diff --git a/paddle/fluid/imperative/reducer.cc b/paddle/fluid/imperative/reducer.cc
index 3f0703f05a80a523cb2818c2104943f010b15191..54a2b647d427602e0bf533a82f6909bb80746dbc 100644
--- a/paddle/fluid/imperative/reducer.cc
+++ b/paddle/fluid/imperative/reducer.cc
@@ -20,47 +20,98 @@ namespace imperative {
 #if defined(PADDLE_WITH_NCCL)
 std::shared_ptr<Reducer> Reducer::s_instance_ = NULL;
 
+// context is used to select the stream for concat
+void Group::ConcatTensors(const platform::CUDADeviceContext &context) {
+  switch (dtype_) {
+    case framework::proto::VarType::FP16:
+      ConcatTensorsForAllReduce<platform::float16>(context, dense_tensors_,
+                                                   &dense_contents_);
+      break;
+    case framework::proto::VarType::FP32:
+      ConcatTensorsForAllReduce<float>(context, dense_tensors_,
+                                       &dense_contents_);
+      break;
+    case framework::proto::VarType::FP64:
+      ConcatTensorsForAllReduce<double>(context, dense_tensors_,
+                                        &dense_contents_);
+      break;
+    default:
+      PADDLE_THROW(platform::errors::Unimplemented(
+          "Data type (%s) is not supported when it concats tensors for "
+          "allreduce.",
+          framework::DataTypeToString(dtype_)));
+  }
+}
+
+// context is used to select the stream for split
+void Group::SplitTensors(const platform::CUDADeviceContext &context) {
+  switch (dtype_) {
+    case framework::proto::VarType::FP16:
+      SplitTensorsForAllReduce<platform::float16>(context, &dense_contents_,
+                                                  &dense_tensors_);
+      break;
+    case framework::proto::VarType::FP32:
+      SplitTensorsForAllReduce<float>(context, &dense_contents_,
+                                      &dense_tensors_);
+      break;
+    case framework::proto::VarType::FP64:
+      SplitTensorsForAllReduce<double>(context, &dense_contents_,
+                                       &dense_tensors_);
+      break;
+    default:
+      PADDLE_THROW(platform::errors::Unimplemented(
+          "Data type (%s) is not supported when it splits tensors for "
+          "allreduce.",
+          framework::DataTypeToString(dtype_)));
+  }
+}
+
+std::ostream &operator<<(std::ostream &out, const Group &group) {
+  const auto &vars = group.variable_indices_;
+  out << "numul: " << group.all_length_ << " ;is_sparse: " << group.is_sparse_
+      << " ;var number: " << vars.size() << "\n";
+  auto begin = vars.begin();
+  auto end = vars.end();
+  out << "[";
+  for (int i = 0; begin != end && i < 100; ++i, ++begin) {
+    if (i > 0) out << ' ';
+    out << *begin;
+  }
+  if (begin != end) {
+    out << " ...";
+  }
+  out << "]\n";
+  return out;
+}
+
 Reducer::Reducer(const std::vector<std::shared_ptr<imperative::VarBase>> &vars,
                  const std::vector<std::vector<size_t>> &group_indices,
                  const std::vector<bool> &is_sparse_gradient,
-                 std::shared_ptr<imperative::ParallelContext> parallel_ctx)
+                 std::shared_ptr<imperative::ParallelContext> parallel_ctx,
+                 const std::vector<size_t> &group_size_limits)
     : vars_(vars),
       group_indices_(group_indices),
       is_sparse_gradient_(is_sparse_gradient),
-      parallel_ctx_(parallel_ctx) {
+      parallel_ctx_(parallel_ctx),
+      group_size_limits_(group_size_limits) {
   VLOG(3) << "Start construct the Reducer ...";
   // initialize groups
   InitializeGroups(group_indices);
-
-  {
-    for (size_t group_index = 0; group_index < group_indices.size();
-         ++group_index) {
-      for (size_t var_index = 0; var_index < group_indices[group_index].size();
-           ++var_index) {
-        size_t global_var_index = group_indices[group_index][var_index];
-        const auto variable_index = VariableIndex{
-            .group_index = group_index, .inside_group_index = var_index,
-        };
-        VLOG(3) << "add hook for var[" << vars_[global_var_index]->GradVarName()
-                << "], it's in group [" << group_index << "]";
-        vars_[global_var_index]->SharedVar()->AddGradVarLeafBackwardHook(
-            std::unique_ptr<LambdaGradAccumulatorPostHook>(
-                new LambdaGradAccumulatorPostHook([=](VariableWrapper *grad) {
-                  this->AddDistHook(grad, variable_index);
-                })));
-      }
-    }
+  for (size_t global_var_index = 0; global_var_index < vars_.size();
+       ++global_var_index) {
+    vars_[global_var_index]->SharedVar()->AddGradVarLeafBackwardHook(
+        std::unique_ptr<LambdaGradAccumulatorPostHook>(
+            new LambdaGradAccumulatorPostHook([=](VariableWrapper *grad) {
+              this->AddDistHook(grad, global_var_index);
+            })));
   }
-
+  // create streams
   compute_stream_ = static_cast<platform::CUDADeviceContext *>(
                         platform::DeviceContextPool::Instance().Get(place_))
                         ->stream();
   comm_stream_ = platform::NCCLCommContext::Instance().Get(0, place_)->stream();
-  events_.resize(group_indices.size());
-  for (auto &event : events_) {
-    event = platform::CudaEventResourcePool::Instance().New(
-        BOOST_GET_CONST(platform::CUDAPlace, place_).device);
-  }
+  // create events
+  CreateGroupEvents(group_indices.size());
   comm_enent_ = platform::CudaEventResourcePool::Instance().New(
       BOOST_GET_CONST(platform::CUDAPlace, place_).device);
 
