diff --git a/paddle/function/BufferArg.cpp b/paddle/function/BufferArg.cpp
new file mode 100644
index 0000000000000..65c6f303041d8
--- /dev/null
+++ b/paddle/function/BufferArg.cpp
@@ -0,0 +1,31 @@
+/* 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 <glog/logging.h>
+
+#include "BufferArg.h"
+
+namespace paddle {
+
+const SequenceArg& BufferArg::sequence() const {
+  // CHECK_EQ(bufferType_, TENSOR_SEQUENCE_DATA);
+  return dynamic_cast<const SequenceArg&>(*this);
+}
+
+const SparseMatrixArg& BufferArg::sparse() const {
+  // CHECK_EQ(bufferType_, TENSOR_SPARSE);
+  return dynamic_cast<const SparseMatrixArg&>(*this);
+}
+
+}  // namespace paddle
diff --git a/paddle/function/BufferArg.h b/paddle/function/BufferArg.h
new file mode 100644
index 0000000000000..9649913fa8d9b
--- /dev/null
+++ b/paddle/function/BufferArg.h
@@ -0,0 +1,281 @@
+/* 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 <glog/logging.h>
+
+#include "TensorShape.h"
+#include "TensorType.h"
+#include "paddle/math/CpuSparseMatrix.h"
+#include "paddle/math/Matrix.h"
+#include "paddle/math/SparseMatrix.h"
+
+namespace paddle {
+
+enum BufferType {
+  TENSOR_NORMAL = 0,
+  TENSOR_SEQUENCE_ID = 1,
+  TENSOR_SEQUENCE_DATA = 2,
+  TENSOR_SPARSE = 3
+};
+
+enum SparseDataType {
+  SPARSE_NO_VALUE = 0,  // do not need value pointer, all values are 1
+  SPARSE_FLOAT_VALUE = 1
+};
+
+enum SparseDataFormat { SPARSE_CSR_FORMAT = 0, SPARSE_CSC_FORMAT = 1 };
+
+class BufferArg;
+class SequenceArg;
+class SparseMatrixArg;
+typedef std::shared_ptr<BufferArg> BufferArgPtr;
+
+/**
+ * \brief BufferArg used as the argument type of Function.
+ *
+ * The arguments of the Paddle Function have four Buffer types.
+ * 1. BufferArg for a dense Buffer of any dimension.
+ * 2. SequenceIdArg for a Buffer of sequence start positions.
+ * 3. SequenceArg for a Buffer of sequence data.
+ * 4. SparseMatrixArg for a Buffer of sparse matrix.
+ *
+ * There is an ArgType property for the BufferArg used as Function Output.
+ * Whether the result of the Function calculation is assigned to the
+ * output Buffer or added to the output Buffer is determined by the
+ * argType_ property of the output BufferArg.
+ */
+
+// ArgType is only used by output BufferArg.
+// For input argument, argType_ is ignored.
+// For output argument, need to set the argType_ of the BufferArg.
+enum ArgType {
+  UNSPECIFIED = 0,
+  ASSIGN_TO = 1,
+  ADD_TO = 2,
+};
+class BufferArg {
+public:
+  void setArgType(ArgType argType) { argType_ = argType; }
+
+  ArgType getArgType() const { return argType_; }
+
+public:
+  BufferArg(void* buf,
+            ValueType valueType,
+            const TensorShape& shape,
+            ArgType argType = UNSPECIFIED)
+      : buf_(buf), valueType_(valueType), shape_(shape), argType_(argType) {}
+
+  BufferArg(void* buf, ValueType valueType)
+      : buf_(buf), valueType_(valueType) {}
+
+  BufferArg(const Matrix& matrix, ArgType argType = UNSPECIFIED)
+      : buf_(
+            const_cast<void*>(reinterpret_cast<const void*>(matrix.getData()))),
+        valueType_(DataType<real>::value),
+        shape_(2),
+        argType_(argType) {
+    shape_.setDim(0, matrix.getHeight());
+    shape_.setDim(1, matrix.getWidth());
+  }
+
+  BufferArg(const Matrix& matrix,
+            const TensorShape& shape,
+            ArgType argType = UNSPECIFIED)
+      : buf_(
+            const_cast<void*>(reinterpret_cast<const void*>(matrix.getData()))),
+        valueType_(DataType<real>::value),
+        shape_(shape),
+        argType_(argType) {
+    CHECK_EQ(matrix.getElementCnt(), shape.getElements());
+  }
+
+  BufferArg(const Vector& vector, ArgType argType = UNSPECIFIED)
+      : buf_(
+            const_cast<void*>(reinterpret_cast<const void*>(vector.getData()))),
+        valueType_(DataType<real>::value),
+        shape_(1),
+        argType_(argType) {
+    shape_.setDim(0, vector.getSize());
+  }
+
+  BufferArg(const IVector& vector, ArgType argType = UNSPECIFIED)
+      : buf_(
+            const_cast<void*>(reinterpret_cast<const void*>(vector.getData()))),
+        valueType_(VALUE_TYPE_INT32),
+        shape_(1),
+        argType_(argType) {
+    shape_.setDim(0, vector.getSize());
+  }
+
+  template <DeviceType DType>
+  typename Tensor<real, DType>::Matrix matrix() const {
+    CHECK(buf_);
+    CHECK(valueType_ == DataType<real>::value);
+    // CHECK(deviceType_ == DType);
+    CHECK_EQ((size_t)2, shape_.ndims());
+    return typename Tensor<real, DType>::Matrix(
+        reinterpret_cast<real*>(buf_), shape_[0], shape_[1]);
+  }
+
+  template <typename VType, DeviceType DType>
+  typename Tensor<VType, DType>::Vector vector() const {
+    CHECK(buf_);
+    CHECK(valueType_ == DataType<VType>::value);
+    // CHECK(deviceType_ == DType);
+    CHECK_EQ((size_t)1, shape_.ndims());
+    return typename Tensor<VType, DType>::Vector(
+        shape_[0], reinterpret_cast<VType*>(buf_));
+  }
+
+  virtual ~BufferArg() {}
+
+  template <typename T>
+  T* data() const {
+    return reinterpret_cast<T*>(buf_);
+  }
+
+  void* data() const { return buf_; }
+  ValueType valueType() const { return valueType_; }
+  BufferType bufferType() const { return bufferType_; }
+  const TensorShape& shape() const { return shape_; }
+
+  const SequenceArg& sequence() const;
+  const SparseMatrixArg& sparse() const;
+
+protected:
+  void* buf_;
+  ValueType valueType_;
+  TensorShape shape_;
+  BufferType bufferType_;
+  ArgType argType_ = UNSPECIFIED;
+  // leading dimensions. The size is dims_.size()
+  // Dims lds_;
+};
+
+// sequence start positions in a mini-batch of sequences
+// shape_.ndims() == 1
+// valueType_ = int32
+// if a < b then value_.buf_[a] < value_.buf_[b]
+class SequenceIdArg : public BufferArg {
+public:
+  SequenceIdArg(void* buf,
+                const TensorShape& shape,
+                ArgType argType = UNSPECIFIED)
+      : BufferArg(buf, VALUE_TYPE_INT32, shape, argType) {
+    CHECK_EQ(shape_.ndims(), (size_t)1);
+    numSeqs_ = shape_[0] - 1;
+  }
+
+  SequenceIdArg(const IVector& vector) : BufferArg(vector) {
+    numSeqs_ = shape_[0] - 1;
+  }
+
+  ~SequenceIdArg() {}
+
+  size_t numSeqs() const { return numSeqs_; }
+
+private:
+  size_t numSeqs_;
+};
+
+// sequence data
+class SequenceArg : public BufferArg {
+public:
+  SequenceArg(void* buf,
+              ValueType valueType,
+              const TensorShape& shape,
+              const SequenceIdArg& startPositions,
+              ArgType argType = UNSPECIFIED)
+      : BufferArg(buf, valueType, shape, argType),
+        startPositions_(startPositions) {}
+
+  SequenceArg(const Matrix& matrix,
+              const IVector& vector,
+              ArgType argType = UNSPECIFIED)
+      : BufferArg(matrix, argType), startPositions_(vector) {}
+
+  ~SequenceArg() {}
+
+  void* getIdBuf() const { return startPositions_.data(); }
+  size_t numSeqs() const { return startPositions_.numSeqs(); }
+
+private:
+  SequenceIdArg startPositions_;
+};
+
+// sparse matrix
+// valueType_ == float or double
+// shape_.ndims() == 2
+class SparseMatrixArg : public BufferArg {
+public:
+  SparseMatrixArg(void* buf,
+                  ValueType valueType,
+                  const TensorShape& shape,
+                  const BufferArg& row,
+                  const BufferArg& col,
+                  size_t nnz,
+                  SparseDataFormat format,
+                  SparseDataType type,
+                  ArgType argType = UNSPECIFIED)
+      : BufferArg(buf, valueType, shape, argType),
+        row_(row),
+        col_(col),
+        nnz_(nnz),
+        format_(format),
+        type_(type) {
+    CHECK((valueType == VALUE_TYPE_FLOAT) || (valueType == VALUE_TYPE_DOUBLE));
+    CHECK_EQ(shape_.ndims(), (size_t)2);
+    CHECK_EQ(row_.shape().ndims(), (size_t)1);
+    CHECK_EQ(col_.shape().ndims(), (size_t)1);
+    if (format == SPARSE_CSR_FORMAT) {
+      CHECK_EQ(nnz, col.shape()[0]);
+    } else if (format == SPARSE_CSC_FORMAT) {
+      CHECK_EQ(nnz, row.shape()[0]);
+    }
+  }
+
+  SparseMatrixArg(const CpuSparseMatrix& sparse, ArgType argType = UNSPECIFIED)
+      : BufferArg(sparse, argType),
+        row_(reinterpret_cast<void*>(sparse.getRows()), VALUE_TYPE_INT32),
+        col_(reinterpret_cast<void*>(sparse.getCols()), VALUE_TYPE_INT32) {}
+
+  SparseMatrixArg(const GpuSparseMatrix& sparse, ArgType argType = UNSPECIFIED)
+      : BufferArg(sparse, argType),
+        row_(reinterpret_cast<void*>(sparse.getRows()), VALUE_TYPE_INT32),
+        col_(reinterpret_cast<void*>(sparse.getCols()), VALUE_TYPE_INT32) {}
+
+  ~SparseMatrixArg() {}
+
+  void* getRowBuf() const { return row_.data(); }
+
+  void* getColBuf() const { return col_.data(); }
+
+  size_t nnz() const { return nnz_; }
+
+  SparseDataFormat dataFormat() const { return format_; }
+
+  SparseDataType dataType() const { return type_; }
+
+private:
+  BufferArg row_;
+  BufferArg col_;
+  size_t nnz_;
+  SparseDataFormat format_;
+  SparseDataType type_;
+};
+
+}  // namespace paddle
diff --git a/paddle/function/BufferArgTest.cpp b/paddle/function/BufferArgTest.cpp
new file mode 100644
index 0000000000000..a9ee3ab079e33
--- /dev/null
+++ b/paddle/function/BufferArgTest.cpp
@@ -0,0 +1,90 @@
+/* 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 "BufferArg.h"
+#include <gtest/gtest.h>
+#include "Function.h"
+#include "paddle/math/MemoryHandle.h"
+
+namespace paddle {
+
+TEST(BufferTest, BufferArg) {
+  TensorShape shape({8, 10});
+  CpuMemoryHandle memory(shape.getElements() *
+                         sizeOfValuType(VALUE_TYPE_FLOAT));
+  BufferArg buffer(memory.getBuf(), VALUE_TYPE_FLOAT, shape);
+  EXPECT_EQ(buffer.data(), memory.getBuf());
+}
+
+TEST(BufferTest, SequenceIdArg) {
+  TensorShape shape({10});
+  CpuMemoryHandle memory(shape.getElements() *
+                         sizeOfValuType(VALUE_TYPE_INT32));
+  SequenceIdArg buffer(memory.getBuf(), shape);
+  EXPECT_EQ(buffer.data(), memory.getBuf());
+  EXPECT_EQ(buffer.numSeqs(), 9);
+}
+
+TEST(BufferTest, asArgument) {
+  MatrixPtr matrix = Matrix::create(100, 200);
+  VectorPtr vector = Vector::create(100, false);
+  CpuSparseMatrix sparse(200, 300, 50);
+
+  // prepare arguments
+  BufferArgs argments;
+  argments.addArg(*matrix);
+  argments.addArg(*vector);
+  argments.addArg(sparse);
+
+  // function
+  auto function = [=](const BufferArgs& inputs) {
+    EXPECT_EQ(inputs.size(), 3);
+
+    // check inputs[0]
+    EXPECT_EQ(inputs[0].shape().ndims(), 2);
+    EXPECT_EQ(inputs[0].shape()[0], 100);
+    EXPECT_EQ(inputs[0].shape()[1], 200);
+    EXPECT_EQ(inputs[0].data(), matrix->getData());
+
+    EXPECT_EQ(inputs[0].matrix<DEVICE_TYPE_CPU>().getHeight(),
+              matrix->getHeight());
+    EXPECT_EQ(inputs[0].matrix<DEVICE_TYPE_CPU>().getWidth(),
+              matrix->getWidth());
+    EXPECT_EQ(inputs[0].matrix<DEVICE_TYPE_CPU>().getData(), matrix->getData());
+
+    // check inputs[1]
+    EXPECT_EQ(inputs[1].shape().ndims(), 1);
+    EXPECT_EQ(inputs[1].shape()[0], 100);
+    EXPECT_EQ(inputs[1].data(), vector->getData());
+    CpuVector inVector = inputs[1].vector<real, DEVICE_TYPE_CPU>();
+    EXPECT_EQ(inVector.getSize(), vector->getSize());
+    EXPECT_EQ(inVector.getData(), vector->getData());
+
+    // check inputs[2]
+    EXPECT_EQ(inputs[2].shape().ndims(), 2);
+    EXPECT_EQ(inputs[2].shape()[0], 200);
+    EXPECT_EQ(inputs[2].shape()[1], 300);
+    EXPECT_EQ(inputs[2].data(), sparse.getData());
+    // CHECK_EQ(inputs[2].sparse().nnz(), 50);
+    // CHECK_EQ(inputs[2].sparse().dataFormat(), SPARSE_CSR_FORMAT);
+    // CHECK_EQ(inputs[2].sparse().dataType(), SPARSE_FLOAT_VALUE);
+    EXPECT_EQ(inputs[2].sparse().getRowBuf(), sparse.getRows());
+    EXPECT_EQ(inputs[2].sparse().getColBuf(), sparse.getCols());
+  };
+
+  // call function
+  function(argments);
+}
+
+}  // namespace paddle
diff --git a/paddle/function/CMakeLists.txt b/paddle/function/CMakeLists.txt
index de85eeca82174..75a2acc55ec3d 100644
--- a/paddle/function/CMakeLists.txt
+++ b/paddle/function/CMakeLists.txt
@@ -3,6 +3,7 @@ file(GLOB cpp_files . *Op.cpp)
 
