Neural networks emulate real-valued circuits with explicit complexity bounds controlled by gate count and structure; any definable model with a parallelization condition is a universal approximator precisely when it contains a non-affine nonlinearity.
arXiv preprint arXiv:2409.12335 , year=
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Any convex L-Lipschitz functional on a compact convex subset of a separable Hilbert space can be uniformly approximated to arbitrary accuracy by an explicit convex L-Lipschitz reconstruction from finitely many linear measurements, exactly implementable by a ReLU-MLP.
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Neural networks emulate real-valued circuits with explicit complexity bounds controlled by gate count and structure; any definable model with a parallelization condition is a universal approximator precisely when it contains a non-affine nonlinearity.
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