I've recently read about maxout in slides of a lecture and in the paper.
Is maxout the same as max pooling?
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They are almost identical:
The second key reason that maxout performs well is that it improves the bagging style training phase of dropout. Note that the arguments in section 7 motivating the use of maxout also apply equally to rectified linear units (Salinas & Abbott, 1996; Hahnloser, 1998; Glorot et al., 2011). The only difference between maxout and max pooling over a set of rectified linear units is that maxout does not include a 0 in the max.
Source: Maxout Networks.
That paper of Goodfellow is a little bit cryptic. For what I understand, the max out networks let the net to find the best activation function for the specific problem. This is done through a winner take all algorithm in intermediate layers. Accidentally this kind of networks compress the information in term of paths. This means that the information is stored in the net in term weights and paths that the net create. In my opinion this is not the same as the max pooling, even though we use a winner take all in both cases, we perform a max pool in a layer to reduce the dimensionality of the problem.