Maxout networks (Goodfellow et al., 2013) make the activation itself learnable: each unit outputs the maximum of several linear functions of its input. The paper shows this family can approximate any convex function and works well with dropout.
Implement maxout_forward(x, W, b, k), computing out * k linear pieces and returning the maximum over each group of k.
W has out * k rows.Compute all pieces with one affine map, reshape to (N, out, k), then take the max over the last axis.
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