 list(APPEND h_files Function.h)
 list(APPEND cpp_files Function.cpp)
+list(APPEND cpp_files BufferArg.cpp)
 
 if(WITH_GPU)
     file(GLOB cu_files . *OpGpu.cu)
@@ -18,8 +19,12 @@ if(WITH_TESTING)
     # TODO:
     # file(GLOB test_files . *OpTest.cpp)
     # add_executable(${test_bin} EXCLUDE_FROM_ALL ${test_files})
-    add_simple_unittest(CrossMapNormalOpTest)
-    add_simple_unittest(ContextProjectionOpTest)
+    # add_simple_unittest(CrossMapNormalOpTest)
+    add_simple_unittest(TensorShapeTest)
+    add_simple_unittest(TensorTypeTest)
+    add_simple_unittest(BufferArgTest)
+    add_simple_unittest(FunctionTest)
+    # add_simple_unittest(ContextProjectionOpTest)
 endif()
 endif()
 
diff --git a/paddle/function/ContextProjectionOp.cpp b/paddle/function/ContextProjectionOp.cpp
index 07907fc1ba797..cb448562ebb37 100644
--- a/paddle/function/ContextProjectionOp.cpp
+++ b/paddle/function/ContextProjectionOp.cpp
@@ -19,17 +19,15 @@ limitations under the License. */
 namespace paddle {
 
