deformable_conv_v1_op.h

// Copyright (c) 2019 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.
//
// Part of the following code in this file refs to
// https://github.com/msracver/Deformable-ConvNets/blob/master/faster_rcnn/operator_cxx/deformable_convolution.cu
//
// Copyright (c) 2017 Microsoft
// Licensed under The Apache-2.0 License [see LICENSE for details]
// \file deformable_psroi_pooling.cu
// \brief
// \author Yi Li, Guodong Zhang, Jifeng Dai

#pragma once
#include <algorithm>
#include <vector>
#include "paddle/fluid/framework/op_registry.h"
#include "paddle/fluid/operators/deformable_conv_func.h"
#include "paddle/fluid/operators/deformable_conv_op.h"
#include "paddle/fluid/operators/math/blas.h"
#include "paddle/fluid/operators/math/math_function.h"

namespace paddle {
namespace operators {

using Tensor = framework::Tensor;
using CPUDeviceContext = platform::CPUDeviceContext;

template <typename T>
void DeformableCol2imCPUKernel(
    const int num_kernels, const T* data_col, const T* data_offset,
    const int channels, const int height, const int width, const int kernel_h,
    const int kernel_w, const int pad_h, const int pad_w, const int stride_h,
    const int stride_w, const int dilation_h, const int dilation_w,
    const int channel_per_deformable_group, const int batch_size,
    const int deformable_group, const int height_col, const int width_col,
    T* grad_im) {
  for (int thread = 0; thread < num_kernels; thread++) {
    const int j = (thread / width_col / height_col / batch_size) % kernel_w;
    const int i =
        (thread / width_col / height_col / batch_size / kernel_w) % kernel_h;
    const int c =
        thread / width_col / height_col / batch_size / kernel_w / kernel_h;

    const int deformable_group_index = c / channel_per_deformable_group;

    int w_out = thread % width_col;
    int h_out = (thread / width_col) % height_col;
    int b = (thread / width_col / height_col) % batch_size;
    int w_in = w_out * stride_w - pad_w;
    int h_in = h_out * stride_h - pad_h;

    const T* data_offset_ptr = data_offset +
                               (b * deformable_group + deformable_group_index) *
                                   2 * kernel_h * kernel_w * height_col *
                                   width_col;
    const int data_offset_h_ptr =
        ((2 * (i * kernel_w + j)) * height_col + h_out) * width_col + w_out;
    const int data_offset_w_ptr =
        ((2 * (i * kernel_w + j) + 1) * height_col + h_out) * width_col + w_out;
    const T offset_h = data_offset_ptr[data_offset_h_ptr];
    const T offset_w = data_offset_ptr[data_offset_w_ptr];
    const T cur_inv_h_data = h_in + i * dilation_h + offset_h;
    const T cur_inv_w_data = w_in + j * dilation_w + offset_w;

    const T cur_top_grad = data_col[thread];
    const int cur_h = static_cast<int>(cur_inv_h_data);
    const int cur_w = static_cast<int>(cur_inv_w_data);
    for (int dy = -2; dy <= 2; dy++) {
      for (int dx = -2; dx <= 2; dx++) {
        if (cur_h + dy >= 0 && cur_h + dy < height && cur_w + dx >= 0 &&
            cur_w + dx < width && abs(cur_inv_h_data - (cur_h + dy)) < 1 &&
            abs(cur_inv_w_data - (cur_w + dx)) < 1) {
          int cur_bottom_grad_pos =
              ((b * channels + c) * height + cur_h + dy) * width + cur_w + dx;
          T weight =
              DmcnGetGradientWeight(cur_inv_h_data, cur_inv_w_data, cur_h + dy,
                                    cur_w + dx, height, width);

