aiqbench analysis
This research introduces Spectral Higher-Order Neural Networks (SHONNs), a framework that mitigates parameter explosion in neural hypergraphs through spectral-based weight sharing. By demonstrating superior performance on challenging N-bit parity tasks, the study establishes sharp expressivity bounds for these architectures while reducing computational costs. The work advances theoretical understanding of higher-order learning models and their practical scalability without relying on external hardware or policy shifts.
Spectral Higher-Order Neural Networks Have Sharp Expressivity Bounds
arXiv:2607.19042v1 Announce Type: cross 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.
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.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2607.19042 [cs.LG]
(or arXiv:2607.19042v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2607.19042 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 230 words
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