@@ -76,7 +127,20 @@ void Reducer::ReleaseReducer() {
   comm_enent_.reset();
 }
 
-int64_t Reducer::InitializeDenseGroups(
+void Reducer::CreateGroupEvents(int group_num) {
+  // release old events
+  for (auto &event : events_) {
+    event.reset();
+  }
+  events_.clear();
+  events_.resize(group_num);
+  for (auto &event : events_) {
+    event = platform::CudaEventResourcePool::Instance().New(
+        BOOST_GET_CONST(platform::CUDAPlace, place_).device);
+  }
+}
+
+void Reducer::InitializeDenseGroups(
     const std::vector<size_t> &variable_indices_, Group *p_group) {
   int64_t all_length = 0;
   for (size_t index = 0; index < variable_indices_.size(); ++index) {
@@ -85,18 +149,18 @@ int64_t Reducer::InitializeDenseGroups(
     const auto var_name = var->Name();
     PADDLE_ENFORCE_EQ(is_sparse_gradient_[variable_index], false,
                       platform::errors::PreconditionNotMet(
-                          "Tensor `%s`'s GRAD must be LoDTensor, but received "
+                          "Tensor %s's GRAD must be LoDTensor, but received "
                           "GRAD is SelectedRows",
                           var_name));
 
     auto lod_tensor = var->MutableVar()->GetMutable<framework::LoDTensor>();
     PADDLE_ENFORCE_EQ(lod_tensor->IsInitialized(), true,
                       platform::errors::PreconditionNotMet(
-                          "Tensor `%s` is not initialized.", var_name));
+                          "Tensor %s is not initialized.", var_name));
     auto size = lod_tensor->numel();
     PADDLE_ENFORCE_GT(
         size, 0, platform::errors::PreconditionNotMet(
-                     "The number of tensor `%s`'s elements is 0.", var_name));
+                     "The number of tensor %s's elements is 0.", var_name));
     all_length += size;
 
     p_group->length_.push_back(size);
@@ -124,7 +188,7 @@ int64_t Reducer::InitializeDenseGroups(
       place_ = place;
     }
   }
-  return all_length;
+  p_group->all_length_ = all_length;
 }
 
 // Each parameter will be initialized according to the group information.
@@ -137,6 +201,8 @@ void Reducer::InitializeGroups(
   // clear the group
   groups_.clear();
   groups_.reserve(group_indices.size());
+  variable_locators_.clear();
+  variable_locators_.resize(vars_.size());
 
   auto group_nums = group_indices.size();
   for (size_t group_index = 0; group_index < group_nums; ++group_index) {
@@ -144,10 +210,8 @@ void Reducer::InitializeGroups(
     PADDLE_ENFORCE_GT(
         variable_indices_.size(), 0,
         platform::errors::PreconditionNotMet(
-            "The number of group_index[`%d`]'s elements is 0.", group_index));
+            "The number of group[%d]'s elements is 0.", group_index));
     Group group;
-    group.variable_indices_ = variable_indices_;
-    int64_t all_length = 0;
 
     // It's just for check the sparse or dense
     auto first_varbase = vars_[variable_indices_.front()];
@@ -159,17 +223,27 @@ void Reducer::InitializeGroups(
       group.is_sparse_ = true;
     } else {
       // process the dense gradient.
-      all_length = InitializeDenseGroups(variable_indices_, &group);
+      InitializeDenseGroups(variable_indices_, &group);
       // Alloc the continuous space
       auto tensor = group.dense_contents_.GetMutable<framework::LoDTensor>();
-      tensor->Resize(framework::make_ddim({all_length}))
+      tensor->Resize(framework::make_ddim({group.all_length_}))
           .mutable_data(place_, group.dtype_);
     }
-    // Debug Message For Reducer
-    VLOG(3) << "the groups_[" << group_index << "] basic message:";
-    VLOG(3) << "numul: " << all_length << " ;is_sparse: " << group.is_sparse_
-            << " ;var number: " << group.variable_indices_.size();
+
+    // map variables to this group by VariableLocator
+    size_t inside_group_index = 0;
+    for (const auto var_index : group_indices[group_index]) {
+      variable_locators_[var_index] = VariableLocator{
+          .group_index = group_index,
+          .inside_group_index = inside_group_index++,
+      };
+    }
+    group.variable_indices_ = std::move(variable_indices_);
     groups_.emplace_back(std::move(group));
+
+    // Debug Message For Reducer
+    VLOG(3) << "The Group[" << group_index << "]:";
+    VLOG(3) << groups_.back();
   }
 }
 
@@ -192,11 +266,16 @@ void Reducer::PrepareForBackward() {
 // counter is 0, it means that allreduce can be emitted, and
 // concat + allreduce + split is emitted in turn according to next_group_.
 // 3, FinalizeBackward: after the end, synchronize each stream.
-void Reducer::AddDistHook(VariableWrapper *var_warpper,
-                          const VariableIndex &var_index) {
-  auto group_index = var_index.group_index;
+void Reducer::AddDistHook(VariableWrapper *var_warpper, size_t var_index) {
+  const auto &var_locator = variable_locators_[var_index];
+  auto group_index = var_locator.group_index;
   auto &group = groups_[group_index];
 
