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[]->cpu_data();

  Dtype* top_data = top[]->mutable_cpu_data();

  Dtype* scale_data = scale_.mutable_cpu_data();

  int channels = bottom[]->shape(softmax_axis_);

  int dim = bottom[]->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[]->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 = ; 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 = ; j < channels; j++) {

      for (int k = ; 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_,

        , -., sum_multiplier_.cpu_data(), scale_data, ., top_data);

    // exponentiation

    caffe_exp<Dtype>(dim, top_data, top_data);

    // sum after exp

    caffe_cpu_gemv<Dtype>(CblasTrans, channels, inner_num_, .,

        top_data, sum_multiplier_.cpu_data(), ., scale_data);

    // division

    for (int j = ; 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[]->cpu_diff();

  const Dtype* top_data = top[]->cpu_data();

  Dtype* bottom_diff = bottom[]->mutable_cpu_diff();

  Dtype* scale_data = scale_.mutable_cpu_data();

  int channels = top[]->shape(softmax_axis_);

  int dim = top[]->count() / outer_num_;

  caffe_copy(top[]->count(), top_diff, bottom_diff); //先用top_diff初始化bottom_diff

  for (int i = ; 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 = ; 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_, ,

        -., sum_multiplier_.cpu_data(), scale_data, ., bottom_diff + i * dim);

  }

  // 逐点相乘

  caffe_mul(top[]->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~