_compute()
+
+        self.outputs = {
+            "Alpha": alpha,
+            "EmissionExps": emission_exps,
+            "TransitionExps": transition_exps,
+            "LogLikelihood": log_likelihood
+        }
+
+    def setUp(self):
+        self.op_type = "linear_chain_crf"
+        self.set_test_data()
+
+    def test_check_output(self):
+        self.check_output()
+
+    def test_check_grad(self):
+        self.check_grad(["Emission", "Transition"], "LogLikelihood")
+
+    def test_check_grad_ignore_transition(self):
+        self.check_grad(
+            ["Emission"], "LogLikelihood", no_grad_set=set("Transition"))
+
+
+if __name__ == "__main__":
+    unittest.main()