 template <>
-void ContextProjectionForward<DEVICE_TYPE_CPU>(CpuMatrix* out_mat,
-                                               const CpuMatrix* input_mat,
-                                               const CpuMatrix* weight_mat,
+void ContextProjectionForward<DEVICE_TYPE_CPU>(CpuMatrix& out_mat,
+                                               const CpuMatrix& input_mat,
+                                               const CpuMatrix& weight_mat,
                                                const CpuIVector& seq_vec,
                                                size_t context_length,
                                                int context_start,
                                                size_t begin_pad) {
   const int* starts = seq_vec.getData();
   const size_t num_sequences = seq_vec.getSize() - 1;
-  auto w_mat = const_cast<CpuMatrix*>(weight_mat);
-  auto in_mat = const_cast<CpuMatrix*>(input_mat);
   for (size_t i = 0; i < num_sequences; ++i) {
     for (size_t j = 0; j < context_length; ++j) {
       int begin = starts[i] + context_start + j;
@@ -39,10 +37,11 @@ void ContextProjectionForward<DEVICE_TYPE_CPU>(CpuMatrix* out_mat,
       if (begin < starts[i]) {
         int64_t pad_size =
             std::min(starts[i] - begin, starts[i + 1] - starts[i]);
-        MatrixPtr mat = out_mat->subMatrix(starts[i], pad_size);
-        if (w_mat) {
-          MatrixPtr sub = w_mat->subMatrix(j, pad_size);
-          mat->addAtOffset(*sub, j * in_mat->getWidth());
+        MatrixPtr mat = out_mat.subMatrix(starts[i], pad_size);
+        if (weight_mat) {
+          MatrixPtr sub =
+              const_cast<CpuMatrix&>(weight_mat).subMatrix(j, pad_size);
+          mat->addAtOffset(*sub, j * input_mat.getWidth());
         }
         dst_begin = starts[i] + pad_size;
         begin = starts[i];
@@ -50,19 +49,22 @@ void ContextProjectionForward<DEVICE_TYPE_CPU>(CpuMatrix* out_mat,
       if (end > starts[i + 1]) {
         int64_t pad_size =
             std::min(end - starts[i + 1], starts[i + 1] - starts[i]);
-        MatrixPtr mat = out_mat->subMatrix(starts[i + 1] - pad_size, pad_size);
-        if (w_mat) {
-          MatrixPtr sub = w_mat->subMatrix(
-              begin_pad + context_start + j - pad_size, pad_size);
-          mat->addAtOffset(*sub, j * in_mat->getWidth());
+        MatrixPtr mat = out_mat.subMatrix(starts[i + 1] - pad_size, pad_size);
+        if (weight_mat) {
+          MatrixPtr sub =
+              const_cast<CpuMatrix&>(weight_mat)
+                  .subMatrix(begin_pad + context_start + j - pad_size,
+                             pad_size);
+          mat->addAtOffset(*sub, j * input_mat.getWidth());
         }
         dst_end = starts[i + 1] - pad_size;
         end = starts[i + 1];
       }
       if (end <= begin) continue;
-      MatrixPtr src = in_mat->subMatrix(begin, end - begin);
-      MatrixPtr dst = out_mat->subMatrix(dst_begin, dst_end - dst_begin);
-      dst->addAtOffset(*src, j * in_mat->getWidth());
+      MatrixPtr src =
+          const_cast<CpuMatrix&>(input_mat).subMatrix(begin, end - begin);
+      MatrixPtr dst = out_mat.subMatrix(dst_begin, dst_end - dst_begin);
+      dst->addAtOffset(*src, j * input_mat.getWidth());
     }
   }
 }
@@ -82,40 +84,32 @@ class ContextProjectionForwardFunc : public FunctionBase {
     begin_pad_ = config.get<size_t>("begin_pad");
   }
 
-  void calc(const Arguments& inputs,
-            const Arguments& outputs,
-            const Arguments& inouts) override {
-    CHECK_EQ(3, static_cast<int>(inputs.size()));
-    CHECK_EQ(1, static_cast<int>(outputs.size()));
-    CHECK_EQ(0, static_cast<int>(inouts.size()));
+  void calc(const BufferArgs& inputs, const BufferArgs& outputs) override {
+    CHECK_EQ((size_t)3, inputs.size());
+    CHECK_EQ((size_t)1, outputs.size());
 
-    CHECK(outputs[0].getData() && inputs[0].getData() && inputs[2].getData());
-    CHECK_EQ(static_cast<int>(outputs[0].dims_.size()), 2);
-    CHECK_EQ(static_cast<int>(inputs[0].dims_.size()), 2);
-    CHECK_EQ(static_cast<int>(inputs[1].dims_.size()), 2);
-    CHECK_EQ(static_cast<int>(inputs[2].dims_.size()), 1);
+    CHECK(outputs[0].data() && inputs[0].data() && inputs[2].data());
+    CHECK_EQ(outputs[0].shape().ndims(), (size_t)2);
+    CHECK_EQ(inputs[0].shape().ndims(), (size_t)2);
+    CHECK_EQ(inputs[1].shape().ndims(), (size_t)2);
+    CHECK_EQ(inputs[2].shape().ndims(), (size_t)1);
     /// dim of output = dim of input * context_length
-    CHECK_EQ(outputs[0].dims_[1], inputs[0].dims_[1] * context_length_);
+    CHECK_EQ(outputs[0].shape()[1], inputs[0].shape()[1] * context_length_);
     /// dim of input == dim of weight
-    CHECK_EQ(inputs[0].dims_[1], inputs[1].dims_[1]);
+    CHECK_EQ(inputs[0].shape()[1], inputs[1].shape()[1]);
     /// input and output has the same batch_size
-    CHECK_EQ(inputs[0].dims_[0], outputs[0].dims_[0]);
-
-    auto out_mat = std::make_shared<typename MatrixT<Device>::type>(
-        outputs[0].getData(), outputs[0].dims_[0], outputs[0].dims_[1]);
-    const auto in_mat = std::make_shared<typename MatrixT<Device>::type>(
-        inputs[0].getData(), inputs[0].dims_[0], inputs[0].dims_[1]);
-    const auto w_mat =
-        !inputs[1].getData()
-            ? nullptr
-            : std::make_shared<typename MatrixT<Device>::type>(
-                  inputs[1].getData(), inputs[1].dims_[0], inputs[1].dims_[1]);
-    typename SequenceT<Device>::type seq_vec(
-        inputs[2].dims_[0], reinterpret_cast<int*>(inputs[2].getData()));
-
-    ContextProjectionForward<Device>(out_mat.get(),
-                                     in_mat.get(),
-                                     w_mat.get(),
+    CHECK_EQ(inputs[0].shape()[0], outputs[0].shape()[0]);
+
+    CHECK_EQ(outputs[0].getArgType(), ADD_TO);
+    auto out_mat = outputs[0].matrix<Device>();
+    auto in_mat = inputs[0].matrix<Device>();
+    auto w_mat = !inputs[1].data()
+                     ? typename Tensor<real, Device>::Matrix(nullptr, 0, 0)
+                     : inputs[1].matrix<Device>();
+    auto seq_vec = inputs[2].vector<int, Device>();
+    ContextProjectionForward<Device>(out_mat,
+                                     in_mat,
+                                     w_mat,
                                      seq_vec,
                                      context_length_,
                                      context_start_,
@@ -129,18 +123,17 @@ class ContextProjectionForwardFunc : public FunctionBase {
 };
 
 template <>
-void ContextProjectionBackward<DEVICE_TYPE_CPU>(CpuMatrix* out_grad_mat,
-                                                CpuMatrix* in_grad_mat,
-                                                CpuMatrix* w_grad_mat,
+void ContextProjectionBackward<DEVICE_TYPE_CPU>(CpuMatrix& out_grad_mat,
+                                                CpuMatrix& in_grad_mat,
+                                                CpuMatrix& w_grad_mat,
                                                 const CpuIVector& seq_vec,
                                                 size_t context_length,
                                                 int context_start,
                                                 size_t begin_pad,
                                                 bool is_padding,
                                                 size_t total_pad) {
-  CHECK(out_grad_mat);
-  size_t input_dim = in_grad_mat ? in_grad_mat->getWidth()
-                                 : w_grad_mat ? w_grad_mat->getWidth() : 0;
+  size_t input_dim = in_grad_mat ? in_grad_mat.getWidth()
+                                 : w_grad_mat ? w_grad_mat.getWidth() : 0;
   const int* starts = seq_vec.getData();
   size_t num_sequences = seq_vec.getSize() - 1;
   for (size_t i = 0; i < num_sequences; ++i) {
@@ -153,8 +146,8 @@ void ContextProjectionBackward<DEVICE_TYPE_CPU>(CpuMatrix* out_grad_mat,
         int64_t pad_size =
             std::min(starts[i] - begin, starts[i + 1] - starts[i]);
         if (is_padding && w_grad_mat) {
-          MatrixPtr mat = out_grad_mat->subMatrix(starts[i], pad_size);
-          MatrixPtr sub = w_grad_mat->subMatrix(j, pad_size);
+          MatrixPtr mat = out_grad_mat.subMatrix(starts[i], pad_size);
+          MatrixPtr sub = w_grad_mat.subMatrix(j, pad_size);
           sub->addAtOffset(*mat, j * input_dim);
         }
         dst_begin = starts[i] + pad_size;
@@ -165,8 +158,8 @@ void ContextProjectionBackward<DEVICE_TYPE_CPU>(CpuMatrix* out_grad_mat,
             std::min(end - starts[i + 1], starts[i + 1] - starts[i]);
         if (is_padding && w_grad_mat) {
           MatrixPtr mat =
-              out_grad_mat->subMatrix(starts[i + 1] - pad_size, pad_size);
-          MatrixPtr sub = w_grad_mat->subMatrix(
+              out_grad_mat.subMatrix(starts[i + 1] - pad_size, pad_size);
+          MatrixPtr sub = w_grad_mat.subMatrix(
               begin_pad + context_start + j - pad_size, pad_size);
           sub->addAtOffset(*mat, j * input_dim);
         }
@@ -175,8 +168,8 @@ void ContextProjectionBackward<DEVICE_TYPE_CPU>(CpuMatrix* out_grad_mat,
       }
       if (end <= begin) continue;
       if (!in_grad_mat) continue;
-      MatrixPtr src = in_grad_mat->subMatrix(begin, end - begin);
-      MatrixPtr dst = out_grad_mat->subMatrix(dst_begin, dst_end - dst_begin);
+      MatrixPtr src = in_grad_mat.subMatrix(begin, end - begin);
+      MatrixPtr dst = out_grad_mat.subMatrix(dst_begin, dst_end - dst_begin);
       src->addAtOffset(*dst, j * input_dim);
     }
   }
@@ -199,44 +192,36 @@ class ContextProjectionBackwardFunc : public FunctionBase {
     total_pad_ = config.get<size_t>("total_pad");
   }
 