+  if (!has_rebuilt_group_) {
+    rebuild_vars_.push_back(vars_[var_index]);
+    rebuild_var_indices_.push_back(var_index);
+  }
+
   if (!group.is_sparse_) {
     // Only dense_contents_ need memory copy
     MarkVariableReady(var_index, var_warpper);
@@ -211,21 +290,22 @@ void Reducer::AddDistHook(VariableWrapper *var_warpper,
   }
 }
 
-void Reducer::MarkVariableReady(const VariableIndex &var_index,
+void Reducer::MarkVariableReady(size_t var_index,
                                 VariableWrapper *var_warpper) {
-  auto group_index = var_index.group_index;
-  auto variable_index = var_index.inside_group_index;
+  const auto &var_locator = variable_locators_[var_index];
+  auto group_index = var_locator.group_index;
+  auto inside_group_index = var_locator.inside_group_index;
   auto &group = groups_[group_index];
-  auto length = group.length_[variable_index];
+  auto length = group.length_[inside_group_index];
 
   auto tensor = var_warpper->MutableVar()->GetMutable<framework::LoDTensor>();
-  group.dense_tensors_[variable_index].ShareDataWith(*tensor).Resize(
+  group.dense_tensors_[inside_group_index].ShareDataWith(*tensor).Resize(
       {static_cast<int64_t>(length)});
 }
 
 void Reducer::MarkGroupReady(size_t group_index) {
   if (group_index > next_group_) {
-    VLOG(3) << "Maybe it need adjust the order of group";
+    VLOG(3) << "It will adjust the order of group in next batch automatically";
     return;
   }
 
@@ -257,10 +337,31 @@ void Reducer::MarkGroupReady(size_t group_index) {
   }
 }
 
+std::vector<std::vector<size_t>> Reducer::RebuildGruops() {
+  std::reverse(rebuild_vars_.begin(), rebuild_vars_.end());
+  std::reverse(rebuild_var_indices_.begin(), rebuild_var_indices_.end());
+  auto rebuild_group_indices =
+      AssignGroupBySize(rebuild_vars_, is_sparse_gradient_, group_size_limits_,
+                        rebuild_var_indices_);
+  has_rebuilt_group_ = true;
+  rebuild_vars_.clear();
+  rebuild_var_indices_.clear();
+  std::reverse(rebuild_group_indices.begin(), rebuild_group_indices.end());
+  return rebuild_group_indices;
+}
+
 void Reducer::FinalizeBackward() {
   PADDLE_ENFORCE_CUDA_SUCCESS(cudaEventRecord(comm_enent_.get(), comm_stream_));
   PADDLE_ENFORCE_CUDA_SUCCESS(
       cudaStreamWaitEvent(compute_stream_, comm_enent_.get(), 0));
+  if (!has_rebuilt_group_) {
+    VLOG(3) << "Start rebuilding the groups";
+    auto rebuild_group_indices = RebuildGruops();
+    auto rebuild_group_number = rebuild_group_indices.size();
+    group_indices_ = std::move(rebuild_group_indices);
+    CreateGroupEvents(rebuild_group_number);
+    InitializeGroups(group_indices_);
+  }
   VLOG(3) << "In the batch, Reducer is finished...";
 }
 
@@ -274,12 +375,28 @@ void Reducer::FinalizeBackward() {
 std::vector<std::vector<size_t>> AssignGroupBySize(
     const std::vector<std::shared_ptr<imperative::VarBase>> &vars,
     const std::vector<bool> &is_sparse_gradient,
-    const std::vector<size_t> &group_size_limits) {
+    const std::vector<size_t> &group_size_limits,
+    const std::vector<int64_t> &tensor_indices) {
   PADDLE_ENFORCE_EQ(vars.size(), is_sparse_gradient.size(),
                     platform::errors::PreconditionNotMet(
                         "vars len must be equal to is_sparse_gradient len, but "
                         "[%lu] != [%lu]",
                         vars.size(), is_sparse_gradient.size()));
+  auto check_perm = [](const std::vector<int64_t> &x) -> bool {
+    size_t len = x.size();
+    std::vector<size_t> cnt(len, 0);
+    for (size_t i = 0; i < len; ++i) {
+      if (x[i] >= static_cast<int64_t>(len) || x[i] < 0 || cnt[x[i]]) {
+        return false;
+      }
+      cnt[x[i]]++;
+    }
+    return true;
+  };
+  PADDLE_ENFORCE_EQ(true, check_perm(tensor_indices),
+                    platform::errors::PreconditionNotMet(
+                        "tensor_indices must be a permutation from 0 to %lu",
+                        tensor_indices.size()));
   // the return vector
   std::vector<std::vector<size_t>> res;
 
@@ -294,9 +411,15 @@ std::vector<std::vector<size_t>> AssignGroupBySize(
 
   for (size_t i = 0; i < vars.size(); ++i) {
     const auto &var = vars[i];
-    if (is_sparse_gradient[i]) {
+
+    size_t tensor_real_index = i;
+    if (!tensor_indices.empty()) {
+      tensor_real_index = tensor_indices[i];
+    }
+
+    if (is_sparse_gradient[tensor_real_index]) {
       // we keep sparse var a single group
-      res.push_back({i});
+      res.push_back({tensor_real_index});
       continue;
     }
 
