The convolution filter in CNN is a generalized linear model (GLM) for the underlying data patch. What is the intuition behind this statement?

Question

Lin's Network in Network paper (https://arxiv.org/pdf/1312.4400v3.pdf) posits that the convolution filter in a CNN is akin to a GLM.

How is the filter acting like a GLM on the matrix?

Thanks!

Answer 1

When you apply a convolutional filter to a patch you are doing a linear dot product and then applying a non-linear activation function. Both CNN filters and GLMs do the linear dot product and the non-linear activation function in CNNs is analogous to the non-linear link function in GLMs.