Layer 4 · Foundations

Convolutional Networks

The math of discrete convolution, output-shape formulas, parameter counting, and translation equivariance.

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A 2D discrete convolution (as used in deep learning, technically a cross-correlation) between input $I$ and kernel $K$ of size $k \times k$ is:

(I * K) [i, j] = u = 0 \sum k - 1 v = 0 \sum k - 1 I [i + u, j + v] K [u, v]