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Let's assume that we have a regression problem. Our input is just binarized image that contains a single rectangle and we want to predict just a float number. Actually, this floating-point number depends on rectangle angle, rectangle size and rectangle location. Is this problem can be solved by a neural network?

I think, it can not be solved by a neural network, because rectangle angle, size and location are latent variables and without learning these latent variable, above problem can not be solved. What do you think?

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It can definitely be learned, the question is the approach. It would be expensive and difficult from a modeling directive to do this Densely, so usually convolutions are the way to go. An issue with convolutions is that is generally focuses on equivariant and relative features, so if you need specific location within the approach might be worth the simple alteration of CoordConv. Regardless of approach, that type of input to output is possible, you just have to consider it when modeling.

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