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In which scenario, when assembling a CNN, would you want to have two adjacent pooling layers, without a convolutional layer in between?

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Assuming you're not referring to any particular type of pooling operation, it's possible that you could have, for example, a mean pool followed by a max or min pool. What this could do is combine the idea of reducing the dimensionality of your data from a holistic perspective with the mean pool, and then choosing the best of your averages with your max pool.

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