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In her book Artificial Intelligence - A Guide for Thinking Humans, Melanie Mitchell explains that convolutional neural networks fail to build a useful model for these two classes of images, yielding chance classification for unseen images.

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Image from: https://www.foundalis.com/res/bps/bongard/p057.htm

This surprises me because convolutional networks look very close to the idea embedded in the images: they can detect an object regardless of its position. If splitted in two convenient regions, and taking any of them as a filter, the other region would be perfectly detected in the sameness case, and would yield a low match in the different class.

How should this additional step of splitting be added to the convnet classifier to be able to model sameness?

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  • $\begingroup$ Thanks. Do you mean attention as in transformers? $\endgroup$
    – Jaume Oliver Lafont
    Commented Mar 31, 2023 at 14:19
  • $\begingroup$ Without the splitting, I think that convolving the negative image with itself, then normalizing the maximum wrt the energy of the image, yields about 1/2 for sameness and close to 0 for different. $\endgroup$
    – Jaume Oliver Lafont
    Commented Mar 31, 2023 at 21:40
  • $\begingroup$ Yes. So in this scheme (ACNN, autoconvolutional neural networks), one single parameter is to be learned, the threshold to separate classes. This would be translation invariant, but not wrt rotation or size change. $\endgroup$
    – Jaume Oliver Lafont
    Commented Apr 1, 2023 at 10:49

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