-  void calc(const Arguments& inputs,
-            const Arguments& outputs,
-            const Arguments& inouts) override {
-    CHECK_EQ(3, static_cast<int>(inputs.size()));
-    CHECK_EQ(1, static_cast<int>(outputs.size()));
-    CHECK_EQ(0, static_cast<int>(inouts.size()));
+  void calc(const BufferArgs& inputs, const BufferArgs& outputs) override {
+    CHECK_EQ((size_t)3, inputs.size());
+    CHECK_EQ((size_t)1, outputs.size());
 
-    CHECK(outputs[0].getData() && inputs[2].getData());
-    CHECK_EQ(static_cast<int>(outputs[0].dims_.size()), 2);
-    CHECK_EQ(static_cast<int>(inputs[0].dims_.size()), 2);
-    CHECK_EQ(static_cast<int>(inputs[1].dims_.size()), 2);
-    CHECK_EQ(static_cast<int>(inputs[2].dims_.size()), 1);
+    CHECK(outputs[0].data() && inputs[2].data());
+    CHECK_EQ(outputs[0].shape().ndims(), (size_t)2);
+    CHECK_EQ(inputs[0].shape().ndims(), (size_t)2);
+    CHECK_EQ(inputs[1].shape().ndims(), (size_t)2);
+    CHECK_EQ(inputs[2].shape().ndims(), (size_t)1);
 
     /// dim of input == dim of weight
-    CHECK_EQ(inputs[0].dims_[1], inputs[1].dims_[1]);
+    CHECK_EQ(inputs[0].shape()[1], inputs[1].shape()[1]);
     /// input and output has the same batch_size
-    CHECK_EQ(inputs[0].dims_[0], outputs[0].dims_[0]);
+    CHECK_EQ(inputs[0].shape()[0], outputs[0].shape()[0]);
     /// dim of output = dim of input * context_length
-    CHECK_EQ(outputs[0].dims_[1], inputs[0].dims_[1] * context_length_);
+    CHECK_EQ(outputs[0].shape()[1], inputs[0].shape()[1] * context_length_);
 
-    auto out_grad_mat = std::make_shared<typename MatrixT<Device>::type>(
-        outputs[0].getData(), outputs[0].dims_[0], outputs[0].dims_[1]);
-    auto in_grad_mat =
-        !inputs[0].getData()
-            ? nullptr
-            : std::make_shared<typename MatrixT<Device>::type>(
-                  inputs[0].getData(), inputs[0].dims_[0], inputs[0].dims_[1]);
-    auto w_grad_mat =
-        !inputs[1].getData()
-            ? nullptr
-            : std::make_shared<typename MatrixT<Device>::type>(
-                  inputs[1].getData(), inputs[1].dims_[0], inputs[1].dims_[1]);
-    typename SequenceT<Device>::type seq_vec(
-        inputs[2].dims_[0], reinterpret_cast<int*>(inputs[2].getData()));
+    CHECK_EQ(outputs[0].getArgType(), ADD_TO);
 
-    ContextProjectionBackward<Device>(out_grad_mat.get(),
-                                      in_grad_mat ? in_grad_mat.get() : nullptr,
-                                      w_grad_mat ? w_grad_mat.get() : nullptr,
+    auto out_grad_mat = outputs[0].matrix<Device>();
+    auto in_grad_mat =
+        !inputs[0].data() ? typename Tensor<real, Device>::Matrix(nullptr, 0, 0)
+                          : inputs[0].matrix<Device>();
+    auto w_grad_mat = !inputs[1].data()
+                          ? typename Tensor<real, Device>::Matrix(nullptr, 0, 0)
+                          : inputs[1].matrix<Device>();
+    auto seq_vec = inputs[2].vector<int, Device>();
+    ContextProjectionBackward<Device>(out_grad_mat,
+                                      in_grad_mat,
+                                      w_grad_mat,
                                       seq_vec,
                                       context_length_,
                                       context_start_,
@@ -253,6 +238,7 @@ class ContextProjectionBackwardFunc : public FunctionBase {
   size_t total_pad_;
 };
 
+#if 0
 /**
  * \param inputs[0] input grad.
  * \param inputs[1] input sequence.
@@ -349,6 +335,7 @@ class ContextProjectionBackwardWeightFunc : public FunctionBase {
   size_t begin_pad_;
   size_t total_pad_;
 };
+#endif
 
 REGISTER_TYPED_FUNC(ContextProjectionForward,
                     CPU,
@@ -363,6 +350,7 @@ REGISTER_TYPED_FUNC(ContextProjectionForward,
 REGISTER_TYPED_FUNC(ContextProjectionBackward,
                     GPU,
                     ContextProjectionBackwardFunc);
+#if 0
 REGISTER_TYPED_FUNC(ContextProjectionBackwardData,
                     GPU,
                     ContextProjectionBackwardDataFunc);
@@ -370,4 +358,5 @@ REGISTER_TYPED_FUNC(ContextProjectionBackwardWeight,
                     GPU,
                     ContextProjectionBackwardWeightFunc);
 #endif
+#endif
 }  // namespace paddle
diff --git a/paddle/function/ContextProjectionOp.h b/paddle/function/ContextProjectionOp.h
index 93eb050fde35f..a558df5e072f2 100644
--- a/paddle/function/ContextProjectionOp.h
+++ b/paddle/function/ContextProjectionOp.h
@@ -31,14 +31,15 @@ namespace paddle {
  * \param[in]   is_padding        whether padding 0 or not.
  *
  */
-template <DeviceType Device>
-void ContextProjectionForward(typename MatrixT<Device>::type* output,
-                              const typename MatrixT<Device>::type* input,
-                              const typename MatrixT<Device>::type* weight,
-                              const typename SequenceT<Device>::type& sequence,
-                              size_t context_length,
-                              int context_start,
-                              size_t begin_pad);
+template <DeviceType DType>
+void ContextProjectionForward(
+    typename Tensor<real, DType>::Matrix& output,
+    const typename Tensor<real, DType>::Matrix& input,
+    const typename Tensor<real, DType>::Matrix& weight,
+    const typename Tensor<int, DType>::Vector& sequence,
+    size_t context_length,
+    int context_start,
+    size_t begin_pad);
 
 /**
  * \brief   Context Projection Backward.
@@ -53,30 +54,31 @@ void ContextProjectionForward(typename MatrixT<Device>::type* output,
  * \param[in]   is_padding        whether padding 0 or not.
  *
  */
-template <DeviceType Device>
-void ContextProjectionBackward(typename MatrixT<Device>::type* out_grad,
-                               typename MatrixT<Device>::type* in_grad,
-                               typename MatrixT<Device>::type* w_grad,
-                               const typename SequenceT<Device>::type& seq_vec,
-                               size_t context_length,
-                               int context_start,
-                               size_t begin_pad,
-                               bool is_padding,
-                               size_t total_pad);
+template <DeviceType DType>
+void ContextProjectionBackward(
+    typename Tensor<real, DType>::Matrix& out_grad,
+    typename Tensor<real, DType>::Matrix& in_grad,
+    typename Tensor<real, DType>::Matrix& w_grad,
+    const typename Tensor<int, DType>::Vector& seq_vec,
+    size_t context_length,
+    int context_start,
+    size_t begin_pad,
+    bool is_padding,
+    size_t total_pad);
 
-template <DeviceType Device>
+template <DeviceType DType>
 void ContextProjectionBackwardData(
-    typename MatrixT<Device>::type* out_grad,
-    typename MatrixT<Device>::type* in_grad,
-    const typename SequenceT<Device>::type& sequence,
+    typename Tensor<real, DType>::Matrix& out_grad,
+    typename Tensor<real, DType>::Matrix& in_grad,
+    const typename Tensor<int, DType>::Vector& sequence,
     size_t context_length,
     int context_start);
 
