为了教育，我正在尝试在卷积神经网络中实现N维卷积层。
我想实现反向传播功能。但是，我不确定这样做的最有效方法。
目前，我正在使用signal.fftconvolve：
在转发步骤中，对过滤器进行卷积，内核对所有过滤器进行转发；
在反向传播步骤中，对所有过滤器的导数（在所有维度上都使用FlipAllAxes函数进行卷积）与数组（https://jefkine.com/general/2016/09/05/backpropagation-in-convolutional-neural-networks/）进行卷积并求和。输出I为每个滤镜与每个导数卷积的每个图像的总和。
我对如何使导数卷积]感到特别困惑。使用下面的类进行反向传播会导致权重大小爆炸。
用输出和滤波器对微分卷积进行编程的正确方法是什么？
编辑：
根据本文（Fast Training of Convolutional Networks through FFTs），该文献试图完全按照我的意愿去做：
前一层的导数由当前层的导数与权重的卷积给出：
dL / dy_f = dL / dx * w_f ^ T
权重的导数是导数与原始输入的卷积的分段和：
dL / dy = dL / dx * x
据我所知，我已经在下面实现了这一点。但是，这似乎没有得到预期的结果，因为我使用该层编写的网络在训练过程中表现出剧烈的波动。
import numpy as np
from scipy import signal
class ConvNDLayer:
def __init__(self,channels, kernel_size, dim):
self.channels = channels
self.kernel_size = kernel_size;
self.dim = dim
self.last_input = None
self.filt_dims = np.ones(dim+1).astype(int)
self.filt_dims[1:] = self.filt_dims[1:]*kernel_size
self.filt_dims[0]= self.filt_dims[0]*channels
self.filters = np.random.randn(*self.filt_dims)/(kernel_size)**dim
def FlipAllAxes(self, array):
sl = slice(None,None,-1)
return array[tuple([sl]*array.ndim)]
def ViewAsWindows(self, array, window_shape, step=1):
# -- basic checks on arguments
if not isinstance(array, cp.ndarray):
raise TypeError("`array` must be a Cupy ndarray")
ndim = array.ndim
if isinstance(window_shape, numbers.Number):
window_shape = (window_shape,) * ndim
if not (len(window_shape) == ndim):
raise ValueError("`window_shape` is incompatible with `arr_in.shape`")
if isinstance(step, numbers.Number):
if step < 1:
raise ValueError("`step` must be >= 1")
step = (step,) * ndim
if len(step) != ndim:
raise ValueError("`step` is incompatible with `arr_in.shape`")
arr_shape = array.shape
window_shape = np.asarray(window_shape, dtype=arr_shape.dtype))
if ((arr_shape - window_shape) < 0).any():
raise ValueError("`window_shape` is too large")
if ((window_shape - 1) < 0).any():
raise ValueError("`window_shape` is too small")
# -- build rolling window view
slices = tuple(slice(None, None, st) for st in step)
window_strides = array.strides
indexing_strides = array[slices].strides
win_indices_shape = (((array.shape -window_shape)
// step) + 1)
new_shape = tuple(list(win_indices_shape) + list(window_shape))
strides = tuple(list(indexing_strides) + list(window_strides))
arr_out = as_strided(array, shape=new_shape, strides=strides)
return arr_out
def UnrollAxis(self, array, axis):
# This so it works with a single dimension or a sequence of them
axis = cp.asnumpy(cp.atleast_1d(axis))
axis2 = cp.asnumpy(range(len(axis)))
# Put unrolled axes at the beginning
array = cp.moveaxis(array, axis,axis2)
# Unroll
return array.reshape((-1,) + array.shape[len(axis):])
def Forward(self, array):
output_shape =cp.zeros(array.ndim + 1)
output_shape[1:] = cp.asarray(array.shape)
output_shape[0]= self.channels
output_shape = output_shape.astype(int)
output = cp.zeros(cp.asnumpy(output_shape))
self.last_input = array
for i, kernel in enumerate(self.filters):
conv = self.Convolve(array, kernel)
output[i] = conv
return output
def Backprop(self, d_L_d_out, learn_rate):
d_A= cp.zeros_like(self.last_input)
d_W = cp.zeros_like(self.filters)
for i, (kernel, d_L_d_out_f) in enumerate(zip(self.filters, d_L_d_out)):
d_A += signal.fftconvolve(d_L_d_out_f, kernel.T, "same")
conv = signal.fftconvolve(d_L_d_out_f, self.last_input, "same")
conv = self.ViewAsWindows(conv, kernel.shape)
axes = np.arange(kernel.ndim)
conv = self.UnrollAxis(conv, axes)
d_W[i] = np.sum(conv, axis=0)
output = d_A*learn_rate
self.filters = self.filters - d_W*learn_rate
return output
为了教育，我正在尝试在卷积神经网络中实现N维卷积层。我想实现反向传播功能。但是，我不确定...
通常将梯度与learn_rate相乘是不够的。