Research
A Hand-Checkable Proof That Two Hidden ReLU Layers Compute the Maximum of Six Numbers
arXiv:2610.04256v1 Announce Type: new Abstract: Exactly computing the maximum function is a standard test case for studying depth in ReLU networks. Two hidden layers are known to suffice for up to twe
arXiv:2610.04256v1 Announce Type: new Abstract: Exactly computing the maximum function is a standard test case for studying depth in ReLU networks. Two hidden layers are known to suffice for up to twelve inputs through computer-assisted constructions. For six real inputs, we give an explicit hexagon identity whose local structure yields a self-contained analytical proof of this depth bound. The identity was found by computer-assisted search; we prove it through explicit cancellations that can be checked entirely by hand, without executing a verification program. The identity also yields an explicit network with hidden widths 17 and 41, zero biases, and rational weights.
Related
- Shallower ReLU Network Representations via Exact Linear Algebra
- Representing MAX functions using two-hidden-layer ReLU networks
Source: arXiv cs.LG | 2026-10-06