I want to know if this is the correct way of propagating the error back. (in1, in2, mode'full', axesNone) source Convolve two N-dimensional arrays using the overlap-add method.
SCIPY CONVOLVE FULL
I need to calculate the error delta in layer l, so for that I'm performing a convolution between the kernel and the error delta of the l+1 layer (having then to multiply the gradients of layer l), and performing a valid convolution gives obviously an error delta whose dimensions don't match with the l layer activation, but it does doing a full convolution (figured out just by chance). This question comes from the need of having to propagate back the error delta between two convolutional layers. from scipy import array, zeros, signal from scipy.fftpack import fft, ifft, convolve def conv (f, g): transform f and g to frequency domain F fft (f) G. In the field of CNNs, the convolution is always explained as an operation to "reduce" the dimensions of an input image in order to extract its features. I tried to write my own circular convolution function in python using the fact that for two signals f and g we have. It's hard to get an understanding or juts an intuition by the result, and just by the description of the mode parameter and looking for literature about convolution operation. Using the same image and kernel, the operation gives: In : convolve2d(image, kernel).shape What I cannot find even an intuition for is the full mode (which the documentation refers as The output is the full discrete linear convolution of the inputs.). The following gif would explain the operation in the same mode: Convolve in1 and in2 with output size determined by mode, and boundary conditions determined by boundary and fillvalue. In : assert (convolve2d(image, kernel, mode="same") = convolve2d(padded_image, kernel, mode="valid")).all() 2d 2d(in1, in2, mode'full', boundary'fill', fillvalue0) source Convolve two 2-dimensional arrays. In : padded_image = np.pad(image, (2, 2)) Also, that same is just the same, but with zero padding, i.e.: In : import numpy as np
I've figured out, just by comparing results and shapes, that the valid mode corresponds to the operation the previous gif shows and that every place refers as "convolution". Checking the documentation, it mentions three different modes: full, valid and same. I'm using 2d instead of my own implementation for performance reasons.
The convolution operation in order to extract features that is described in literature and posts used for this is quite intuitive and easy to understand (shown by the next gif), and even trivial to implement in a naive way: I'm learning about convolutional neural networks.
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