diff --git a/paddle/fluid/framework/data_feed.cc b/paddle/fluid/framework/data_feed.cc
index b5f7e6c22405d6928f0e423458d6cd720f2d09a8..365c80da34eb287f50d2f0dcbf3844001ab43ec8 100644
--- a/paddle/fluid/framework/data_feed.cc
+++ b/paddle/fluid/framework/data_feed.cc
@@ -72,7 +72,6 @@ bool DataFeed::PickOneFile(std::string* filename) {
   }
   VLOG(3) << "file_idx_=" << *file_idx_;
   *filename = filelist_[(*file_idx_)++];
-  // LOG(ERROR) << "pick file:" << *filename;
   return true;
 }
 
@@ -466,6 +465,17 @@ void MultiSlotDataFeed::Init(
     if (slot.is_used()) {
       use_slots_.push_back(all_slots_[i]);
       use_slots_is_dense_.push_back(slot.is_dense());
+      std::vector<int> local_shape;
+      if (slot.is_dense()) {
+        // for batch size holder if is_dense
+        if (slot.shape(0) > 0) {
+          local_shape.push_back(0);
+        }
+      }
+      for (size_t i = 0; i < slot.shape_size(); ++i) {
+        local_shape.push_back(slot.shape(i));
+      }
+      use_slots_shape_.push_back(local_shape);
     }
   }
   feed_vec_.resize(use_slots_.size());
@@ -752,8 +762,8 @@ void MultiSlotDataFeed::PutToFeedVec(
     LoD data_lod{offset};
     feed_vec_[i]->set_lod(data_lod);
     if (use_slots_is_dense_[i]) {
-      int dim = total_instance / batch_size_;
-      feed_vec_[i]->Resize({batch_size_, dim});
+      use_slots_shape_[i][0] = batch_size_;
+      feed_vec_[i]->Resize(framework::make_ddim(use_slots_shape_[i]));
     }
   }
 #endif
@@ -785,6 +795,16 @@ void MultiSlotInMemoryDataFeed::Init(
     if (slot.is_used()) {
       use_slots_.push_back(all_slots_[i]);
       use_slots_is_dense_.push_back(slot.is_dense());
+      std::vector<int> local_shape;
+      if (slot.is_dense()) {
+        if (slot.shape(0) > 0) {
+          local_shape.push_back(0);
+        }
+      }
+      for (size_t i = 0; i < slot.shape_size(); ++i) {
+        local_shape.push_back(slot.shape(i));
+      }
+      use_slots_shape_.push_back(local_shape);
     }
   }
   feed_vec_.resize(use_slots_.size());
@@ -940,8 +960,8 @@ void MultiSlotInMemoryDataFeed::PutToFeedVec(
     LoD data_lod{offset};
     feed_vec_[i]->set_lod(data_lod);
     if (use_slots_is_dense_[i]) {
-      int dim = total_instance / batch_size_;
-      feed_vec_[i]->Resize({batch_size_, dim});
+      use_slots_shape_[i][0] = batch_size_;
+      feed_vec_[i]->Resize(framework::make_ddim(use_slots_shape_[i]));
     }
   }
 #endif
diff --git a/paddle/fluid/framework/data_feed.h b/paddle/fluid/framework/data_feed.h
index 648c874a0b8763b18118e18adf3b3e93acfd104b..d098c7858a98c644bd3cad78d3cf1e3b35ca026b 100644
--- a/paddle/fluid/framework/data_feed.h
+++ b/paddle/fluid/framework/data_feed.h
@@ -142,6 +142,7 @@ class DataFeed {
   // object)
   std::vector<std::string> all_slots_;
   std::vector<std::string> all_slots_type_;
+  std::vector<std::vector<int>> use_slots_shape_;
   std::vector<int>
       use_slots_index_;  // -1: not used; >=0: the index of use_slots_
 
diff --git a/paddle/fluid/framework/data_feed.proto b/paddle/fluid/framework/data_feed.proto
index 77911306299b77748a2ad9437d49680748885003..03996e0e20a1729ee300a5ad37abc325876930b7 100644
--- a/paddle/fluid/framework/data_feed.proto
+++ b/paddle/fluid/framework/data_feed.proto
@@ -19,6 +19,7 @@ message Slot {
   required string type = 2;
   optional bool is_dense = 3 [ default = false ];
   optional bool is_used = 4 [ default = false ];
+  repeated int32 shape = 5; // we can define N-D Tensor
 }
 
