caffe中 softmax 函数的前向传播和反向传播

1.前向传播：

template <typename Dtype>
void SoftmaxLayer<Dtype>::Forward_cpu(const vector<Blob<Dtype>*>& bottom,
    const vector<Blob<Dtype>*>& top) {
  const Dtype* bottom_data = bottom[0]->cpu_data();
  Dtype* top_data = top[0]->mutable_cpu_data();
  Dtype* scale_data = scale_.mutable_cpu_data();
  int channels = bottom[0]->shape(softmax_axis_);
  int dim = bottom[0]->count() / outer_num_; //dim表示要分类的类别数，count()得到的是总共的输入Blob数，outer_num_得到的是是每一类的Blob数
  caffe_copy(bottom[0]->count(), bottom_data, top_data); //先将输入拷贝到输出缓冲区
  // We need to subtract the max to avoid numerical issues, compute the exp,
  // and then normalize，减去最大值，避免数值问题，计算指数，归一化
  for (int i = 0; i < outer_num_; ++i) {
    // 初始化scale_的data域为第一个平面，其中scale用来存放临时计算结果
    caffe_copy(inner_num_, bottom_data + i * dim, scale_data);
    for (int j = 0; j < channels; j++) {
      for (int k = 0; k < inner_num_; k++) {
        scale_data[k] = std::max(scale_data[k],
            bottom_data[i * dim + j * inner_num_ + k]);
      }
    }
    // 输出缓冲区减去最大值
    caffe_cpu_gemm<Dtype>(CblasNoTrans, CblasNoTrans, channels, inner_num_,
        1, -1., sum_multiplier_.cpu_data(), scale_data, 1., top_data);
    // exponentiation
    caffe_exp<Dtype>(dim, top_data, top_data);
    // sum after exp
    caffe_cpu_gemv<Dtype>(CblasTrans, channels, inner_num_, 1.,
        top_data, sum_multiplier_.cpu_data(), 0., scale_data);
    // division
    for (int j = 0; j < channels; j++) {
      caffe_div(inner_num_, top_data, scale_data, top_data);
      top_data += inner_num_;
    }
  }
}

一般的我们有top[0]来存放数据，top[1]来存放标签（对于bottom也一样）

2.反向传播：

template <typename Dtype>
void SoftmaxLayer<Dtype>::Backward_cpu(const vector<Blob<Dtype>*>& top,
    const vector<bool>& propagate_down,
    const vector<Blob<Dtype>*>& bottom) {
  const Dtype* top_diff = top[0]->cpu_diff();
  const Dtype* top_data = top[0]->cpu_data();
  Dtype* bottom_diff = bottom[0]->mutable_cpu_diff();
  Dtype* scale_data = scale_.mutable_cpu_data();
  int channels = top[0]->shape(softmax_axis_);
  int dim = top[0]->count() / outer_num_;
  caffe_copy(top[0]->count(), top_diff, bottom_diff); //先用top_diff初始化bottom_diff
  for (int i = 0; i < outer_num_; ++i) {
    // 计算top_diff和top_data的点积，然后从bottom_diff中减去该值
    for (int k = 0; k < inner_num_; ++k) {
      scale_data[k] = caffe_cpu_strided_dot<Dtype>(channels,
          bottom_diff + i * dim + k, inner_num_,
          top_data + i * dim + k, inner_num_);
    }
    // 减值
    caffe_cpu_gemm<Dtype>(CblasNoTrans, CblasNoTrans, channels, inner_num_, 1,
        -1., sum_multiplier_.cpu_data(), scale_data, 1., bottom_diff + i * dim);
  }
  // 逐点相乘
  caffe_mul(top[0]->count(), bottom_diff, top_data, bottom_diff);
}

解释：

补充：最后部分，Zi!=Zj和Zi=Zj部分写反了，大家注意一下~