ReLU networks approximate traceable definable subsets of the unit cube in L^p with size O(ε^{-p(n-1)/m}) and yield ERM learning rates of order N^{-m/(m+pn-p)} for hinge loss under uniform component bounds.
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LHSD estimates local intrinsic dimension in high-D spaces by spectral filtering of the log-density Hessian via SLQ to isolate zero-curvature tangent directions.
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Fast approximation and learning of binary classification tasks in o-minimal structures using ReLU neural networks
ReLU networks approximate traceable definable subsets of the unit cube in L^p with size O(ε^{-p(n-1)/m}) and yield ERM learning rates of order N^{-m/(m+pn-p)} for hinge loss under uniform component bounds.
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Local Hessian Spectral Filtering for Robust Intrinsic Dimension Estimation
LHSD estimates local intrinsic dimension in high-D spaces by spectral filtering of the log-density Hessian via SLQ to isolate zero-curvature tangent directions.