          *(grad_im + cur_bottom_grad_pos) =
              *(grad_im + cur_bottom_grad_pos) + weight * cur_top_grad;
        }
      }
    }
  }
}

template <typename T>
inline void DeformableCol2imCPU(const platform::CPUDeviceContext& ctx,
                                const T* data_col, const T* data_offset,
                                const std::vector<int64_t> im_shape,
                                const std::vector<int64_t> col_shape,
                                const std::vector<int64_t> kernel_shape,
                                const std::vector<int> pad,
                                const std::vector<int> stride,
                                const std::vector<int> dilation,
                                const int deformable_group, T* grad_im) {
  int channel_per_deformable_group = im_shape[0] / deformable_group;
  int num_kernels = col_shape[0] * col_shape[1] * col_shape[2] * col_shape[3];

  DeformableCol2imCPUKernel(
      num_kernels, data_col, data_offset, im_shape[0], im_shape[1], im_shape[2],
      kernel_shape[2], kernel_shape[3], pad[0], pad[1], stride[0], stride[1],
      dilation[0], dilation[1], channel_per_deformable_group, col_shape[1],
      deformable_group, col_shape[2], col_shape[3], grad_im);
}

template <typename T>
void DeformableCol2imCoordCPUKernel(
    const int num_kernels, const T* data_col, const T* data_im,
    const T* data_offset, const int channels, const int height, const int width,
    const int kernel_h, const int kernel_w, const int pad_h, const int pad_w,
    const int stride_h, const int stride_w, const int dilation_h,
    const int dilation_w, const int channel_per_deformable_group,
    const int batch_size, const int offset_channels, const int deformable_group,
    const int height_col, const int width_col, T* grad_offset) {
  for (int i = 0; i < num_kernels; i++) {
    T val = 0, mval = 0;
    const int w = i % width_col;
    const int h = (i / width_col) % height_col;
    const int c = (i / width_col / height_col) % offset_channels;
    const int b = (i / width_col / height_col) / offset_channels;

    const int deformable_group_index = c / (2 * kernel_h * kernel_w);
    const int col_step = kernel_h * kernel_w;
    int cnt = 0;
    const T* data_col_ptr = data_col +
                            deformable_group_index *
                                channel_per_deformable_group * batch_size *
                                width_col * height_col;
    const T* data_im_ptr = data_im +
                           (b * deformable_group + deformable_group_index) *
                               channel_per_deformable_group / kernel_h /
                               kernel_w * height * width;
    const T* data_offset_ptr = data_offset +
                               (b * deformable_group + deformable_group_index) *
                                   2 * kernel_h * kernel_w * height_col *
                                   width_col;

    const int offset_c = c - deformable_group_index * 2 * kernel_h * kernel_w;

    for (int col_c = offset_c / 2; col_c < channel_per_deformable_group;
         col_c += col_step) {
      const int col_pos =
          (((col_c * batch_size + b) * height_col) + h) * width_col + w;
      const int bp_dir = offset_c % 2;

      int j = (col_pos / width_col / height_col / batch_size) % kernel_w;
      int i =
          (col_pos / width_col / height_col / batch_size / kernel_w) % kernel_h;
      int w_out = col_pos % width_col;
      int h_out = (col_pos / width_col) % height_col;
      int w_in = w_out * stride_w - pad_w;
      int h_in = h_out * stride_h - pad_h;
      const int data_offset_h_ptr =
          (((2 * (i * kernel_w + j)) * height_col + h_out) * width_col + w_out);
      const int data_offset_w_ptr =
          (((2 * (i * kernel_w + j) + 1) * height_col + h_out) * width_col +
           w_out);
      const T offset_h = data_offset_ptr[data_offset_h_ptr];
      const T offset_w = data_offset_ptr[data_offset_w_ptr];
      T inv_h = h_in + i * dilation_h + offset_h;
      T inv_w = w_in + j * dilation_w + offset_w;
      if (inv_h <= -1 || inv_w <= -1 || inv_h >= height || inv_w >= width) {
        inv_h = inv_w = -2;
      } else {
        mval += data_col_ptr[col_pos] *
                DmcnIm2colBilinear(data_im_ptr + cnt * height * width, width,
                                   height, width, inv_h, inv_w);
      }
      const T weight = DmcnGetCoordinateWeight(
          inv_h, inv_w, height, width, data_im_ptr + cnt * height * width,
          width, bp_dir);
      val += weight * data_col_ptr[col_pos];
      cnt += 1;
    }
    grad_offset[i] = val;
  }
}

