Spectral Higher-Order Neural Networks
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914431642894336 |
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| author | Peri, Gianluca Carletti, Timoteo Fanelli, Duccio Febbe, Diego |
| author_facet | Peri, Gianluca Carletti, Timoteo Fanelli, Duccio Febbe, Diego |
| contents | Neural networks are fundamental tools of modern machine learning. The standard paradigm assumes binary interactions (across feedforward linear passes) between inter-tangled units, organized in sequential layers. Generalized architectures have been also designed that move beyond pairwise interactions, so as to account for higher-order couplings among computing neurons. Higher-order networks are however usually deployed as augmented graph neural networks (GNNs), and, as such, prove solely advantageous in contexts where the input exhibits an explicit hypergraph structure. Here, we present Spectral Higher-Order Neural Networks (SHONNs), a new algorithmic strategy to incorporate higher-order interactions in general-purpose, feedforward, network structures. SHONNs leverages a reformulation of the model in terms of spectral attributes. This allows to mitigate the common stability and parameter scaling problems that come along weighted, higher-order, forward propagations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_28420 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral Higher-Order Neural Networks Peri, Gianluca Carletti, Timoteo Fanelli, Duccio Febbe, Diego Machine Learning Artificial Intelligence Neural networks are fundamental tools of modern machine learning. The standard paradigm assumes binary interactions (across feedforward linear passes) between inter-tangled units, organized in sequential layers. Generalized architectures have been also designed that move beyond pairwise interactions, so as to account for higher-order couplings among computing neurons. Higher-order networks are however usually deployed as augmented graph neural networks (GNNs), and, as such, prove solely advantageous in contexts where the input exhibits an explicit hypergraph structure. Here, we present Spectral Higher-Order Neural Networks (SHONNs), a new algorithmic strategy to incorporate higher-order interactions in general-purpose, feedforward, network structures. SHONNs leverages a reformulation of the model in terms of spectral attributes. This allows to mitigate the common stability and parameter scaling problems that come along weighted, higher-order, forward propagations. |
| title | Spectral Higher-Order Neural Networks |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2603.28420 |