 message MultiSlotDesc { repeated Slot slots = 1; }
diff --git a/paddle/fluid/framework/downpour_worker.cc b/paddle/fluid/framework/downpour_worker.cc
index 4ca7842fa261a1b8178438d35ca5d626146663d4..386ffd84c57063e950cd8b0d57304c66190be4c4 100644
--- a/paddle/fluid/framework/downpour_worker.cc
+++ b/paddle/fluid/framework/downpour_worker.cc
@@ -21,40 +21,40 @@ namespace framework {
 
 void DownpourWorker::Initialize(const TrainerDesc& desc) {
   param_ = desc.downpour_param();
-  for (size_t i = 0; i < param_.sparse_table_size(); ++i) {
+  for (int i = 0; i < param_.sparse_table_size(); ++i) {
     uint64_t table_id =
         static_cast<uint64_t>(param_.sparse_table(i).table_id());
     TableParameter table = param_.sparse_table(i);
     sparse_key_names_[table_id].resize(table.sparse_key_name_size());
-    for (size_t j = 0; j < table.sparse_key_name_size(); ++j) {
+    for (int j = 0; j < table.sparse_key_name_size(); ++j) {
       sparse_key_names_[table_id][j] = table.sparse_key_name(j);
     }
     sparse_value_names_[table_id].resize(table.sparse_value_name_size());
-    for (size_t j = 0; j < table.sparse_value_name_size(); ++j) {
+    for (int j = 0; j < table.sparse_value_name_size(); ++j) {
       sparse_value_names_[table_id][j] = table.sparse_value_name(j);
     }
     sparse_grad_names_[table_id].resize(table.sparse_grad_name_size());
-    for (size_t j = 0; j < table.sparse_grad_name_size(); ++j) {
+    for (int j = 0; j < table.sparse_grad_name_size(); ++j) {
       sparse_grad_names_[table_id][j] = table.sparse_grad_name(j);
     }
     label_var_name_[table_id] = table.label_var_name();
   }
 
-  for (size_t i = 0; i < param_.dense_table_size(); ++i) {
+  for (int i = 0; i < param_.dense_table_size(); ++i) {
     uint64_t table_id = static_cast<uint64_t>(param_.dense_table(i).table_id());
     auto table = param_.dense_table(i);
     dense_value_names_[table_id].resize(table.dense_value_name_size());
-    for (size_t j = 0; j < table.dense_value_name_size(); ++j) {
+    for (int j = 0; j < table.dense_value_name_size(); ++j) {
       dense_value_names_[table_id][j] = table.dense_value_name(j);
     }
     dense_grad_names_[table_id].resize(table.dense_grad_name_size());
-    for (size_t j = 0; j < table.dense_grad_name_size(); ++j) {
+    for (int j = 0; j < table.dense_grad_name_size(); ++j) {
       dense_grad_names_[table_id][j] = table.dense_grad_name(j);
     }
   }
 
   skip_ops_.resize(param_.skip_ops_size());
-  for (size_t i = 0; i < param_.skip_ops_size(); ++i) {
+  for (int i = 0; i < param_.skip_ops_size(); ++i) {
     skip_ops_[i] = param_.skip_ops(i);
   }
 
@@ -83,14 +83,14 @@ void DownpourWorker::CollectLabelInfo(size_t table_idx) {
   LoDTensor* tensor = var->GetMutable<LoDTensor>();
   int64_t* label_ptr = tensor->data<int64_t>();
 
