Convolution and its three modes

Convolution slides a small array — the kernel, or filter — across a larger one, multiplying and summing at each position. It is the operation at the heart of every convolutional neural network, and it is also how every blur, sharpen and edge-detection filter works.

x = np.array([1., 2., 3., 4., 5.])
k = np.array([1., 0., -1.])

np.convolve(x, k, 'full')    # length 5+3-1 = 7
np.convolve(x, k, 'valid')   # length 5-3+1 = 3
np.convolve(x, k, 'same')    # length 5

valid uses only positions where the kernel fits completely — this is why convolution shrinks an image by kernel_size - 1.

On notebook 13’s real 160×160 crop with the 3×3 Sobel kernel: valid gives 158×158, same gives 160×160, full gives 162×162.