Convolutional Layer In Python Using Numpy

I am trying to implement a convolutional layer in Python using Numpy. The input is a 4-dimensional array of shape [N, H, W, C], where: N: Batch size H: Height of image W: Width of

Solution 1:

This a straightforward implementation of this kind of keras-like (?) convolution. It might be hard to understand for beginners because it uses a lot of broadcasting and stride tricks.

from numpy.lib.stride_tricks import as_strided
def conv2d(a, b):
    a = as_strided(a,(len(a),a.shape[1]-len(b)+1,a.shape[2]-b.shape[1]+1,len(b),b.shape[1],a.shape[3]),a.strides[:3]+a.strides[1:])
    return np.einsum('abcijk,ijkd', a, b[::-1,::-1])

BTW: if you are doing convolution with very-big kernel, use Fourier-based algorithm instead.

EDIT: The [::-1,::-1] should be removed in the case that convolution does not involve flipping the kernel first (like what's in tensorflow).

EDIT:np.tensordot(a, b, axes=3) performs much better than np.einsum("abcijk,ijkd", a, b), and is highly recommended. So, the function becomes:

from numpy.lib.stride_tricks import as_strided

def conv2d(a, b):
  Hout = a.shape[1] - b.shape[0] + 1
  Wout = a.shape[2] - b.shape[1] + 1

  a = as_strided(a, (a.shape[0], Hout, Wout, b.shape[0], b.shape[1], a.shape[3]), a.strides[:3] + a.strides[1:])

  return np.tensordot(a, b, axes=3)