-  int global_index = 0;
+  size_t global_index = 0;
   for (size_t i = 0; i < sparse_key_names_[table_id].size(); ++i) {
     VLOG(3) << "sparse_key_names_[" << i
             << "]: " << sparse_key_names_[table_id][i];
     Variable* fea_var = thread_scope_->FindVar(sparse_key_names_[table_id][i]);
     LoDTensor* tensor = fea_var->GetMutable<LoDTensor>();
     int64_t* ids = tensor->data<int64_t>();
-    int fea_idx = 0;
+    size_t fea_idx = 0;
     // tensor->lod()[0].size() == batch_size + 1
     for (auto lod_idx = 1u; lod_idx < tensor->lod()[0].size(); ++lod_idx) {
       for (; fea_idx < tensor->lod()[0][lod_idx]; ++fea_idx) {
@@ -138,7 +138,7 @@ void DownpourWorker::FillSparseValue(size_t table_idx) {
     auto& tensor_lod = tensor->lod()[0];
     LoD data_lod{tensor_lod};
     tensor_emb->set_lod(data_lod);
-    for (auto index = 0u; index < len; ++index) {
+    for (int index = 0; index < len; ++index) {
       if (ids[index] == 0u) {
         memcpy(ptr + table.emb_dim() * index, init_value.data() + 2,
                sizeof(float) * table.emb_dim());
@@ -192,7 +192,7 @@ void DownpourWorker::TrainFilesWithProfiler() {
     read_time += timeline.ElapsedSec();
     total_time += timeline.ElapsedSec();
     VLOG(3) << "program config size: " << param_.program_config_size();
-    for (size_t i = 0; i < param_.program_config(0).pull_sparse_table_id_size();
+    for (int i = 0; i < param_.program_config(0).pull_sparse_table_id_size();
          ++i) {
       uint64_t tid = static_cast<uint64_t>(
           param_.program_config(0).pull_sparse_table_id(i));
@@ -244,8 +244,8 @@ void DownpourWorker::TrainFilesWithProfiler() {
     }
 
     if (need_to_push_sparse_) {
-      for (size_t i = 0;
-           i < param_.program_config(0).push_sparse_table_id_size(); ++i) {
+      for (int i = 0; i < param_.program_config(0).push_sparse_table_id_size();
+           ++i) {
         uint64_t tid = static_cast<uint64_t>(
             param_.program_config(0).push_sparse_table_id(i));
         TableParameter table;
@@ -268,8 +268,8 @@ void DownpourWorker::TrainFilesWithProfiler() {
 
     if (need_to_push_dense_) {
       timeline.Start();
-      for (size_t i = 0;
-           i < param_.program_config(0).push_dense_table_id_size(); ++i) {
+      for (int i = 0; i < param_.program_config(0).push_dense_table_id_size();
+           ++i) {
         uint64_t tid = static_cast<uint64_t>(
             param_.program_config(0).push_dense_table_id(i));
         fleet_ptr_->PushDenseVarsAsync(
@@ -315,8 +315,8 @@ void DownpourWorker::TrainFilesWithProfiler() {
     }
 
     if (need_to_push_dense_) {
-      for (size_t i = 0;
-           i < param_.program_config(0).push_dense_table_id_size(); ++i) {
+      for (int i = 0; i < param_.program_config(0).push_dense_table_id_size();
+           ++i) {
         uint64_t tid = static_cast<uint64_t>(
             param_.program_config(0).push_dense_table_id(i));
         pull_dense_worker_->IncreaseThreadVersion(thread_id_, tid);
@@ -362,7 +362,7 @@ void DownpourWorker::TrainFiles() {
   int cur_batch;
   while ((cur_batch = device_reader_->Next()) > 0) {
     // pull sparse here
-    for (size_t i = 0; i < param_.program_config(0).pull_sparse_table_id_size();
+    for (int i = 0; i < param_.program_config(0).pull_sparse_table_id_size();
          ++i) {
       uint64_t tid = static_cast<uint64_t>(
           param_.program_config(0).pull_sparse_table_id(i));
@@ -397,8 +397,8 @@ void DownpourWorker::TrainFiles() {
 
     if (need_to_push_sparse_) {
       // push gradients here
-      for (size_t i = 0;
-           i < param_.program_config(0).push_sparse_table_id_size(); ++i) {
+      for (int i = 0; i < param_.program_config(0).push_sparse_table_id_size();
+           ++i) {
         uint64_t tid = static_cast<uint64_t>(
             param_.program_config(0).push_sparse_table_id(i));
         TableParameter table;
@@ -416,8 +416,8 @@ void DownpourWorker::TrainFiles() {
     }
 
     if (need_to_push_dense_) {
-      for (size_t i = 0;
-           i < param_.program_config(0).push_dense_table_id_size(); ++i) {
+      for (int i = 0; i < param_.program_config(0).push_dense_table_id_size();
+           ++i) {
         uint64_t tid = static_cast<uint64_t>(
             param_.program_config(0).push_dense_table_id(i));
         fleet_ptr_->PushDenseVarsAsync(
@@ -461,8 +461,8 @@ void DownpourWorker::TrainFiles() {
     }
 