template <typename T>
inline void DeformableCol2imCoordCPU(
    const platform::CPUDeviceContext& ctx, const T* data_col, const T* data_im,
    const T* data_offset, const std::vector<int64_t> im_shape,
    const std::vector<int64_t> col_shape,
    const std::vector<int64_t> kernel_shape, const std::vector<int> paddings,
    const std::vector<int> strides, const std::vector<int> dilations,
    const int deformable_groups, T* grad_offset) {
  int num_kernels = 2 * kernel_shape[2] * kernel_shape[3] * col_shape[1] *
                    col_shape[2] * col_shape[3] * deformable_groups;
  int channel_per_deformable_group = col_shape[0] / deformable_groups;

  DeformableCol2imCoordCPUKernel(
      num_kernels, data_col, data_im, data_offset, im_shape[0], im_shape[1],
      im_shape[2], kernel_shape[2], kernel_shape[3], paddings[0], paddings[1],
      strides[0], strides[1], dilations[0], dilations[1],
      channel_per_deformable_group, col_shape[1],
      2 * kernel_shape[2] * kernel_shape[3] * deformable_groups,
      deformable_groups, col_shape[2], col_shape[3], grad_offset);
}

template <typename T>
void DeformableIm2colCPUKernel(
    const int num_kernels, const T* data_im, const T* data_offset,
    const int height, const int width, const int kernel_h, const int kernel_w,
    const int pad_h, const int pad_w, const int stride_h, const int stride_w,
    const int dilation_h, const int dilation_w,
    const int channel_per_deformable_group, const int batch_size,
    const int num_channels, const int deformable_group, const int height_col,
    const int width_col, T* data_col) {
  for (int i = 0; i < num_kernels; i++) {
    const int w_col = i % width_col;
    const int h_col = (i / width_col) % height_col;
    const int b_col = (i / width_col) / height_col % batch_size;
    const int c_im = (i / width_col / height_col) / batch_size;
    const int c_col = c_im * kernel_h * kernel_w;

    const int deformable_group_index = c_im / channel_per_deformable_group;

    const int h_in = h_col * stride_h - pad_h;
    const int w_in = w_col * stride_w - pad_w;

    T* data_col_ptr =
        data_col +
        ((c_col * batch_size + b_col) * height_col + h_col) * width_col + w_col;
    const T* data_im_ptr =
        data_im + (b_col * num_channels + c_im) * height * width;
    const T* data_offset_ptr =
        data_offset +
        (b_col * deformable_group + deformable_group_index) * 2 * kernel_h *
            kernel_w * height_col * width_col;

    for (int i = 0; i < kernel_h; ++i) {
      for (int j = 0; j < kernel_w; ++j) {
        const int data_offset_h_ptr =
            ((2 * (i * kernel_w + j)) * height_col + h_col) * width_col + w_col;
        const int data_offset_w_ptr =
            ((2 * (i * kernel_w + j) + 1) * height_col + h_col) * width_col +
            w_col;

        const T offset_h = data_offset_ptr[data_offset_h_ptr];
        const T offset_w = data_offset_ptr[data_offset_w_ptr];
        T val = static_cast<T>(0);
        const T h_im = h_in + i * dilation_h + offset_h;
        const T w_im = w_in + j * dilation_w + offset_w;
        if (h_im > -1 && w_im > -1 && h_im < height && w_im < width) {
          val =
              DmcnIm2colBilinear(data_im_ptr, width, height, width, h_im, w_im);
        }
        *data_col_ptr = val;
        data_col_ptr += batch_size * height_col * width_col;
      }
    }
  }
}