@@ -313,7 +436,7 @@ std::vector<std::vector<size_t>> AssignGroupBySize(
               << " is not tensor or selected_rows, so skip it";
       continue;
     }
-    group_info.first.push_back(i);
+    group_info.first.push_back(tensor_real_index);
     group_info.second += framework::SizeOfType(var_dtype) * var_size;
 
     if (group_limit_index.find(var_dtype_str) == group_limit_index.end()) {
@@ -344,10 +467,12 @@ std::vector<std::vector<size_t>> AssignGroupBySize(
         platform::errors::PreconditionNotMet(
             "AssignGroupBySize construct empty group, please check."));
   }
-  std::sort(res.begin(), res.end(),
-            [](const std::vector<size_t> &x, const std::vector<size_t> &y) {
-              return x.front() < y.front();
-            });
+  if (tensor_indices.empty()) {
+    std::sort(res.begin(), res.end(),
+              [](const std::vector<size_t> &x, const std::vector<size_t> &y) {
+                return x.front() < y.front();
+              });
+  }
   return res;
 }
 #endif
diff --git a/paddle/fluid/imperative/reducer.h b/paddle/fluid/imperative/reducer.h
index 5e38f8abb182811ff5428f38976993fd88e78e0a..3e65685d5c26252d5625bf474cd9b61a113bca0d 100644
--- a/paddle/fluid/imperative/reducer.h
+++ b/paddle/fluid/imperative/reducer.h
@@ -86,6 +86,8 @@ class Group {
   std::vector<framework::Tensor> dense_tensors_;
 
   std::vector<size_t> length_;
+
+  int64_t all_length_{0};
   // Global indices of participating variables in the group
   std::vector<size_t> variable_indices_;
 
@@ -97,53 +99,15 @@ class Group {
   framework::proto::VarType::Type dtype_;
 
   // context is used to select the stream for concat
-  void ConcatTensors(const platform::CUDADeviceContext& context) {
-    switch (dtype_) {
-      case framework::proto::VarType::FP16:
-        ConcatTensorsForAllReduce<platform::float16>(context, dense_tensors_,
-                                                     &dense_contents_);
-        break;
-      case framework::proto::VarType::FP32:
-        ConcatTensorsForAllReduce<float>(context, dense_tensors_,
-                                         &dense_contents_);
-        break;
-      case framework::proto::VarType::FP64:
-        ConcatTensorsForAllReduce<double>(context, dense_tensors_,
-                                          &dense_contents_);
-        break;
-      default:
-        PADDLE_THROW(platform::errors::Unimplemented(
-            "Data type (%s) is not supported when it concats tensors for "
-            "allreduce.",
-            framework::DataTypeToString(dtype_)));
-    }
-  }
+  void ConcatTensors(const platform::CUDADeviceContext& context);
 
   // context is used to select the stream for split
-  void SplitTensors(const platform::CUDADeviceContext& context) {
-    switch (dtype_) {
-      case framework::proto::VarType::FP16:
-        SplitTensorsForAllReduce<platform::float16>(context, &dense_contents_,
-                                                    &dense_tensors_);
-        break;
-      case framework::proto::VarType::FP32:
-        SplitTensorsForAllReduce<float>(context, &dense_contents_,
-                                        &dense_tensors_);
-        break;
-      case framework::proto::VarType::FP64:
-        SplitTensorsForAllReduce<double>(context, &dense_contents_,
-                                         &dense_tensors_);
-        break;
-      default:
-        PADDLE_THROW(platform::errors::Unimplemented(
-            "Data type (%s) is not supported when it splits tensors for "
-            "allreduce.",
-            framework::DataTypeToString(dtype_)));
-    }
-  }
+  void SplitTensors(const platform::CUDADeviceContext& context);
+
+  friend std::ostream& operator<<(std::ostream&, const Group&);
 };
 
-struct VariableIndex {
+struct VariableLocator {
   // record the index in groups_
   size_t group_index;
   size_t inside_group_index;
@@ -155,22 +119,21 @@ class Reducer {
       const std::vector<std::shared_ptr<imperative::VarBase>>& vars,
       const std::vector<std::vector<size_t>>& group_indices,
       const std::vector<bool>& is_sparse_gradient,
-      std::shared_ptr<imperative::ParallelContext> parallel_ctx);
+      std::shared_ptr<imperative::ParallelContext> parallel_ctx,
+      const std::vector<size_t>& group_size_limits);
 
   virtual ~Reducer() {}
 
   void InitializeGroups(const std::vector<std::vector<size_t>>& group_indices);
 
-  int64_t InitializeDenseGroups(const std::vector<size_t>& variable_indices_,
-                                Group* p_group);
+  void InitializeDenseGroups(const std::vector<size_t>& variable_indices_,
+                             Group* p_group);
 
   void PrepareForBackward();
 
-  void AddDistHook(VariableWrapper* var_warpper,
-                   const VariableIndex& var_index);
+  void AddDistHook(VariableWrapper* var_warpper, size_t var_index);
 
-  void MarkVariableReady(const VariableIndex& var_index,
-                         VariableWrapper* var_warpper);
+  void MarkVariableReady(size_t var_index, VariableWrapper* var_warpper);
 
   void MarkGroupReady(size_t group_index);
 
