                   const framework::Tensor& input, const int axis,
                   std::vector<framework::Tensor>& outputs) {
     // TODO(zcd): Add input data validity checking
-    int num = outputs.size();
-    int input_row = 1;
+    int o_num = outputs.size();
+    int out_row = 1;
     auto dim_0 = outputs[0].dims();
     for (int i = 0; i < axis; ++i) {
-      input_row *= dim_0[i];
-    }
-
-    int output_col_0 = outputs[0].numel() / input_row;
-    int input_col = 0;
+      out_row *= dim_0[i];
+    }
+
+    int out_col = outputs[0].numel() / out_row;
+    int in_col = 0, in_row = out_row;
     bool sameShape = true;
 
-    framework::Vector<int16_t> outputs_data(num * sizeof(T*) / 2);
-    framework::Vector<int> outputs_cols(num + 1);
+    framework::Vector<int16_t> outputs_data(o_num * sizeof(T*) / 2);
+    framework::Vector<int> outputs_cols(o_num + 1);
+    T** outputs_ptr = reinterpret_cast<T**>(outputs_data.data());
+
     outputs_cols[0] = 0;
-    T** outputs_ptr = reinterpret_cast<T**>(outputs_data.data());
-
-    for (int i = 0; i < num; ++i) {
-      int t_col = outputs[i].numel() / input_row;
+    for (int i = 0; i < o_num; ++i) {
+      int t_col = outputs[i].numel() / out_row;
       if (sameShape) {
-        if (t_col != output_col_0) sameShape = false;
+        if (t_col != out_col) sameShape = false;
       }
-      input_col += t_col;
-      outputs_cols[i + 1] = input_col;
+      in_col += t_col;
+      outputs_cols[i + 1] = in_col;
       outputs_ptr[i] = outputs[i].data<T>();
     }
 
-    T** outs_gpu =
+    T** dev_out_gpu_data =
         reinterpret_cast<T**>(outputs_data.CUDAMutableData(context.GetPlace()));
-    const int* outs_col_gpu = outputs_cols.CUDAData(context.GetPlace());
 
     // computation
     const int kThreadsPerBlock = 1024;
     int block_cols = kThreadsPerBlock;
-    if (input_col < kThreadsPerBlock) {  // block_cols is aligned by 32.
-      block_cols = ((input_col + 31) >> 5) << 5;
+    if (in_col < kThreadsPerBlock) {  // block_cols is aligned by 32.
+      block_cols = ((in_col + 31) >> 5) << 5;
     }
     int block_rows = kThreadsPerBlock / block_cols;
     dim3 block_size = dim3(block_cols, block_rows, 1);

}

template <typename T>
__global__ void KernelConcat(T** inputs, const int input_col,
                             const int output_rows, const int output_cols,
                             T* output) {
  int tid_x = blockIdx.x * blockDim.x + threadIdx.x;
  for (; tid_x < output_cols; tid_x += blockDim.x * gridDim.x) {
    int split = tid_x * 1.0 / input_col;
    int in_offset = tid_x - split * input_col;
    T* input_ptr = inputs[split];
    int tid_y = blockIdx.y * blockDim.y + threadIdx.y;
    for (; tid_y < output_rows; tid_y += blockDim.y * gridDim.y) {
      output[tid_y * output_cols + tid_x] =
          input_ptr[tid_y * input_col + in_offset];
    }
  }
}

template <typename T>
__global__ void KernelConcatGrad(const T* input, const int input_row,
                                 const int input_col, const int* output_cols,
                                 int col_size, T** outputs) {
  int tid_x = blockIdx.x * blockDim.x + threadIdx.x;
  int segment = upper_bound<int>(output_cols, col_size, tid_x) - 1;
  int curr_offset = output_cols[segment];
  int curr_segment = segment;
  for (; tid_x < input_col; tid_x += blockDim.x * gridDim.x) {
    T curr_col_offset;
    while ((curr_col_offset = output_cols[curr_segment + 1]) <= tid_x) {
      curr_offset = curr_col_offset;
      ++curr_segment;
    }

    int local_col = tid_x - curr_offset;
    int segment_width = curr_col_offset - curr_offset;
    T* output_ptr = outputs[curr_segment];
    int tid_y = blockIdx.y * blockDim.y + threadIdx.y;
    for (; tid_y < input_row; tid_y += blockDim.y * gridDim.y)
      output_ptr[tid_y * segment_width + local_col] =
          input[tid_y * input_col + tid_x];
  }
}

template <typename T>
__global__ void KernelConcatGrad(const T* input, const int input_row,
                                 const int input_col, const int output_col,
                                 T** outputs) {
  int tid_x = blockIdx.x * blockDim.x + threadIdx.x;
  for (; tid_x < input_col; tid_x += blockDim.x * gridDim.x) {
    int split = tid_x / output_col;
    int in_offset = tid_x - split * output_col;
    T* output_ptr = outputs[split];
    int tid_y = blockIdx.y * blockDim.y + threadIdx.y;
    for (; tid_y < input_row; tid_y += blockDim.y * gridDim.y)
      output_ptr[tid_y * output_col + in_offset] =
          input[tid_y * input_col + tid_x];
  }
}


                  const std::vector<framework::Tensor>& input, const int axis,
                  framework::Tensor* output) {
    // TODO(zcd): Add input data validity checking
    int in_num = input.size();
    int in_row = 1;
    auto dim_0 = input[0].dims();
    for (int i = 0; i < axis; ++i) {
      in_row *= dim_0[i];
    }
    int in_col = input[0].numel() / in_row;
    int out_row = in_row, out_col = 0;

    framework::Vector<int16_t> inputs_data(in_num * sizeof(T*) / 2);
    framework::Vector<int> inputs_col(in_num + 1);
    T** inputs_ptr = reinterpret_cast<T**>(inputs_data.data());

    inputs_col[0] = 0;
    bool sameShape = true;
    for (int i = 0; i < in_num; ++i) {
      int t_cols = input[i].numel() / in_row;
      if (sameShape) {
        if (t_cols != in_col) sameShape = false;
      }
      out_col += t_cols;
      inputs_col[i + 1] = out_col;
      inputs_ptr[i] = const_cast<T*>(input[i].data<T>());
    }

    T** dev_ins_data =
        reinterpret_cast<T**>(inputs_data.CUDAMutableData(context.GetPlace()));

    // computation
    // set the thread block and grid according to CurrentDeviceId
    const int kThreadsPerBlock = 1024;
    int block_cols = kThreadsPerBlock;
    if (out_col < kThreadsPerBlock) {  // block_cols is aligned by 32.
      block_cols = ((out_col + 31) >> 5) << 5;
    }
    int block_rows = kThreadsPerBlock / block_cols;
    dim3 block_size = dim3(block_cols, block_rows, 1);
