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arXiv · 2607.19042

Spectral Higher-Order Neural Networks Have Sharp Expressivity Bounds

Gianluca Peri·Diego Febbe·Duccio Fanelli
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Abstract

Neural hypergraphs are a natural generalization of neural networks, the reference models in modern machine learning. Yet, their deployment has proven demanding: the number of weighted hyperedges required leads to an intractable parameter explosion. However, a novel parametrization that leverages spectral attributes for neural hypergraphs has been recently proposed, that enables to recycle parameters via a weight sharing scheme and consequently yields a significant reduction of the associated computational cost. Preliminary tests carried out on spectral higher-order architectures pointed to meaningful improvements in both performance and interpretability. Building on these results, we advance the benchmarking efforts by evaluating the spectral higher order framework on N-bit parity tasks, a well-established testbed known to be particularly challenging. As we will convincingly argue, Spectral Higher-Order Neural Networks (SHONNs) possess a versatile and highly tunable hypothesis space.

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Gianluca Peri, Diego Febbe, Duccio Fanelli. 2026-07-21. Spectral Higher-Order Neural Networks Have Sharp Expressivity Bounds. https://arxiv.org/abs/2607.19042

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