@@ -178,15 +141,21 @@ class Reducer {
 
   void ReleaseReducer();
 
+  std::vector<std::vector<size_t>> RebuildGruops();
+
+  void CreateGroupEvents(int group_num);
+
   // Reducer Singleton
   static std::shared_ptr<Reducer> SetInstance(
       const std::vector<std::shared_ptr<imperative::VarBase>>& vars,
       const std::vector<std::vector<size_t>>& group_indices,
       const std::vector<bool>& is_sparse_gradient,
-      std::shared_ptr<imperative::ParallelContext> parallel_ctx) {
+      std::shared_ptr<imperative::ParallelContext> parallel_ctx,
+      const std::vector<size_t>& group_size_limits) {
     if (NULL == s_instance_) {
       s_instance_.reset(new paddle::imperative::Reducer(
-          vars, group_indices, is_sparse_gradient, parallel_ctx));
+          vars, group_indices, is_sparse_gradient, parallel_ctx,
+          group_size_limits));
     }
     return s_instance_;
   }
@@ -208,17 +177,26 @@ class Reducer {
   std::once_flag once_flag_;
   std::vector<bool> is_sparse_gradient_;
   std::shared_ptr<imperative::ParallelContext> parallel_ctx_;
+  std::vector<VariableLocator> variable_locators_;
 
+  // Following variables are to help sync stream
   std::vector<std::shared_ptr<platform::CudaEventObject>> events_;
   std::shared_ptr<platform::CudaEventObject> comm_enent_;
   cudaStream_t compute_stream_;
   cudaStream_t comm_stream_;
+
+  // Following variables are to help rebuild group
+  bool has_rebuilt_group_{false};
+  std::vector<std::shared_ptr<imperative::VarBase>> rebuild_vars_;
+  std::vector<int64_t> rebuild_var_indices_;
+  const std::vector<size_t> group_size_limits_;
 };
 
 std::vector<std::vector<size_t>> AssignGroupBySize(
     const std::vector<std::shared_ptr<imperative::VarBase>>& tensors,
     const std::vector<bool>& is_sparse_gradient,
-    const std::vector<size_t>& group_size_limits);
+    const std::vector<size_t>& group_size_limits,
+    const std::vector<int64_t>& tensor_indices = {});
 #endif
 
