[jira] [Commented] (SINGA-249) Convolution BP

["wangwei (JIRA)" <ji...@apache.org>]

    [ https://issues.apache.org/jira/browse/SINGA-249?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=15521015#comment-15521015 ] 

wangwei commented on SINGA-249:
-------------------------------

1. dw is the averaged gradient over all images in the mini-batch. The average operation is conducted at the [beginning of backward|https://github.com/apache/incubator-singa/blob/master/src/model/feed_forward_net.cc#L198]. Hence, we need to aggregate dw by `dw+=..`. 
2. for each image, the forward process is  `Tensor out= Mult(weight_, col_data);` ([line 117 |https://github.com/apache/incubator-singa/blob/master/src/model/layer/convolution.cc#L117]). Hence, the backward process is `dw+ = Mult(grad_col_data, col_data.T())` (grad_col_data is grad_b in line 166.

> Convolution BP
> --------------
>
>                 Key: SINGA-249
>                 URL: https://issues.apache.org/jira/browse/SINGA-249
>             Project: Singa
>          Issue Type: Wish
>         Environment: ubuntu 14.04，singa 1.0
>            Reporter: hacker99
>
> I'm curious about how to calculate the gradient of the back propagation algorithm eg. Convolution layer. Can anyone explain to me the details of the implementation of the formula and the code? Very grateful, if there is some documents or just tell why   dw += Mult(grad_b, col_data.T())?
> #code from src/model/layer/convolution.cc
> const std::pair<Tensor, vector<Tensor>> Convolution::Backward(
>     int flag, const Tensor &grad) {
>   CHECK_EQ(grad.device()->lang(), kCpp);
>   CHECK_EQ(grad.nDim(), 4u);
>   CHECK(!buf_.empty());
>   Tensor src_data = buf_.top();
>   buf_.pop();
>   vector<Tensor> param_grad;
>   Tensor dx;
>   Tensor db, dw;
>   dx.ResetLike(src_data);
>   db.ResetLike(bias_);
>   dw.ResetLike(weight_);
>   dw.SetValue(0.0f);
>   size_t batchsize = grad.shape(0);
>   size_t imagesize = src_data.Size() / batchsize;
>   if (bias_term_) {
>     Tensor tmp1 =
>         Reshape(grad, Shape{batchsize * num_filters_,
>                             grad.Size() / (batchsize * num_filters_)});
>     Tensor tmp2(Shape{batchsize * num_filters_});
>     SumColumns(tmp1, &tmp2);
>     Tensor tmp3 = Reshape(tmp2, Shape{batchsize, num_filters_});
>     SumRows(tmp3, &db);
>   }
>   auto in_data = src_data.data<float>();
>   Tensor col_data(Shape{col_height_, col_width_});
>   float *data_col = new float[col_height_ * col_width_];
>   float *dx_b = new float[imagesize];
>   for (size_t b = 0; b < batchsize; b++) {
>     Im2col(in_data + b * imagesize, channels_, height_, width_, kernel_h_,
>            kernel_w_, pad_h_, pad_w_, stride_h_, stride_w_, data_col);
>     col_data.CopyDataFromHostPtr(data_col, col_height_ * col_width_);
>     Tensor grad_b(Shape{num_filters_, conv_height_ * conv_width_});
>     CopyDataToFrom(&grad_b, grad, grad_b.Size(), 0, b * grad_b.Size());
>     dw += Mult(grad_b, col_data.T());
>     Tensor dcol_b = Mult(weight_.T(), grad_b);
>     auto dcol_data = dcol_b.data<float>();
>     Col2im(dcol_data, channels_, height_, width_, kernel_h_, kernel_w_, pad_h_,
>            pad_w_, stride_h_, stride_w_, dx_b);
>     dx.CopyDataFromHostPtr(dx_b, imagesize, b * imagesize);
>   }
>   param_grad.push_back(dw);
>   param_grad.push_back(db);
>   delete[] data_col;
>   delete[] dx_b;
>   return std::make_pair(dx, param_grad);
> }



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