Strategic PAC learnability from geometric definability
Yuval Filmus, Shay Moran, Elizaveta Nesterova, Nir Rosenfeld, Alexander Shlimovich
NeuroIPS 2026
Consider a hypothesis class of shapes in $\mathbb R^d$. What happens to its VC dimension if we slightly expand all hypotheses in the class, with respect to some metric? It turns out that it can explode from 1 to infinity. In this paper, we show that this unfortunate phenomenon doesn’t happen if the class and the metric are definable in first-order logic with $\exp$.
@inproceedings{FMNRS26,
title = {Strategic {PAC} learnability from geometric definability},
booktitle = {The Fortieth Annual Conference on Neural Information Processing Systems (NeuroIPS 2026)},
author = {Yuval Filmus and Shay Moran and Elizaveta Nesterova and Nir Rosenfeld and Alexander Shlimovich},
year = {2026}}
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