 }  // namespace imperative
diff --git a/paddle/fluid/imperative/tests/CMakeLists.txt b/paddle/fluid/imperative/tests/CMakeLists.txt
index 782f6dad58d46eb539186e331108c74ddb728ac9..b236ece541e820d0b230a9176a52be28c7b789c1 100644
--- a/paddle/fluid/imperative/tests/CMakeLists.txt
+++ b/paddle/fluid/imperative/tests/CMakeLists.txt
@@ -12,3 +12,7 @@ cc_test(test_layer SRCS test_layer.cc DEPS layer proto_desc operator op_registry
 cc_test(test_prepare_op SRCS test_prepare_op.cc DEPS prepared_operator op_info split_op layer concat_and_split activation_op place)
 cc_test(test_tracer SRCS test_tracer.cc DEPS tracer layer proto_desc operator op_registry variable_helper mul_op reduce_sum_op elementwise_add_op memcpy)
 cc_test(test_hooks SRCS test_hooks.cc DEPS tracer basic_engine layer proto_desc operator op_registry variable_helper mul_op elementwise_add_op memcpy)
+
+if (WITH_NCCL)
+cc_test(test_group SRCS test_group.cc DEPS reducer concat_and_split memcpy)
+endif()
diff --git a/paddle/fluid/imperative/tests/test_group.cc b/paddle/fluid/imperative/tests/test_group.cc
new file mode 100644
index 0000000000000000000000000000000000000000..2e967d296d84436a1a05b6414671352e9013285f
--- /dev/null
+++ b/paddle/fluid/imperative/tests/test_group.cc
@@ -0,0 +1,66 @@
+// Copyright (c) 2020 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 <memory>
+#include <ostream>
+#include <sstream>
+#include <string>
+
+#include "glog/logging.h"
+#include "gtest/gtest.h"
+
+#if defined(PADDLE_WITH_NCCL)
+#include "paddle/fluid/imperative/reducer.h"
+#endif
+
+namespace paddle {
+namespace imperative {
+
+#if defined(PADDLE_WITH_NCCL)
+TEST(TestGroup, TestPrintGroupMessage) {
+  Group group;
+  std::stringstream stream1, stream2;
+  stream1 << group;
+  ASSERT_STREQ(stream1.str().c_str(),
+               "numul: 0 ;is_sparse: 0 ;var number: 0\n[]\n");
+
+  std::vector<size_t> vars;
+  size_t vars_num = 102;
+  for (size_t i = 0; i < vars_num; ++i) {
+    vars.push_back(i);
+  }
+  group.variable_indices_ = vars;
+  group.all_length_ = 102;
+  group.is_sparse_ = false;
+
+  std::string head = "numul: 102 ;is_sparse: 0 ;var number: 102\n";
+  head = head + "[";
+  auto begin = vars.begin();
+  auto end = vars.end();
+  for (int i = 0; begin != end && i < 100; ++i, ++begin) {
+    if (i > 0) head += ' ';
+    head += std::to_string(*begin);
+  }
+  if (begin != end) {
+    head += " ...";
+  }
+  head += "]\n";
+  stream2 << group;
+  ASSERT_STREQ(stream2.str().c_str(), head.c_str());
+}
+
+#endif
+
+}  // namespace imperative
+}  // namespace paddle
diff --git a/paddle/fluid/operators/gather.cu.h b/paddle/fluid/operators/gather.cu.h
index 16864f28baaf91d548d611ef198bd8598fe8960a..94fe45dac0ce782d6e8f81c737de10b5aefdaaa5 100644
--- a/paddle/fluid/operators/gather.cu.h
+++ b/paddle/fluid/operators/gather.cu.h
@@ -53,7 +53,13 @@ __global__ void GatherNdCUDAKernel(const T* input, const int* input_dims,
     int64_t temp = slice_size;
     for (int64_t j = end_size - 1; j >= 0; --j) {
       auto index_value = indices[indices_i * end_size + j];
-      assert(index_value >= 0 && index_value < input_dims[j]);
+      PADDLE_ENFORCE(
+          index_value >= 0 && index_value < input_dims[j],
+          "The index is out of bounds, "
+          "please check whether the dimensions of index and "
+          "input meet the requirements. It should "
+          "be less than [%d] and greater or equal to 0, but received [%d]",
+          input_dims[j], index_value);
       gather_i += (index_value * temp);
       temp *= input_dims[j];
     }
diff --git a/paddle/fluid/operators/matmul_v2_op.h b/paddle/fluid/operators/matmul_v2_op.h
index 2fa1ebdeecf7cc684113ec7b50e66409e025cbb3..129ea7c156d0fcd2daf5f250eea44bf47a81f442 100644
--- a/paddle/fluid/operators/matmul_v2_op.h
+++ b/paddle/fluid/operators/matmul_v2_op.h
@@ -44,7 +44,6 @@ template <typename DeviceContext, typename T>
 void ReduceSumForMatmulGrad(const Tensor* input, Tensor* output,
                             const std::vector<int>& reduce_dims,
                             const paddle::framework::ExecutionContext& ctx) {
-  if (reduce_dims.empty()) return;
 #ifdef __NVCC__
   auto stream = ctx.cuda_device_context().stream();
   TensorReduce<T, T, cub::Sum, IdentityFunctor<T>>(
@@ -573,47 +572,48 @@ class MatMulV2GradKernel : public framework::OpKernel<T> {
       // So we should avoid the case in reality.
       VLOG(3) << "It need cost much time to reduce sum for the broadcast and "
                  "wastes the memory. So we should avoid the case in reality";
+      Tensor dx_help, dy_help;
       if (transpose_x) {
         if (transpose_y) {
           // X'Y': dA = Y'G', dB = G'X'
           if (dx)
-            MatMulFunction<DeviceContext, T>(&y, &dout, y_dims, dout_dims, dx,
-                                             true, true, ctx);
+            MatMulFunction<DeviceContext, T>(&y, &dout, y_dims, dout_dims,
+                                             &dx_help, true, true, ctx);
           if (dy)
-            MatMulFunction<DeviceContext, T>(&dout, &x, dout_dims, x_dims, dy,
-                                             true, true, ctx);
+            MatMulFunction<DeviceContext, T>(&dout, &x, dout_dims, x_dims,
+                                             &dy_help, true, true, ctx);
         } else {
           // X'Y: dX = YG', dY = XG
           if (dx)
-            MatMulFunction<DeviceContext, T>(&y, &dout, y_dims, dout_dims, dx,
-                                             false, true, ctx);
+            MatMulFunction<DeviceContext, T>(&y, &dout, y_dims, dout_dims,
+                                             &dx_help, false, true, ctx);
           if (dy)
-            MatMulFunction<DeviceContext, T>(&x, &dout, x_dims, dout_dims, dy,
-                                             false, false, ctx);
+            MatMulFunction<DeviceContext, T>(&x, &dout, x_dims, dout_dims,
+                                             &dy_help, false, false, ctx);
         }
       } else {
         if (transpose_y) {
           // XY': dX = GY, dY = G'X
           if (dx)
-            MatMulFunction<DeviceContext, T>(&dout, &y, dout_dims, y_dims, dx,
-                                             false, false, ctx);
+            MatMulFunction<DeviceContext, T>(&dout, &y, dout_dims, y_dims,
+                                             &dx_help, false, false, ctx);
           if (dy)
-            MatMulFunction<DeviceContext, T>(&dout, &x, dout_dims, x_dims, dy,
-                                             true, false, ctx);
+            MatMulFunction<DeviceContext, T>(&dout, &x, dout_dims, x_dims,
+                                             &dy_help, true, false, ctx);
         } else {
           // XY: dX = GY', dY = X'G
           if (dx)
-            MatMulFunction<DeviceContext, T>(&dout, &y, dout_dims, y_dims, dx,
-                                             false, true, ctx);
+            MatMulFunction<DeviceContext, T>(&dout, &y, dout_dims, y_dims,
+                                             &dx_help, false, true, ctx);
           if (dy)
-            MatMulFunction<DeviceContext, T>(&x, &dout, x_dims, dout_dims, dy,
-                                             true, false, ctx);
+            MatMulFunction<DeviceContext, T>(&x, &dout, x_dims, dout_dims,
+                                             &dy_help, true, false, ctx);
         }
       }
 
