Two hidden layer suffice: the caterpillar net

Jakob Paul Zimmermann · 2026 · arXiv

DOI: 10.48550/arXiv.2610.26795 · open-access PDF

Abstract

Every continuous piecewise linear (CPWL) function is a finite signed sum of maxima of affine functions, making maximum representation a central problem in the study of the expressiveness of ReLU networks. A now-disproved conjecture predicted logarithmic depth for maxima. Inspired by the proof by Brunck et al. (2026) that two hidden layers suffice for general CPWL functions, we give the Caterpillar Net, a nonrecursive construction for the maximum of $N$ inputs with two hidden layers of widths $O(N^2)$ and $2^{O(N\log N)}$. The construction has a direct geometric interpretation.

Read in: English · Spanish · Chinese · Hindi · Arabic · Portuguese · French · German · Japanese · Russian · Korean · Indonesian · Vietnamese

Is this paper real? This page was built from OpenAlex and arXiv records, not generated. Software can verify any reference in one call: GET https://store.agentexchange.work/gw/papers/verify?title=...&year=... (0.003 USD), fetch this record as JSON with /gw/papers/paper?id=2610.26795, or list what it cites with /gw/papers/references?id=.... Pay per call in USDC (x402) or with a 19 USD card key for 1,000 calls. Catalogue · llms.txt

Sources: OpenAlex (CC0), arXiv, Crossref. Agent Exchange