-template <DeviceType Device>
+template <DeviceType DType>
 void ContextProjectionBackwardWeight(
-    typename MatrixT<Device>::type* out_grad,
-    typename MatrixT<Device>::type* w_grad,
-    const typename SequenceT<Device>::type& seq_vec,
+    typename Tensor<real, DType>::Matrix& out_grad,
+    typename Tensor<real, DType>::Matrix& w_grad,
+    const typename Tensor<int, DType>::Vector& seq_vec,
     size_t context_length,
     int context_start,
     size_t total_pad,
diff --git a/paddle/function/ContextProjectionOpGpu.cu b/paddle/function/ContextProjectionOpGpu.cu
index 1ec7058f96c82..6a4a01a651041 100644
--- a/paddle/function/ContextProjectionOpGpu.cu
+++ b/paddle/function/ContextProjectionOpGpu.cu
@@ -120,20 +120,19 @@ void hl_context_projection_forward(const real* input,
 }
 
 template <>
-void ContextProjectionForward<DEVICE_TYPE_GPU>(GpuMatrix* output,
-                                               const GpuMatrix* input,
-                                               const GpuMatrix* weight,
+void ContextProjectionForward<DEVICE_TYPE_GPU>(GpuMatrix& output,
+                                               const GpuMatrix& input,
+                                               const GpuMatrix& weight,
                                                const GpuIVector& sequence,
                                                size_t context_length,
                                                int context_start,
                                                size_t begin_pad) {
-  CHECK(input && output);
-  hl_context_projection_forward(input->getData(),
+  hl_context_projection_forward(input.getData(),
                                 sequence.getData(),
-                                weight ? weight->getData() : nullptr,
-                                output->getData(),
+                                weight ? weight.getData() : nullptr,
+                                output.getData(),
                                 sequence.getSize() - 1,
-                                input->getWidth(),
+                                input.getWidth(),
                                 context_length,
                                 context_start,
                                 begin_pad);
@@ -217,17 +216,16 @@ void hl_context_projection_backward_data(real* out_grad,
 }
 
 template <>
-void ContextProjectionBackwardData<DEVICE_TYPE_GPU>(GpuMatrix* out_grad,
-                                                    GpuMatrix* in_grad,
+void ContextProjectionBackwardData<DEVICE_TYPE_GPU>(GpuMatrix& out_grad,
+                                                    GpuMatrix& in_grad,
                                                     const GpuIVector& sequence,
                                                     size_t context_length,
                                                     int context_start) {
-  CHECK(in_grad && out_grad);
-  hl_context_projection_backward_data(out_grad->getData(),
+  hl_context_projection_backward_data(out_grad.getData(),
                                       sequence.getData(),
-                                      in_grad->getData(),
+                                      in_grad.getData(),
                                       sequence.getSize() - 1,
-                                      in_grad->getWidth(),
+                                      in_grad.getWidth(),
                                       context_length,
                                       context_start);
 }
@@ -348,19 +346,18 @@ void hl_context_projection_backward_weight(real* out_grad,
 
 template <>
 void ContextProjectionBackwardWeight<DEVICE_TYPE_GPU>(
-        GpuMatrix* out_grad,
-        GpuMatrix* w_grad,
+        GpuMatrix& out_grad,
+        GpuMatrix& w_grad,
         const GpuIVector& seq_vec,
         size_t context_length,
         int context_start,
         size_t total_pad,
         size_t begin_pad) {
-  CHECK(out_grad && w_grad);
-  hl_context_projection_backward_weight(out_grad->getData(),
+  hl_context_projection_backward_weight(out_grad.getData(),
                                         seq_vec.getData(),
-                                        w_grad->getData(),
+                                        w_grad.getData(),
                                         seq_vec.getSize() - 1,
-                                        w_grad->getWidth(),
+                                        w_grad.getWidth(),
                                         total_pad,
                                         context_length,
                                         context_start,
@@ -368,16 +365,15 @@ void ContextProjectionBackwardWeight<DEVICE_TYPE_GPU>(
 }
 
 template <>
-void ContextProjectionBackward<DEVICE_TYPE_GPU>(GpuMatrix* out_grad,
-                                                GpuMatrix* in_grad,
-                                                GpuMatrix* w_grad,
+void ContextProjectionBackward<DEVICE_TYPE_GPU>(GpuMatrix& out_grad,
+                                                GpuMatrix& in_grad,
+                                                GpuMatrix& w_grad,
                                                 const GpuIVector& sequence,
                                                 size_t context_length,
                                                 int context_start,
                                                 size_t begin_pad,
                                                 bool is_padding,
                                                 size_t total_pad) {
-    CHECK(out_grad);
     if (in_grad) {
         ContextProjectionBackwardData<DEVICE_TYPE_GPU>(
                 out_grad,
diff --git a/paddle/function/CrossMapNormalOp.cpp b/paddle/function/CrossMapNormalOp.cpp
index 96a7a30eebbf0..92980c503fdaa 100644
--- a/paddle/function/CrossMapNormalOp.cpp
+++ b/paddle/function/CrossMapNormalOp.cpp
@@ -112,6 +112,8 @@ void CrossMapNormalGrad<DEVICE_TYPE_CPU>(real* inputsGrad,
 }
 
 /**
+ * \brief {o_0, o_1} = calc(i_0)
+ *
  * \param inputs[0] input value.
  * \param outputs[0] output value.
  * \param outputs[1] denoms.
@@ -125,27 +127,24 @@ class CrossMapNormalFunc : public FunctionBase {
     pow_ = config.get<real>("pow");
   }
 
-  void calc(const Arguments& inputs,
-            const Arguments& outputs,
-            const Arguments& inouts) override {
-    CHECK_EQ(1, static_cast<int>(inputs.size()));
-    CHECK_EQ(2, static_cast<int>(outputs.size()));
-    CHECK_EQ(0, static_cast<int>(inouts.size()));
-
-    CHECK_EQ(static_cast<int>(inputs[0].dims_.size()), 4);
-    for (size_t i = 0; i < inputs[0].dims_.size(); i++) {
-      CHECK_EQ(inputs[0].dims_[i], outputs[0].dims_[i]);
-      CHECK_EQ(inputs[0].dims_[i], outputs[1].dims_[i]);
-    }
+  void calc(const BufferArgs& inputs, const BufferArgs& outputs) override {
+    CHECK_EQ((size_t)1, inputs.size());
+    CHECK_EQ((size_t)2, outputs.size());
+
+    CHECK_EQ(inputs[0].shape().ndims(), (size_t)4);
+    CHECK(inputs[0].shape() == outputs[0].shape());
+    CHECK(inputs[0].shape() == outputs[1].shape());
 
-    size_t samples = inputs[0].dims_[0];
-    size_t channels = inputs[0].dims_[1];
-    size_t height = inputs[0].dims_[2];
-    size_t width = inputs[0].dims_[3];
+    CHECK_EQ(outputs[0].getArgType(), ASSIGN_TO);
+    CHECK_EQ(outputs[1].getArgType(), ASSIGN_TO);
+    size_t samples = inputs[0].shape()[0];
+    size_t channels = inputs[0].shape()[1];
+    size_t height = inputs[0].shape()[2];
+    size_t width = inputs[0].shape()[3];
 
-    CrossMapNormal<Device>(outputs[0].getData(),
-                           outputs[1].getData(),
-                           inputs[0].getData(),
+    CrossMapNormal<Device>(outputs[0].data<real>(),
+                           outputs[1].data<real>(),
+                           inputs[0].data<real>(),
                            samples,
                            channels,
                            height,
@@ -162,6 +161,8 @@ class CrossMapNormalFunc : public FunctionBase {
 };
 
 /**
+ * \brief {o_0} = calc(i_0, i_1, i_2, i_3)
+ *
  * \param inputs[0] input value.
  * \param inputs[1] output value.
  * \param inputs[2] output grad.
@@ -177,31 +178,29 @@ class CrossMapNormalGradFunc : public FunctionBase {
     pow_ = config.get<real>("pow");
   }
 
-  void calc(const Arguments& inputs,
-            const Arguments& outputs,
-            const Arguments& inouts) override {
-    CHECK_EQ(4, static_cast<int>(inputs.size()));
-    CHECK_EQ(1, static_cast<int>(outputs.size()));
-    CHECK_EQ(0, static_cast<int>(inouts.size()));
-
-    CHECK_EQ(static_cast<int>(inputs[0].dims_.size()), 4);
-    for (size_t i = 0; i < inputs[0].dims_.size(); i++) {
-      CHECK_EQ(inputs[0].dims_[i], inputs[1].dims_[i]);
-      CHECK_EQ(inputs[0].dims_[i], inputs[2].dims_[i]);
-      CHECK_EQ(inputs[0].dims_[i], inputs[3].dims_[i]);
-      CHECK_EQ(inputs[0].dims_[i], outputs[0].dims_[i]);
-    }
-
-    size_t samples = inputs[0].dims_[0];
-    size_t channels = inputs[0].dims_[1];
-    size_t height = inputs[0].dims_[2];
-    size_t width = inputs[0].dims_[3];
-
-    CrossMapNormalGrad<Device>(outputs[0].getData(),
-                               inputs[0].getData(),
-                               inputs[1].getData(),
-                               inputs[2].getData(),
-                               inputs[3].getData(),
+  void calc(const BufferArgs& inputs, const BufferArgs& outputs) override {
+    CHECK_EQ((size_t)4, inputs.size());
+    CHECK_EQ((size_t)1, outputs.size());
+
+    CHECK_EQ(inputs[0].shape().ndims(), (size_t)4);
+    CHECK(inputs[0].shape() == inputs[1].shape());
+    CHECK(inputs[0].shape() == inputs[2].shape());
+    CHECK(inputs[0].shape() == inputs[3].shape());
+    CHECK(inputs[0].shape() == outputs[0].shape());
+
+    // TODO(hedaoyuan): need support ASSIGN_TO mode.
+    CHECK_EQ(outputs[0].getArgType(), ADD_TO);
+
+    size_t samples = inputs[0].shape()[0];
+    size_t channels = inputs[0].shape()[1];
+    size_t height = inputs[0].shape()[2];
+    size_t width = inputs[0].shape()[3];
+
+    CrossMapNormalGrad<Device>(outputs[0].data<real>(),
+                               inputs[0].data<real>(),
+                               inputs[1].data<real>(),
+                               inputs[2].data<real>(),
+                               inputs[3].data<real>(),
                                samples,
                                channels,
                                height,
diff --git a/paddle/function/Function.cpp b/paddle/function/Function.cpp
index 614e76b8ac0c9..dbe3a4e9f608d 100644
--- a/paddle/function/Function.cpp
+++ b/paddle/function/Function.cpp
@@ -76,6 +76,20 @@ FuncConfig& FuncConfig::set<bool>(const std::string& key, bool v) {
   return *this;
 }
 