       // get help dims
-      const std::vector<std::int64_t> dx_help_dims = vectorize(dx->dims());
-      const std::vector<std::int64_t> dy_help_dims = vectorize(dy->dims());
+      const std::vector<std::int64_t> dx_help_dims = vectorize(dx_help.dims());
+      const std::vector<std::int64_t> dy_help_dims = vectorize(dy_help.dims());
 
       std::vector<std::int64_t> dx_broadcast_dims(ndim);
       std::vector<std::int64_t> dy_broadcast_dims(ndim);
@@ -639,11 +639,21 @@ class MatMulV2GradKernel : public framework::OpKernel<T> {
       }
       // reduce sum to get grad by ReduceSum
       if (dx) {
-        ReduceSumForMatmulGrad<DeviceContext, T>(dx, dx, dx_reduce_dims, ctx);
+        if (dx_reduce_dims.empty()) {
+          *dx = std::move(dx_help);
+        } else {
+          ReduceSumForMatmulGrad<DeviceContext, T>(&dx_help, dx, dx_reduce_dims,
+                                                   ctx);
+        }
         dx->Resize(x.dims());
       }
       if (dy) {
-        ReduceSumForMatmulGrad<DeviceContext, T>(dy, dy, dy_reduce_dims, ctx);
+        if (dy_reduce_dims.empty()) {
+          *dy = std::move(dy_help);
+        } else {
+          ReduceSumForMatmulGrad<DeviceContext, T>(&dy_help, dy, dy_reduce_dims,
+                                                   ctx);
+        }
         dy->Resize(y.dims());
       }
     }
diff --git a/paddle/fluid/pybind/imperative.cc b/paddle/fluid/pybind/imperative.cc
index 4a4f55cf57b2f1286997dca34efc9c8f27d84b2a..7a48ffa82a426ede5bd9d9e00bec6154099d272f 100644
--- a/paddle/fluid/pybind/imperative.cc
+++ b/paddle/fluid/pybind/imperative.cc
@@ -1289,9 +1289,11 @@ void BindImperative(py::module *m_ptr) {
           [](const std::vector<std::shared_ptr<imperative::VarBase>> &vars,
              const std::vector<std::vector<size_t>> &group_indices,
              const std::vector<bool> &is_sparse_gradient,
-             std::shared_ptr<imperative::ParallelContext> parallel_ctx) {
+             std::shared_ptr<imperative::ParallelContext> parallel_ctx,
+             const std::vector<size_t> &group_size_limits) {
             return imperative::Reducer::SetInstance(
-                vars, group_indices, is_sparse_gradient, parallel_ctx);
+                vars, group_indices, is_sparse_gradient, parallel_ctx,
+                group_size_limits);
           }))
       .def("prepare_for_backward", &imperative::Reducer::PrepareForBackward,
            py::call_guard<py::gil_scoped_release>());
@@ -1299,6 +1301,7 @@ void BindImperative(py::module *m_ptr) {
   m.def("assign_group_by_size", &imperative::AssignGroupBySize, py::arg("vars"),
         py::arg("is_sparse_gradient"),
         py::arg("group_size_limits") = std::vector<size_t>{25 * 1024 * 1024},
+        py::arg("tensor_indices") = std::vector<int64_t>{},
         py::call_guard<py::gil_scoped_release>());
 #endif
 }
diff --git a/python/paddle/distributed/fleet/base/distributed_strategy.py b/python/paddle/distributed/fleet/base/distributed_strategy.py
index 98b6bc0cc89f1d79c9bae88068bdd3d484fcd659..658143d0a22b8a15a30806c04e7a6bbce0a9118b 100755
--- a/python/paddle/distributed/fleet/base/distributed_strategy.py
+++ b/python/paddle/distributed/fleet/base/distributed_strategy.py
@@ -18,7 +18,6 @@ from paddle.fluid.framework import Variable, set_flags, core
 from paddle.fluid.wrapped_decorator import wrap_decorator
 import google.protobuf.text_format
 import google.protobuf
-from paddle.fluid.framework import dygraph_only
 
 __all__ = ["DistributedStrategy"]
 
diff --git a/python/paddle/fluid/dygraph/parallel.py b/python/paddle/fluid/dygraph/parallel.py
index 77a0308a53348c3aebff5344d7409d486a0954ea..731a9f809d875f3085527acc32c508de4765af10 100644
--- a/python/paddle/fluid/dygraph/parallel.py
+++ b/python/paddle/fluid/dygraph/parallel.py
@@ -441,10 +441,11 @@ class DataParallel(layers.Layer):
             "ParallelContext must be initialized before. You should use init_parallel_env() before" \
             "constructing the DataParallel."
 
-        self._reducer = core.Reducer(trainable_parameters,
-                                     list(reversed(self.group_indices)),
-                                     is_sparse_gradient,
-                                     parallel_helper.__parallel_ctx__clz__)
+        self._reducer = core.Reducer(
+            trainable_parameters,
+            list(reversed(self.group_indices)), is_sparse_gradient,
+            parallel_helper.__parallel_ctx__clz__,
+            [self.last_comm_buffer_size, self.comm_buffer_size])
 
     def forward(self, *inputs, **kwargs):
         if self._strategy.nranks > 1:
diff --git a/python/paddle/fluid/tests/unittests/test_imperative_group.py b/python/paddle/fluid/tests/unittests/test_imperative_group.py
index 299efa6d9c12d468dd77863c53420fed6843f198..f96358096516e67af6269c321a2722c500489959 100644
--- a/python/paddle/fluid/tests/unittests/test_imperative_group.py
+++ b/python/paddle/fluid/tests/unittests/test_imperative_group.py
@@ -155,6 +155,30 @@ class TestDataParallelGroup(unittest.TestCase):
             var_list, [True, False, False, False, False, True], [200, 400])
         self.assertEqual([[0], [1], [2], [3], [4], [5]], res)
 
