xavier

xavier初始化出自论文Understanding the difficulty of training deep feedforward neural network,论文讨论的是全连接神经网络，fan_in指第i层神经元个数，fan_out指第i+1层神经元个数，但是我们的卷积神经网路是局部连接的，此时的fan_in，fan_out是什么意思呢。
在pytorch中，fan_in指kernel_height x kernel_width x in_channel. fan_out指kernel_height x kernel_width x out_channel，从局部连接的过程来看似乎并不十分合理，卷积神经网络的局部连接在感受野内仍然是全连接。fan_in=kh x kw x in_channel没什么疑问，但是fan_out应该等于out_channel更合理啊。待解答。

code，来自pytorch实现

def _calculate_fan_in_and_fan_out(tensor):
    dimensions = tensor.ndimension()
    if dimensions < 2:
        raise ValueError("Fan in and fan out can not be computed for tensor with fewer than 2 dimensions")

    if dimensions == 2:  # Linear
        fan_in = tensor.size(1)
        fan_out = tensor.size(0)
    else:
        num_input_fmaps = tensor.size(1)
        num_output_fmaps = tensor.size(0)
        receptive_field_size = 1
        if tensor.dim() > 2:
            receptive_field_size = tensor[0][0].numel()
        fan_in = num_input_fmaps * receptive_field_size
        fan_out = num_output_fmaps * receptive_field_size

    return fan_in, fan_out