+void BufferArgs::addArg(const Matrix& arg,
+                        const TensorShape& shape,
+                        ArgType argType) {
+  args_.push_back(std::make_shared<BufferArg>(arg, shape, argType));
+}
+
+void BufferArgs::addArg(const CpuSparseMatrix& arg, ArgType argType) {
+  args_.push_back(std::make_shared<SparseMatrixArg>(arg, argType));
+}
+
+void BufferArgs::addArg(const GpuSparseMatrix& arg, ArgType argType) {
+  args_.push_back(std::make_shared<SparseMatrixArg>(arg, argType));
+}
+
 ClassRegistrar<FunctionBase> FunctionBase::funcRegistrar_;
 
 }  // namespace paddle
diff --git a/paddle/function/Function.h b/paddle/function/Function.h
index 9e8cbb8e48c30..249f8f9cfad58 100644
--- a/paddle/function/Function.h
+++ b/paddle/function/Function.h
@@ -16,57 +16,17 @@ limitations under the License. */
 
 #include <map>
 #include <vector>
+#include "BufferArg.h"
 #include "paddle/math/Matrix.h"
 #include "paddle/utils/ClassRegistrar.h"
 
 namespace paddle {
 
-enum DeviceType {
-  DEVICE_TYPE_UNSPECIFIED = 0,
-  DEVICE_TYPE_CPU = 1,
-  DEVICE_TYPE_GPU = 2,
-};
-
-template <DeviceType Device>
-struct MatrixT;
-
-template <>
-struct MatrixT<DEVICE_TYPE_CPU> {
-  using type = CpuMatrix;
-};
-
-template <>
-struct MatrixT<DEVICE_TYPE_GPU> {
-  using type = GpuMatrix;
-};
-
-template <DeviceType Device>
-struct SequenceT;
-
-template <>
-struct SequenceT<DEVICE_TYPE_CPU> {
-  using type = CpuIVector;
-};
-
-template <>
-struct SequenceT<DEVICE_TYPE_GPU> {
-  using type = GpuIVector;
-};
-
-typedef std::vector<size_t> Dims;
-
-class Tensor {
-public:
-  Tensor(real* data, const Dims& dim) : buf_(data), dims_(dim) {}
-
-  real* getData() const { return buf_; }
-
-  real* buf_;
-  Dims dims_;
-};
-
-typedef std::vector<Tensor> Arguments;
-
+/**
+ * Function Configuration.
+ * The argument type of Function::init.
+ * Follow-up will consider moving this data structure to Proto inside.
+ */
 class FuncConfig {
 public:
   union value {
@@ -86,15 +46,70 @@ class FuncConfig {
   std::map<std::string, value> valueMap_;
 };
 
+/**
+ * Argument type for Function::calc().
+ * A BufferArgs contains a set of BufferArg,
+ * because Function can have multiple inputs and outputs.
+ */
+class BufferArgs {
+public:
+  BufferArgs() {}
+  size_t size() const { return args_.size(); }
+
+  // add argument into BufferArgs
+  // Tensor can be Matrix, Vector, IVector.
+  // For inputs, do not need argType.
+  // For outputs, the argType needs to be specified as ASSIGN_TO or ADD_TO.
+  template <typename Tensor>
+  void addArg(const Tensor& arg, ArgType argType = UNSPECIFIED) {
+    args_.push_back(std::make_shared<BufferArg>(arg, argType));
+  }
+
+  // Add arg into BufferArgs and reshape the arg.
+  //
+  // For example, arg represents an image buffer,
+  // but Matrix can only represent a two-dimensional Tensor.
+  // So need an extra argument to describe the shape of the image buffer.
+  void addArg(const Matrix& arg,
+              const TensorShape& shape,
+              ArgType argType = UNSPECIFIED);
+
+  void addArg(const CpuSparseMatrix& arg, ArgType argType = UNSPECIFIED);
+  void addArg(const GpuSparseMatrix& arg, ArgType argType = UNSPECIFIED);
+
+  // get argument
+  const BufferArg& operator[](size_t num) const {
+    CHECK_LT(num, args_.size());
+    return *args_[num];
+  }
+
+private:
+  std::vector<BufferArgPtr> args_;
+};
+
+/**
+ * \brief Base class for Function.
+ * The basic Function implementation requires override init and calc interfaces.
+ *
+ * Function inputs are readonly, Function outputs have two modes: ASSIGN_TO
+ * and ADD_TO.
+ * If output.getArgType() == ASSIGN_TO, this is assign mode, and the calculation
+ * result of Function assigned to the output BufferArg.
+ * If output.getArgType() == ADD_TO, this is add mode, and the calculation
+ * result of Function need added to the output BufferArg.
+ *
+ * For example:
+ * ASSIGN_TO: output = Function(inputs)
+ * ADD_TO: output += Function(inputs)
+ * If Function has more than one output, each output can have different modes.
+ */
 class FunctionBase {
 public:
   virtual ~FunctionBase() {}
 
   virtual void init(const FuncConfig& config) {}
 
-  virtual void calc(const Arguments& inputs,
-                    const Arguments& outputs,
-                    const Arguments& inouts) {}
+  virtual void calc(const BufferArgs& inputs, const BufferArgs& outputs) {}
 