template <typename T>
inline void DeformableIm2colCPU(const platform::CPUDeviceContext& ctx,
                                const T* data_im, const T* data_offset,
                                const std::vector<int64_t> im_shape,
                                const std::vector<int64_t> col_shape,
                                const std::vector<int64_t> filter_shape,
                                const std::vector<int> paddings,
                                const std::vector<int> strides,
                                const std::vector<int> dilations,
                                const int deformable_groups, T* data_col) {
  int channel_per_deformable_group = im_shape[0] / deformable_groups;
  int num_kernels = im_shape[0] * col_shape[1] * col_shape[2] * col_shape[3];

  // get outputs of im2col with offset by bilinear interpolation
  DeformableIm2colCPUKernel(
      num_kernels, data_im, data_offset, im_shape[1], im_shape[2],
      filter_shape[2], filter_shape[3], paddings[0], paddings[1], strides[0],
      strides[1], dilations[0], dilations[1], channel_per_deformable_group,
      col_shape[1], im_shape[0], deformable_groups, col_shape[2], col_shape[3],
      data_col);
}

template <typename T>
class DeformableConvV1CPUKernel : public framework::OpKernel<T> {
 public:
  void Compute(const framework::ExecutionContext& ctx) const override {
    auto* input = ctx.Input<Tensor>("Input");
    auto* offset = ctx.Input<Tensor>("Offset");
    Tensor filter = *ctx.Input<Tensor>("Filter");
    Tensor* output = ctx.Output<Tensor>("Output");
    output->mutable_data<T>(ctx.GetPlace());

    auto& dev_ctx = ctx.template device_context<CPUDeviceContext>();

    const int groups = ctx.Attr<int>("groups");
    const int deformable_groups = ctx.Attr<int>("deformable_groups");
    const int im2col_step = ctx.Attr<int>("im2col_step");
    const std::vector<int> strides = ctx.Attr<std::vector<int>>("strides");
    const std::vector<int> paddings = ctx.Attr<std::vector<int>>("paddings");
    const std::vector<int> dilations = ctx.Attr<std::vector<int>>("dilations");

    const int batch_size = static_cast<int>(input->dims()[0]);

    std::vector<int64_t> filter_shape_vec(framework::vectorize(filter.dims()));
    std::vector<int64_t> output_shape_vec(framework::vectorize(output->dims()));

    // col_shape_vec: {c_i * k_h * k_w, im2col_step, o_h, o_w}
    std::vector<int64_t> col_buffer_shape_vec(filter_shape_vec.size());
    col_buffer_shape_vec[0] =
        input->dims()[1] * filter.dims()[2] * filter.dims()[3];
    col_buffer_shape_vec[1] = im2col_step;
    for (size_t j = 0; j < filter_shape_vec.size() - 2; ++j) {
      col_buffer_shape_vec[j + 2] = output_shape_vec[j + 2];
    }
    framework::DDim col_shape(framework::make_ddim(col_buffer_shape_vec));
    std::vector<int64_t> output_buffer_shape_vec(1);
    output_buffer_shape_vec[0] = batch_size * output_shape_vec[1] *
                                 output_shape_vec[2] * output_shape_vec[3];
    framework::DDim output_shape(framework::make_ddim(output_buffer_shape_vec));
    Tensor col_buffer;
    Tensor output_buffer;
    col_buffer = ctx.AllocateTmpTensor<T, CPUDeviceContext>(col_shape, dev_ctx);
    output_buffer =
        ctx.AllocateTmpTensor<T, CPUDeviceContext>(output_shape, dev_ctx);
    int64_t M = output_shape_vec[1] / groups;
    int64_t N = im2col_step * output_shape_vec[2] * output_shape_vec[3];
    int64_t K =
        input->dims()[1] * filter_shape_vec[2] * filter_shape_vec[3] / groups;

