For large monomial activation degree, critical points in deep fully-connected networks coincide exactly with subnetwork configurations where neurons are inactive or redundant.
Minimal Filling Architectures of Polynomial Neural Networks: Counterexamples, Frontier Search, and Defects
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abstract
We provide counterexamples to the unimodal minimal filling architecture conjecture for polynomial neural networks (PNNs) with power activation functions. Fixing the input and output widths, the conjecture states that any minimal filling architecture has unimodal widths for the hidden layers. We found counterexamples via a frontier search, recursive dimension bounds on neurovarieties, and symbolic computation. Notably, several subarchitectures of our main example exhibit large defect, in contrast with the predominantly small-defect behavior observed in prior literature.
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cs.LG 1years
2026 1verdicts
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Singular Learning and Occam's Razor in Deep Monomial Networks
For large monomial activation degree, critical points in deep fully-connected networks coincide exactly with subnetwork configurations where neurons are inactive or redundant.