   static ClassRegistrar<FunctionBase> funcRegistrar_;
 };
diff --git a/paddle/function/FunctionTest.cpp b/paddle/function/FunctionTest.cpp
new file mode 100644
index 0000000000000..7ce908320a6f6
--- /dev/null
+++ b/paddle/function/FunctionTest.cpp
@@ -0,0 +1,59 @@
+/* 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 "Function.h"
+#include <gtest/gtest.h>
+
+namespace paddle {
+
+template <DeviceType DType>
+void FunctionApi(typename Tensor<real, DType>::Matrix& output,
+                 const typename Tensor<real, DType>::Matrix& input);
+
+template <>
+void FunctionApi<DEVICE_TYPE_CPU>(CpuMatrix& output, const CpuMatrix& input) {
+  EXPECT_EQ(output.getHeight(), 100);
+  EXPECT_EQ(output.getWidth(), 200);
+}
+
+template <>
+void FunctionApi<DEVICE_TYPE_GPU>(GpuMatrix& output, const GpuMatrix& input) {
+  EXPECT_EQ(output.getHeight(), 10);
+  EXPECT_EQ(output.getWidth(), 20);
+}
+
+template <DeviceType DType>
+void Function(const BufferArgs& arguments) {
+  const auto input = arguments[0].matrix<DType>();
+  auto output = arguments[1].matrix<DType>();
+  FunctionApi<DType>(output, input);
+}
+
+TEST(Function, BufferArgs) {
+  CpuMatrix cpuInput = CpuMatrix(100, 200);
+  CpuMatrix cpuOutput = CpuMatrix(100, 200);
+  BufferArgs cpuArgments;
+  cpuArgments.addArg(cpuInput);
+  cpuArgments.addArg(cpuOutput);
+  Function<DEVICE_TYPE_CPU>(cpuArgments);
+
+  GpuMatrix gpuInput = GpuMatrix(10, 20);
+  GpuMatrix gpuOutput = GpuMatrix(10, 20);
+  BufferArgs gpuArgments;
+  gpuArgments.addArg(gpuInput);
+  gpuArgments.addArg(gpuOutput);
+  Function<DEVICE_TYPE_GPU>(gpuArgments);
+}
+
+}  // namespace paddle
diff --git a/paddle/function/TensorShape.h b/paddle/function/TensorShape.h
new file mode 100644
index 0000000000000..e491e3f1d6b26
--- /dev/null
+++ b/paddle/function/TensorShape.h
@@ -0,0 +1,97 @@
+/* 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 <glog/logging.h>
+
+namespace paddle {
+
+/**
+ * TensorShape used to represent shape of normal tensor.
+ */
+class TensorShape {
+public:
+  TensorShape() : ndims_(0), nelements_(0) { initDims(0); }
+
+  TensorShape(size_t ndims) : ndims_(ndims), nelements_(1) { initDims(ndims); };
+
+  TensorShape(std::initializer_list<size_t> dims) {
+    ndims_ = dims.size();
+    initDims(ndims_);
+    dims_.assign(dims);
+    numElements();
+  };
+
+  TensorShape(const TensorShape& t)
+      : ndims_(t.ndims_), nelements_(t.nelements_) {
+    initDims(ndims_);
+    dims_.assign(t.dims_.begin(), t.dims_.end());
+  };
+
+  // get the size of specified dimension
+  size_t operator[](size_t dim) const {
+    CHECK_GE(dim, (size_t)0);
+    CHECK_LT(dim, ndims_);
+    return dims_[dim];
+  }
+
+  // set the size of specified dimension
+  void setDim(size_t dim, size_t size) {
+    CHECK_GE(dim, (size_t)0);
+    CHECK_LT(dim, ndims_);
+    dims_[dim] = size;
+    numElements();
+  }
+
+  // number of dimensions of the tensor
+  size_t ndims() const { return ndims_; }
+
+  size_t getElements() const { return nelements_; }
+
+  bool operator==(const TensorShape& t) const {
+    if (ndims() != t.ndims()) return false;
+    for (size_t i = 0; i < ndims(); i++) {
+      if (dims_[i] != t.dims_[i]) return false;
+    }
+
+    return true;
+  }
+
+  bool operator!=(const TensorShape& t) const { return !(*this == t); }
+
+private:
+  // compute number of elements
+  void numElements() {
+    nelements_ = 1;
+    for (size_t n = 0; n < ndims_; n++) {
+      nelements_ *= dims_[n];
+    }
+  }
+
+  // init dims_
+  void initDims(size_t ndims) {
+    size_t count = ndims < 4 ? 4 : ndims;
+    dims_.assign(count, 1);
+  }
+
+  // number of dimensions
+  // ndims_ may be not equeal dims_.size()
+  size_t ndims_;
+  // number of elements
+  size_t nelements_;
+  std::vector<size_t> dims_;
+};
+
+}  // namespace paddle
diff --git a/paddle/function/TensorShapeTest.cpp b/paddle/function/TensorShapeTest.cpp
new file mode 100644
index 0000000000000..45a2e106e7fc3
--- /dev/null
+++ b/paddle/function/TensorShapeTest.cpp
@@ -0,0 +1,53 @@
+/* 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 "TensorShape.h"
+#include <gtest/gtest.h>
+
+namespace paddle {
+
+TEST(TensorShape, Constructor) {
+  TensorShape t1;
+  EXPECT_EQ(t1.ndims(), 0);
+  EXPECT_EQ(t1.getElements(), 0);
+
+  TensorShape t2(3);
+  EXPECT_EQ(t2.ndims(), 3);
+  EXPECT_EQ(t2.getElements(), 1);
+
+  TensorShape t3({8, 10});
+  EXPECT_EQ(t3.ndims(), 2);
+  EXPECT_EQ(t3.getElements(), 80);
+
+  TensorShape t4(t3);
+  EXPECT_EQ(t4.ndims(), t3.ndims());
+  EXPECT_EQ(t4.getElements(), t3.getElements());
+
+  TensorShape t5({1, 2, 3, 4, 5});
+  EXPECT_EQ(t5.ndims(), 5);
+  EXPECT_EQ(t5.getElements(), 120);
+}
+
+TEST(TensorShape, GetAndSet) {
+  TensorShape t({1, 2, 3});
+  EXPECT_EQ(t.ndims(), 3);
+  EXPECT_EQ(t.getElements(), 6);
+
+  EXPECT_EQ(t[1], 2);
+  t.setDim(1, 100);
+  EXPECT_EQ(t.getElements(), 300);
+  EXPECT_EQ(t[1], 100);
+}
+
+}  // namespace paddle
diff --git a/paddle/function/TensorType.h b/paddle/function/TensorType.h
new file mode 100644
index 0000000000000..98942cff9e2ea
--- /dev/null
+++ b/paddle/function/TensorType.h
@@ -0,0 +1,121 @@
+/* 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/math/Matrix.h"
+
+namespace paddle {
+
+enum ValueType {
+  VALUE_TYPE_INT32 = 0,
+  VALUE_TYPE_FLOAT = 1,
+  VALUE_TYPE_DOUBLE = 2,
+  VALUE_TYPE_BYTE = 3
+};
+
+enum DeviceType {
+  DEVICE_TYPE_UNSPECIFIED = 0,
+  DEVICE_TYPE_CPU = 1,
+  DEVICE_TYPE_GPU = 2
+};
+
+inline int sizeOfValuType(ValueType valueType) {
+  if (valueType == VALUE_TYPE_INT32) {
+    return 4;
+  } else if (valueType == VALUE_TYPE_FLOAT) {
+    return 4;
+  } else if (valueType == VALUE_TYPE_DOUBLE) {
+    return 8;
+  } else {
+    LOG(FATAL) << "Unknown type: " << valueType;
+    return 0;
+  }
+}
+
+template <typename T>
+struct DataType;
+
+template <>
+struct DataType<float> {
+  static const ValueType value = VALUE_TYPE_FLOAT;
+};
+
+template <>
+struct DataType<double> {
+  static const ValueType value = VALUE_TYPE_DOUBLE;
+};
+
+template <>
+struct DataType<int> {
+  static const ValueType value = VALUE_TYPE_INT32;
+};
+
+namespace detail {
+
+template <typename VType, DeviceType Device>
+struct MatrixT;
+
+template <>
+struct MatrixT<real, DEVICE_TYPE_CPU> {
+  using type = CpuMatrix;
+};
+
+template <>
+struct MatrixT<real, DEVICE_TYPE_GPU> {
+  using type = GpuMatrix;
+};
+
+template <>
+struct MatrixT<int, DEVICE_TYPE_CPU> {
+  using type = void;  // Not implemented
+};
+
+template <>
+struct MatrixT<int, DEVICE_TYPE_GPU> {
+  using type = void;  // Not implemented
+};
+
+template <typename VType, DeviceType Device>
+struct VectorT;
+
+template <>
+struct VectorT<real, DEVICE_TYPE_CPU> {
+  using type = CpuVector;
+};
+
+template <>
+struct VectorT<real, DEVICE_TYPE_GPU> {
+  using type = GpuVector;
+};
+
+template <>
+struct VectorT<int, DEVICE_TYPE_CPU> {
+  using type = CpuIVector;
+};
+
+template <>
+struct VectorT<int, DEVICE_TYPE_GPU> {
+  using type = GpuIVector;
+};
+
+}  // namespace detail
+
+template <typename VType, DeviceType DType>
+struct Tensor {
+  typedef typename detail::MatrixT<VType, DType>::type Matrix;
+  typedef typename detail::VectorT<VType, DType>::type Vector;
+};
+
+}  // namespace paddle
diff --git a/paddle/function/TensorTypeTest.cpp b/paddle/function/TensorTypeTest.cpp
new file mode 100644
index 0000000000000..e50e46f3e9911
--- /dev/null
+++ b/paddle/function/TensorTypeTest.cpp
@@ -0,0 +1,64 @@
+/* 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 "TensorType.h"
+#include <gtest/gtest.h>
+
+namespace paddle {
+
+TEST(TensorType, Matrix) {
+  Tensor<real, DEVICE_TYPE_CPU>::Matrix matrix(100, 200);
+  EXPECT_EQ(matrix.getHeight(), 100);
+  EXPECT_EQ(matrix.getWidth(), 200);
+  EXPECT_EQ(matrix.getElementCnt(), 100 * 200);
+  EXPECT_EQ(matrix.useGpu(), false);
+
+  Tensor<real, DEVICE_TYPE_GPU>::Matrix testGpu(100, 200);
+  EXPECT_EQ(testGpu.useGpu(), true);
+}
+
+TEST(TensorType, Vector) {
+  Tensor<real, DEVICE_TYPE_CPU>::Vector cpuVector(100);
+  Tensor<real, DEVICE_TYPE_GPU>::Vector gpuVector(100);
+  EXPECT_EQ(cpuVector.useGpu(), false);
+  EXPECT_EQ(gpuVector.useGpu(), true);
+  EXPECT_EQ(cpuVector.getSize(), 100);
+  EXPECT_EQ(gpuVector.getSize(), 100);
+
+  Tensor<int, DEVICE_TYPE_CPU>::Vector cpuIVector(100);
+  Tensor<int, DEVICE_TYPE_GPU>::Vector gpuIVector(100);
+  EXPECT_EQ(cpuIVector.useGpu(), false);
+  EXPECT_EQ(gpuIVector.useGpu(), true);
+  EXPECT_EQ(cpuIVector.getSize(), 100);
+  EXPECT_EQ(gpuIVector.getSize(), 100);
+}
+
+TEST(TensorType, EmptyMatrix) {
+  CpuMatrix empty(nullptr, 0, 0);
+  CpuMatrix nonEmpty(10, 10);
+  EXPECT_EQ(empty.isEmpty(), true);
+  EXPECT_EQ(nonEmpty.isEmpty(), false);
+  CHECK(nonEmpty);
+  auto function = [](const CpuMatrix& matrix) {
+    if (matrix) {
+      EXPECT_NE(matrix.getData(), nullptr);
+    } else {
+      EXPECT_EQ(matrix.getData(), nullptr);
+    }
+  };
+  function(empty);
+  function(nonEmpty);
+}
+
+}  // namespace paddle
diff --git a/paddle/gserver/layers/ContextProjection.cpp b/paddle/gserver/layers/ContextProjection.cpp
index ee4db219890a1..ebcc87cbf48a3 100644
--- a/paddle/gserver/layers/ContextProjection.cpp
+++ b/paddle/gserver/layers/ContextProjection.cpp
@@ -110,9 +110,8 @@ void ContextProjection::forward() {
   size_t input_dim = in_->value->getWidth();
   size_t dim = out_->value->getWidth();
   CHECK_EQ(dim, input_dim * config_.context_length());
-  size_t batch_size = in_->value->getHeight();
-  CHECK_EQ(static_cast<int>(forward_.size()), 1)
-      << "Only one forward function here";
+  // size_t batch_size = in_->value->getHeight();
+  CHECK_EQ(forward_.size(), (size_t)1) << "Only one forward function here";
 