    Tensor weight_3d;
    weight_3d.ShareDataWith(filter).Resize(
        framework::make_ddim({groups, M, K}));
    Tensor col_buffer_3d;
    col_buffer_3d.ShareDataWith(col_buffer)
        .Resize(framework::make_ddim({groups, K, N}));
    Tensor output_4d;
    output_4d.ShareDataWith(output_buffer)
        .Resize(framework::make_ddim({batch_size / im2col_step, groups, M, N}));
    output_4d.mutable_data<T>(ctx.GetPlace());
    framework::DDim input_shape =
        framework::slice_ddim(input->dims(), 1, input->dims().size());
    std::vector<int64_t> input_shape_vec = framework::vectorize(input_shape);
    int input_dim = input->numel() / input->dims()[0];
    int input_offset_dim = offset->numel() / offset->dims()[0];
    auto blas = math::GetBlas<CPUDeviceContext, T>(dev_ctx);
    const T* input_ptr = input->data<T>();
    const T* offset_ptr = offset->data<T>();
    col_buffer.mutable_data<T>(ctx.GetPlace());
    T* col_buffer_ptr = col_buffer.data<T>();
    for (int i = 0; i < batch_size / im2col_step; ++i) {
      DeformableIm2colCPU(dev_ctx, input_ptr + i * im2col_step * input_dim,
                          offset_ptr + i * im2col_step * input_offset_dim,
                          input_shape_vec, col_buffer_shape_vec,
                          filter_shape_vec, paddings, strides, dilations,
                          deformable_groups, col_buffer_ptr);
      Tensor output_3d = output_4d.Slice(i, i + 1).Resize(
          framework::slice_ddim(output_4d.dims(), 1, output_4d.dims().size()));
      // get the product of pixel and weight
      for (int g = 0; g < groups; ++g) {
        Tensor weight_3d_slice =
            weight_3d.Slice(g, g + 1).Resize(framework::slice_ddim(
                weight_3d.dims(), 1, weight_3d.dims().size()));
        Tensor col_buffer_3d_slice =
            col_buffer_3d.Slice(g, g + 1).Resize(framework::slice_ddim(
                col_buffer_3d.dims(), 1, col_buffer_3d.dims().size()));
        Tensor output_3d_slice =
            output_3d.Slice(g, g + 1).Resize(framework::slice_ddim(
                output_3d.dims(), 1, output_3d.dims().size()));
        blas.MatMul(weight_3d_slice, false, col_buffer_3d_slice, false, T(1.0),
                    &output_3d_slice, T(0.0));
      }
    }
    output->ShareDataWith(output_buffer)
        .Resize(framework::make_ddim(output_shape_vec));
  }
};

template <typename T>
class DeformableConvV1GradCPUKernel : public framework::OpKernel<T> {
 public:
  void Compute(const framework::ExecutionContext& ctx) const override {
    const Tensor* output_grad =
        ctx.Input<Tensor>(framework::GradVarName("Output"));
    Tensor* input_grad = ctx.Output<Tensor>(framework::GradVarName("Input"));
    Tensor* filter_grad = ctx.Output<Tensor>(framework::GradVarName("Filter"));
    Tensor* offset_grad = ctx.Output<Tensor>(framework::GradVarName("Offset"));

    const Tensor* input = ctx.Input<Tensor>("Input");
    Tensor offset = *ctx.Input<Tensor>("Offset");
    Tensor filter = *ctx.Input<Tensor>("Filter");
    if (!input_grad && !filter_grad && !offset_grad) return;

    int groups = ctx.Attr<int>("groups");
    int deformable_groups = ctx.Attr<int>("deformable_groups");
    int im2col_step = ctx.Attr<int>("im2col_step");
    std::vector<int> strides = ctx.Attr<std::vector<int>>("strides");
    std::vector<int> paddings = ctx.Attr<std::vector<int>>("paddings");
    std::vector<int> dilations = ctx.Attr<std::vector<int>>("dilations");

