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Is it popular or effective to concatenate the results of mean-pooling and max-pooling, to get the invariance of the latter and the expressivity of the former?

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I haven't seen it as you describe and I don't think it would be much useful. Pooling layers are being gradually phased out of networks, because they don't seem to be that useful anymore. With the emergence of more and more conv-only architectures, I don't see that likely.

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