# Spectral Higher-Order Neural Networks Have Sharp Expressivity Bounds

arXiv: https://arxiv.org/abs/2607.19042 · HTML: https://mlsanity.com/paper/2607.19042/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 13 references that are in the map.
- First posted on arXiv 21 Jul 2026.

## Builds on (most cited first, 7 of 7)

- [Simplicial Neural Networks](https://mlsanity.com/paper/2010.03633/) (2020)
- [Deep Polynomial Neural Networks](https://mlsanity.com/paper/2006.13026/) (2020)
- [Augmenting Deep Classifiers with Polynomial Neural Networks](https://mlsanity.com/paper/2104.07916/) (2021)
- [Machine learning in spectral domain](https://mlsanity.com/paper/2005.14436/) (2020)
- [Estimating Global Input Relevance and Enforcing Sparse Representations with a Scalable Spectral Neural Network Approach](https://mlsanity.com/paper/2406.01183/) (2024)
- [Deterministic versus stochastic dynamical classifiers: opposing random adversarial attacks with noise](https://mlsanity.com/paper/2409.13470/) (2024)
- [Spectral Higher-Order Neural Networks](https://mlsanity.com/paper/2603.28420/) (2026)

## Abstract (arXiv)

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.