    auto& dev_ctx = ctx.template device_context<CPUDeviceContext>();
    const int batch_size = static_cast<int>(input->dims()[0]);

    framework::DDim input_shape =
        framework::slice_ddim(input->dims(), 1, input->dims().size());
    std::vector<int64_t> input_shape_vec = framework::vectorize(input_shape);
    std::vector<int64_t> filter_shape_vec(framework::vectorize(filter.dims()));
    std::vector<int64_t> output_shape_vec(
        framework::vectorize(output_grad->dims()));

    std::vector<int64_t> col_buffer_shape_vec(filter_shape_vec.size());
    col_buffer_shape_vec[0] =
        input->dims()[1] * filter.dims()[2] * filter.dims()[3];
    col_buffer_shape_vec[1] = im2col_step;
    for (size_t j = 0; j < filter_shape_vec.size() - 2; ++j) {
      col_buffer_shape_vec[j + 2] = output_shape_vec[j + 2];
    }
    framework::DDim col_shape(framework::make_ddim(col_buffer_shape_vec));
    std::vector<int64_t> output_buffer_shape_vec(1);
    output_buffer_shape_vec[0] = batch_size * output_shape_vec[1] *
                                 output_shape_vec[2] * output_shape_vec[3];
    framework::DDim output_shape(framework::make_ddim(output_buffer_shape_vec));
    Tensor col_buffer;
    Tensor output_buffer;
    col_buffer = ctx.AllocateTmpTensor<T, CPUDeviceContext>(col_shape, dev_ctx);
    output_buffer =
        ctx.AllocateTmpTensor<T, CPUDeviceContext>(output_shape, dev_ctx);

    output_buffer.ShareDataWith(*output_grad);

    int64_t M =
        input_shape_vec[0] / groups * filter_shape_vec[2] * filter_shape_vec[3];
    int64_t N = im2col_step * output_shape_vec[2] * output_shape_vec[3];
    int64_t K = output_shape_vec[1] / groups;

    framework::DDim weight_3d_shape = {groups, K, M};
    framework::DDim out_grad_4d_shape = {batch_size / im2col_step, groups, K,
                                         N};
    framework::DDim col_buffer_3d_shape = {groups, M, N};
    framework::DDim filter_grad_shape = {groups, K, M};

    Tensor weight_3d;
    weight_3d.ShareDataWith(filter).Resize(weight_3d_shape);
    Tensor out_grad_4d;
    out_grad_4d.ShareDataWith(output_buffer).Resize(out_grad_4d_shape);
    Tensor col_buffer_3d;
    col_buffer_3d.ShareDataWith(col_buffer).Resize(col_buffer_3d_shape);

    math::SetConstant<CPUDeviceContext, T> set_zero;
    auto blas = math::GetBlas<CPUDeviceContext, T>(dev_ctx);

    col_buffer.mutable_data<T>(ctx.GetPlace());
    col_buffer_3d.mutable_data<T>(ctx.GetPlace());
    out_grad_4d.mutable_data<T>(ctx.GetPlace());

    int input_dim = input->numel() / input->dims()[0];
    int input_offset_dim = offset.numel() / offset.dims()[0];

    if (filter_grad) {
      filter_grad->mutable_data<T>(ctx.GetPlace());
      filter_grad->Resize(filter_grad_shape);
      set_zero(dev_ctx, filter_grad, static_cast<T>(0));
    }

    if (input_grad) {
      input_grad->mutable_data<T>(ctx.GetPlace());
      set_zero(dev_ctx, input_grad, static_cast<T>(0));
    }

    if (offset_grad) {
      offset_grad->mutable_data<T>(ctx.GetPlace());
      set_zero(dev_ctx, offset_grad, static_cast<T>(0));
    }

