Minimal Filling Architectures of Polynomial Neural Networks: Counterexamples, Frontier Search, and Defects
arXiv:2605.09609v2 Announce Type: replace 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 ob
This research is part of ongoing, incremental advancements in theoretical AI, with publication in academic venues like arXiv representing routine dissemination of findings.
While relevant for AI researchers, this specific theoretical finding on minimal filling architectures does not immediately impact strategic decision-making or broader industry trends.
The understanding of polynomial neural networks' theoretical underpinnings is slightly refined for specialists, but practical applications or widespread AI development remain unaffected.
Refined theoretical understanding of PNNs for a small subset of AI researchers.
Potentially informs future theoretical work on neural network architecture optimization in specialized domains.
No discernible third-order consequences beyond the academic research community at this time.
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