多项式神经网络的最小填充架构
Minimal Filling Architectures for Polynomial Neural Networks
Kevin Dao, Jose Israel Rodriguez
AI 速读 基于摘要
该文构造反例推翻“每个最小填充架构的隐藏层宽度都单峰”的猜想，并证明深度不超过三时单峰性成立。
cs.LG · math.AG
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Minimal filling architectures describe the smallest hidden-layer widths for which the neurovariety of a polynomial neural network fills its ambient function space. It was conjectured that every such architecture has unimodal hidden widths. We construct counterexamples to this conjecture using a frontier search and certify the main example through finite-field Jacobian computations and recursive dimension bounds. In the opposite direction, we prove that every minimal filling architecture of depth at most three is unimodal. A nonunimodal minimal filling architecture of depth four shows that the depth bound is sharp.