    for (int i = 0; i < batch_size / im2col_step; ++i) {
      Tensor out_grad_3d =
          out_grad_4d.Slice(i, i + 1).Resize(framework::slice_ddim(
              out_grad_4d.dims(), 1, out_grad_4d.dims().size()));
      for (int g = 0; g < groups; ++g) {
        Tensor weight_3d_slice =
            weight_3d.Slice(g, g + 1).Resize(framework::slice_ddim(
                weight_3d.dims(), 1, weight_3d.dims().size()));
        Tensor out_grad_3d_slice =
            out_grad_3d.Slice(g, g + 1).Resize(framework::slice_ddim(
                out_grad_3d.dims(), 1, out_grad_3d.dims().size()));
        Tensor col_buffer_3d_slice =
            col_buffer_3d.Slice(g, g + 1).Resize(framework::slice_ddim(
                col_buffer_3d.dims(), 1, col_buffer_3d.dims().size()));

        blas.MatMul(weight_3d_slice, true, out_grad_3d_slice, false, T(1.0),
                    &col_buffer_3d_slice, T(0.0));
      }
      col_buffer.Resize(col_shape);

      T* col_buffer_ptr = col_buffer.data<T>();
      const T* input_ptr = input->data<T>();
      const T* offset_ptr = offset.data<T>();

      if (offset_grad) {
        T* offset_grad_ptr = offset_grad->data<T>();
        // get grad of offset
        DeformableCol2imCoordCPU(
            dev_ctx, col_buffer_ptr, input_ptr + i * im2col_step * input_dim,
            offset_ptr + i * im2col_step * input_offset_dim, input_shape_vec,
            col_buffer_shape_vec, filter_shape_vec, paddings, strides,
            dilations, deformable_groups,
            offset_grad_ptr + i * im2col_step * input_offset_dim);
      }
      if (input_grad) {
        T* input_grad_ptr = input_grad->data<T>();
        // get grad of input
        DeformableCol2imCPU(dev_ctx, col_buffer_ptr,
                            offset_ptr + i * im2col_step * input_offset_dim,
                            input_shape_vec, col_buffer_shape_vec,
                            filter_shape_vec, paddings, strides, dilations,
                            deformable_groups,
                            input_grad_ptr + i * im2col_step * input_dim);
        input_grad->Resize(input->dims());
      }

      DeformableIm2colCPU(dev_ctx, input_ptr + i * im2col_step * input_dim,
                          offset_ptr + i * im2col_step * input_offset_dim,
                          input_shape_vec, col_buffer_shape_vec,
                          filter_shape_vec, paddings, strides, dilations,
                          deformable_groups, col_buffer_ptr);

      col_buffer_3d.Resize(col_buffer_3d_shape);

      if (filter_grad) {
        Tensor dweight_3d;
        dweight_3d = ctx.AllocateTmpTensor<T, CPUDeviceContext>(
            filter_grad_shape, dev_ctx);
        for (int g = 0; g < groups; ++g) {
          Tensor out_grad_3d_slice =
              out_grad_3d.Slice(g, g + 1).Resize(framework::slice_ddim(
                  out_grad_3d.dims(), 1, out_grad_3d.dims().size()));
          Tensor col_buffer_3d_slice =
              col_buffer_3d.Slice(g, g + 1).Resize(framework::slice_ddim(
                  col_buffer_3d.dims(), 1, col_buffer_3d.dims().size()));
          Tensor dweight_3d_slice =
              dweight_3d.Slice(g, g + 1).Resize(framework::slice_ddim(
                  dweight_3d.dims(), 1, dweight_3d.dims().size()));

          blas.MatMul(out_grad_3d_slice, false, col_buffer_3d_slice, true,
                      T(1.0), &dweight_3d_slice, T(0.0));
        }
        // update grad of weights
        FilterGradAddupCPUKernel(dweight_3d.numel(), groups, K, M,
                                 dweight_3d.data<T>(), filter_grad->data<T>());
      }
    }
    if (filter_grad) {
      filter_grad->Resize(filter.dims());
    }
  }
};

}  // namespace operators
}  // namespace paddle