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There are programming languages that allow you to verify a proof by induction. For example, I used Coq, but I'm sure there are also others.


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It is possible for some classes of problems. For instance, WolframAlpha can generate an induction proof to the problem posed in the question. According to the author of this proof generator, he built a library of pattern-matched proofs to generate the proofs. More details about his approach can be find in his write-up about the problem. Other alternative (...


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Basic feed forward neural nets (MLPs) are essentially just computing sequences of matrix multiplications (with nonlinear activations in between), so this is in fact easy to code "directly" like you mentioned. The more difficult part is computing the gradients with respect to the parameter matrices (usually with backpropagation). However there ...


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