   REGISTER_TIMER_INFO("ContextProjectionForward", getName().c_str());
   bool is_padding = config_.trainable_padding();
@@ -120,14 +119,16 @@ void ContextProjection::forward() {
   auto w_ptr =
       state_ ? state_.get() : is_padding ? weight_->getW().get() : nullptr;
   auto start_pos = in_->sequenceStartPositions;
-  forward_[0]->calc({Tensor(in_->value->getData(), Dims{batch_size, input_dim}),
-                     Tensor(w_ptr ? w_ptr->getData() : nullptr,
-                            Dims{w_ptr ? w_ptr->getHeight() : 0, input_dim}),
-                     Tensor(reinterpret_cast<real*>(
-                                const_cast<int*>(start_pos->getData(useGpu_))),
-                            Dims{start_pos->getSize()})},
-                    {Tensor(out_->value->getData(), Dims{batch_size, dim})},
-                    {});
+
+  BufferArgs inputs;
+  BufferArgs outputs;
+  inputs.addArg(*in_->value);
+  inputs.addArg(CpuMatrix(w_ptr ? w_ptr->getData() : nullptr,
+                          w_ptr ? w_ptr->getHeight() : 0,
+                          input_dim));
+  inputs.addArg(*in_->sequenceStartPositions->getVector(useGpu_));
+  outputs.addArg(*out_->value, ADD_TO);
+  forward_[0]->calc(inputs, outputs);
 
   if (state_ && config_.context_start() < 0) {
     CHECK_EQ(1, in_->getNumSequences());
@@ -162,15 +163,17 @@ void ContextProjection::backward(const UpdateCallback& callback) {
   bool is_padding = config_.trainable_padding();
   auto start_pos = in_->sequenceStartPositions;
   auto w_ptr = is_padding ? weight_->getWGrad() : nullptr;
-  backward_[0]->calc({Tensor(in_->grad ? in_->grad->getData() : nullptr,
-                             Dims{batch_size, input_dim}),
-                      Tensor(w_ptr ? w_ptr->getData() : nullptr,
-                             Dims{w_ptr ? w_ptr->getHeight() : 0, input_dim}),
-                      Tensor(reinterpret_cast<real*>(
-                                 const_cast<int*>(start_pos->getData(useGpu_))),
-                             Dims{start_pos->getSize()})},
-                     {Tensor(out_->grad->getData(), Dims{batch_size, dim})},
-                     {});
+
+  BufferArgs inputs;
+  BufferArgs outputs;
+  inputs.addArg(CpuMatrix(
+      in_->grad ? in_->grad->getData() : nullptr, batch_size, input_dim));
+  inputs.addArg(CpuMatrix(w_ptr ? w_ptr->getData() : nullptr,
+                          w_ptr ? w_ptr->getHeight() : 0,
+                          input_dim));
+  inputs.addArg(*in_->sequenceStartPositions->getVector(useGpu_));
+  outputs.addArg(*out_->grad, ADD_TO);
+  backward_[0]->calc(inputs, outputs);
 
   if (config_.trainable_padding()) {
     weight_->getParameterPtr()->incUpdate(callback);
diff --git a/paddle/gserver/layers/NormProjectionLayer.cpp b/paddle/gserver/layers/NormProjectionLayer.cpp
index 262d757c67e10..4331009de7e98 100644
--- a/paddle/gserver/layers/NormProjectionLayer.cpp
+++ b/paddle/gserver/layers/NormProjectionLayer.cpp
@@ -59,7 +59,6 @@ bool CMRProjectionNormLayer::init(const LayerMap& layerMap,
 
 void CMRProjectionNormLayer::forward(PassType passType) {
   Layer::forward(passType);
-
   /* malloc memory for the output_ if necessary */
   /* note: one sample correspond to one row */
   MatrixPtr input = inputLayers_[0]->getOutputValue();
@@ -67,34 +66,36 @@ void CMRProjectionNormLayer::forward(PassType passType) {
   int size = getSize();
   resetOutput(batchSize, size);
 
-  MatrixPtr outV = getOutputValue();
-
   Matrix::resizeOrCreate(denoms_, batchSize, size, /* trans */ false, useGpu_);
 
-  dims_ = {batchSize, channels_, imgSizeH_, imgSizeW_};
-  forward_[0]->calc(
-      {Tensor(input->getData(), dims_)},
-      {Tensor(outV->getData(), dims_), Tensor(denoms_->getData(), dims_)},
-      {});
+  shape_ = TensorShape({batchSize, channels_, imgSizeH_, imgSizeW_});
+
+  // prepare forward arguments
+  BufferArgs inputs;
+  BufferArgs outputs;
+  inputs.addArg(*getInputValue(0), shape_);
+  outputs.addArg(*getOutputValue(), shape_, ASSIGN_TO);
+  outputs.addArg(*denoms_, shape_, ASSIGN_TO);
+
+  forward_[0]->calc(inputs, outputs);
 }
 
 void CMRProjectionNormLayer::backward(const UpdateCallback& callback) {
   (void)callback;
 
-  if (NULL == inputLayers_[0]->getOutputGrad()) {
+  if (NULL == getInputGrad(0)) {
     return;
   }
-  /* Do derivation */
-  MatrixPtr preOutGrad = inputLayers_[0]->getOutputGrad();
-  MatrixPtr localGrad = getOutputGrad();
-  MatrixPtr localOutV = getOutputValue();
-  MatrixPtr preOutV = inputLayers_[0]->getOutputValue();
-
-  backward_[0]->calc({Tensor(preOutV->getData(), dims_),
-                      Tensor(localOutV->getData(), dims_),
-                      Tensor(localGrad->getData(), dims_),
-                      Tensor(denoms_->getData(), dims_)},
-                     {Tensor(preOutGrad->getData(), dims_)},
-                     {});
+
+  // prepare backward arguments
+  BufferArgs inputs;
+  BufferArgs outputs;
+  inputs.addArg(*getInputValue(0), shape_);
+  inputs.addArg(*getOutputValue(), shape_);
+  inputs.addArg(*getOutputGrad(), shape_);
+  inputs.addArg(*denoms_, shape_);
+  outputs.addArg(*getInputGrad(0), shape_, ADD_TO);
+
+  backward_[0]->calc(inputs, outputs);
 }
 }  // namespace paddle
diff --git a/paddle/gserver/layers/NormProjectionLayer.h b/paddle/gserver/layers/NormProjectionLayer.h
index 6b2c5dde0d74d..2c0d8a3a718c4 100644
--- a/paddle/gserver/layers/NormProjectionLayer.h
+++ b/paddle/gserver/layers/NormProjectionLayer.h
@@ -41,6 +41,6 @@ class CMRProjectionNormLayer : public ResponseNormLayer {
   void backward(const UpdateCallback& callback = nullptr);
 
 protected:
-  Dims dims_;
+  TensorShape shape_;
 };
 }  // namespace paddle
diff --git a/paddle/math/Matrix.h b/paddle/math/Matrix.h
index ceac0212d25a5..dd24f8821d497 100644
--- a/paddle/math/Matrix.h
+++ b/paddle/math/Matrix.h
@@ -1091,6 +1091,10 @@ class Matrix : public BaseMatrix {
       TensorCpuApply<real>(*this, expr);
     }
   }
+
+  bool isEmpty() const { return data_ == nullptr; }
+
+  explicit operator bool() const { return !isEmpty(); }
 };
 
 inline std::ostream& operator<<(std::ostream& os, const Matrix& mat) {