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Nonsmooth Optimisation and neural networks
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In this paper, we study neural networks from the point of view of nonsmooth optimisation, namely, quasidifferential calculus. We restrict ourselves to the case of uniform approximation by a neural network without hidden layers, the activation functions are restricted to continuous strictly increasing functions. We develop an algorithm for computing the approximation with one hidden layer through a step-by-step procedure. The nonsmooth analysis techniques demonstrated their efficiency. In particular, they partially explain why the developed step-by-step procedure may run without any objective function improvement after just one step of the procedure.
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KKT-based optimality conditions for neural network approximation
KKT-based necessary optimality conditions for one-hidden-layer neural networks under L1 and L_infinity losses are expressed as convex set intersections, with the L_infinity conditions containing a sign error.
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