+    def test_construct_group8(self):
+        # one dtype & one limit capability & have tensor_indices
+        var_list = []
+        var_list.append(self.create_varbase(core.VarDesc.VarType.FP32, [2, 25]))
+        var_list.append(
+            self.create_varbase(core.VarDesc.VarType.FP32, [2, 100]))
+        var_list.append(self.create_varbase(core.VarDesc.VarType.FP32, [2, 50]))
+        var_list.append(self.create_varbase(core.VarDesc.VarType.FP32, [2, 25]))
+        res = core.assign_group_by_size(var_list, [False, False, False, False],
+                                        [400], [3, 0, 1, 2])
+        self.assertEqual([[3, 0], [1], [2]], res)
+
+    def test_construct_group9(self):
+        # one dtype & one limit capability & have tensor_indices
+        var_list = []
+        var_list.append(self.create_varbase(core.VarDesc.VarType.FP32, [2, 25]))
+        var_list.append(self.create_varbase(core.VarDesc.VarType.FP32, [2, 25]))
+        var_list.append(self.create_varbase(core.VarDesc.VarType.FP32, [2, 25]))
+        var_list.append(
+            self.create_varbase(core.VarDesc.VarType.FP32, [2, 1000]))
+        res = core.assign_group_by_size(var_list, [False, False, False, True],
+                                        [300], [1, 0, 2, 3])
+        self.assertEqual([[1, 0], [3], [2]], res)
+
 
 if __name__ == '__main__':
     unittest.main()
diff --git a/python/paddle/fluid/tests/unittests/test_matmul_v2_op.py b/python/paddle/fluid/tests/unittests/test_matmul_v2_op.py
index a6667db6227f984b074827639f2366f378eee5e6..c137a4a9feb1d8ecd548219941f8b739ed3c7c74 100644
--- a/python/paddle/fluid/tests/unittests/test_matmul_v2_op.py
+++ b/python/paddle/fluid/tests/unittests/test_matmul_v2_op.py
@@ -286,6 +286,30 @@ class TestMatMuklOp17(TestMatMulV2Op):
         self.trans_y = False
 
 
+class TestMatMuklOpBroadcast1(TestMatMulV2Op):
+    """
+    case 14_3
+    """
+
+    def config(self):
+        self.x_shape = (3, 1, 10, 10)
+        self.y_shape = (1, 2, 10, 10)
+        self.trans_x = True
+        self.trans_y = True
+
+
+class TestMatMuklOpBroadcast2(TestMatMulV2Op):
+    """
+    case 14_4
+    """
+
+    def config(self):
+        self.x_shape = (3, 1, 10, 10)
+        self.y_shape = (1, 2, 10, 10)
+        self.trans_x = False
+        self.trans_y = True
+
+
 #--------------------test matmul fp16--------------------
 
 
diff --git a/python/paddle/utils/download.py b/python/paddle/utils/download.py
index c5c7de678edee4dc510383a09bfec4c8fbf80950..3af9a83f6a212d91d05a787067f1beb5f7a6244a 100644
--- a/python/paddle/utils/download.py
+++ b/python/paddle/utils/download.py
@@ -140,6 +140,21 @@ def _map_path(url, root_dir):
     return osp.join(root_dir, fpath)
 
 
+def _get_unique_endpoints(trainer_endpoints):
+    # Sorting is to avoid different environmental variables for each card
+    trainer_endpoints.sort()
+    ips = set()
+    unique_endpoints = set()
+    for endpoint in trainer_endpoints:
+        ip = endpoint.split(":")[0]
+        if ip in ips:
+            continue
+        ips.add(ip)
+        unique_endpoints.add(endpoint)
+    logger.info("unique_endpoints {}".format(unique_endpoints))
+    return unique_endpoints
+
+
 def get_path_from_url(url, root_dir, md5sum=None, check_exist=True):
     """ Download from given url to root_dir.
     if file or directory specified by url is exists under
@@ -161,17 +176,20 @@ def get_path_from_url(url, root_dir, md5sum=None, check_exist=True):
     assert is_url(url), "downloading from {} not a url".format(url)
     # parse path after download to decompress under root_dir
     fullpath = _map_path(url, root_dir)
-
+    # Mainly used to solve the problem of downloading data from different 
+    # machines in the case of multiple machines. Different ips will download 
+    # data, and the same ip will only download data once.
+    unique_endpoints = _get_unique_endpoints(ParallelEnv().trainer_endpoints[:])
     if osp.exists(fullpath) and check_exist and _md5check(fullpath, md5sum):
         logger.info("Found {}".format(fullpath))
     else:
-        if ParallelEnv().local_rank == 0:
+        if ParallelEnv().current_endpoint in unique_endpoints:
             fullpath = _download(url, root_dir, md5sum)
         else:
             while not os.path.exists(fullpath):
                 time.sleep(1)
 
-    if ParallelEnv().local_rank == 0:
+    if ParallelEnv().current_endpoint in unique_endpoints:
         if tarfile.is_tarfile(fullpath) or zipfile.is_zipfile(fullpath):
             fullpath = _decompress(fullpath)