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.
Mathematical Theory of Deep Learning
8 Pith papers cite this work. Polarity classification is still indexing.
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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.
Classification fields are infinite recursive hierarchical cluster structures generated by a local refinement rule, and a ReLU network predictor learned from finite prefixes can approximate the generator and extend it to deeper levels with exponential convergence in the completed cell metric.
Every fixed finite feedforward neural network definable in an o-minimal structure has finite sample complexity in the agnostic PAC setting.
Adaptivity never hinders uniform approximation of task families but its advantages vary across four scenarios when moving from unrestricted to ReLU-realizable regimes.
Explicit C2-smooth approximate Kolmogorov superpositions are constructed via translated dilated inner functions and piecewise C2 outer interpolation, achieving N^{-alpha} accuracy for alpha-Holder functions.
A neural-network approximation of heteroclinic dynamics, interpretable as an Amari-type neural-field system, reproduces sequential transitions among cognitive states.
Covariance-aware ridge and combined l1-l2 regularizers for neural networks yield better predictive performance and complexity control than standard penalties in simulations and applications to cooling-load prediction and leukemia classification.
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Modeling sequential cognitive states via population level cortical dynamics
A neural-network approximation of heteroclinic dynamics, interpretable as an Amari-type neural-field system, reproduces sequential transitions among cognitive states.