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Author

Thomas Nagler

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#machine learning Preprint Oct 2026

Optimal approximation of smooth functions by ReLU neural networks

We study uniform approximation of the H\"older ball $\mathcal H_1^s([0,1]^D)$ by fully connected ReLU networks. Except in the one-dimensional Lipschitz case, existing constructions remain separated from the information-theoretic efficiency limit. This article closes the gap for every $s>0$ and $D\ge1$: networks with wi...

Thomas Nagler · 0 citations
#machine learning Preprint Oct 2026

How Well Do Prior-Data Fitted Networks Amortize Bayesian Inference?

Prior-data fitted networks (PFNs) are trained to approximate the Bayesian posterior predictive distribution (PPD) of a synthetic prior, yet results about the approximation quality are surprisingly thin. Taking an empirical risk minimization perspective, we decompose the deployment error of PFNs into prior, context, and...

M. Hulskamp, Julius Kobialka, Emanuel Sommer et al. · 0 citations

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