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Wen-Tao Huang

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#machine learning Preprint Sep 2026

Neural Approximation by Function Composition: Rigidity and Doubly Exponential Convergence

A rigidity theorem is established: for continuous piecewise linear generators with a finite number of segments, any $C^3$ function that can be represented in this way is at most quadratic, which demonstrates how generator dynamics and remainder estimates govern depth allocation and approximation rates of deep neural...

Wen-Tao Huang, Hai-Zhang Zhang · 0 citations

Preprint Aug 2026

Exact-Support Counterexamples to Euclidean-to-Spherical Transfer of Positive Definiteness in Even Dimensions

For every odd integer $d\geq3$, a continuous function $\varphi\colon[0,\infty)\to\mathbb R$ supported in $[0,\pi]$ and isotropic positive definite on $\mathbb R^d$ remains so on $\mathbb S^d$. In even dimensions, recent work shows that this transfer fails under every prescribed positive upper bound on the support. We p...

Wen-Tao Huang, Hai-Zhang Zhang · 0 citations