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The approximation theorem says you can approximate anything. But this is kind of meaningless in so far as you can do KNN and get an arbitrary approximation of your training data also. Proving CNN correctly extract features is, I don't think possible. Or if it is, something involving VC theory is probably the best you can do.


To prove that the KL divergence does not satisfy the triangle inequality, you just need a counterexample. Definitions KL divergence Let's first recapitulate the definition of KL divergence for discrete probability distributions $p$ and $q$ (for simplicity). $$ D_{\text{KL}}(p\parallel q) = \sum_{x\in {\mathcal {X}}} p(x)\log \left( \frac {p(x)}{q(x)} \...

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