     if (need_to_push_dense_) {
-      for (size_t i = 0;
-           i < param_.program_config(0).push_dense_table_id_size(); ++i) {
+      for (int i = 0; i < param_.program_config(0).push_dense_table_id_size();
+           ++i) {
         uint64_t tid = static_cast<uint64_t>(
             param_.program_config(0).push_dense_table_id(i));
         pull_dense_worker_->IncreaseThreadVersion(thread_id_, tid);
diff --git a/paddle/fluid/framework/parallel_executor.cc b/paddle/fluid/framework/parallel_executor.cc
index 4245caf1689c76d72b410c742488c55562c8b998..c4bf2b7e8c017b22f917c9f9bd40e75b8cde08b2 100644
--- a/paddle/fluid/framework/parallel_executor.cc
+++ b/paddle/fluid/framework/parallel_executor.cc
@@ -221,7 +221,7 @@ ParallelExecutor::ParallelExecutor(const std::vector<platform::Place> &places,
     PADDLE_ENFORCE(!member_->use_cuda_,
                    "gpu mode does not support async_mode_ now!");
     graphs.push_back(graph);
-    for (int i = 1; i < places.size(); ++i) {
+    for (size_t i = 1; i < places.size(); ++i) {
       auto *tmp_graph = new ir::Graph(graph->OriginProgram());
       async_graphs_.emplace_back(tmp_graph);
       graphs.push_back(tmp_graph);
@@ -315,7 +315,7 @@ ParallelExecutor::ParallelExecutor(const std::vector<platform::Place> &places,
     graph = build_strategy.Apply(graph, {member_->places_[0]}, loss_var_name,
                                  {member_->local_scopes_[0]}, 1,
                                  member_->use_cuda_, member_->nccl_ctxs_.get());
-    for (int i = 1; i < member_->places_.size(); ++i) {
+    for (size_t i = 1; i < member_->places_.size(); ++i) {
       graphs[i] =
           build_strategy.Apply(graphs[i], {member_->places_[i]}, loss_var_name,
                                {member_->local_scopes_[i]}, 1,
diff --git a/paddle/fluid/framework/trainer_desc.proto b/paddle/fluid/framework/trainer_desc.proto
index 389c1a870fb54ad28806ad49632323b1c93676f4..4fc05ccf5c9be37e80b4ae7263166ad76eb6d6a7 100644
--- a/paddle/fluid/framework/trainer_desc.proto
+++ b/paddle/fluid/framework/trainer_desc.proto
@@ -76,7 +76,7 @@ message PullDenseWorkerParameter {
 
 message TableParameter {
   // dense table only
-  optional int64 table_id = 1;
+  optional uint64 table_id = 1;
   repeated string dense_value_name = 2;
   repeated string dense_grad_name = 3;
   repeated int32 push_dense_wait_times = 5;
diff --git a/python/paddle/fluid/dataset.py b/python/paddle/fluid/dataset.py
index e655fd4a976a8a6fa2811ddc43de3d1f231229d5..1a023f61675ed62c141bb6e71fabbdf0086b0c64 100644
--- a/python/paddle/fluid/dataset.py
+++ b/python/paddle/fluid/dataset.py
@@ -136,6 +136,7 @@ class DatasetBase(object):
             slot_var.name = var.name
             if var.lod_level == 0:
                 slot_var.is_dense = True
+                slot_var.shape.extend(var.shape)
             if var.dtype == core.VarDesc.VarType.FP32:
                 slot_var.type = "float"
             elif var.dtype == core.VarDesc.VarType.INT64:
diff --git a/python/paddle/fluid/executor.py b/python/paddle/fluid/executor.py
index e15197037e1d901855883919b02a1574b7bc9a29..fa8b49a021294e8555e979459615b1956d9b2b55 100644
--- a/python/paddle/fluid/executor.py
+++ b/python/paddle/fluid/executor.py
@@ -712,10 +712,6 @@ class Executor(object):
         if dataset == None:
             raise RuntimeError("dataset is needed and should be initialized")
 
-        if not isinstance(self.place, core.CPUPlace):
-            raise RuntimeError("infer_from_dataset is verified on CPUPlace"
-                               "We will open CUDAPlace in the future")
-
         scope, trainer = self._prepare_trainer(
             program=program,
             dataset=dataset,
@@ -796,10 +792,6 @@ class Executor(object):
         if dataset == None:
             raise RuntimeError("dataset is need and should be initialized")
 
-        if not isinstance(self.place, core.CPUPlace):
-            raise RuntimeError("train_from_dataset is verified on CPUPlace"
-                               "We will open CUDAPlace in the future")
-
         scope, trainer = self._prepare_trainer(
             program=program,
             dataset=dataset,