# Higher Structures in Deep Learning

arXiv: https://arxiv.org/abs/2609.00472 · HTML: https://mlsanity.com/paper/2609.00472/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 46 references that are in the map.
- First posted on arXiv 31 Aug 2026.

## Builds on (most cited first, 20 of 20)

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- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Networks beyond pairwise interactions: structure and dynamics](https://mlsanity.com/paper/2006.01764/) (2020)
- [Logit Standardization in Knowledge Distillation](https://mlsanity.com/paper/2403.01427/) (2024)
- [Simplicial Closure and higher-order link prediction](https://mlsanity.com/paper/1802.06916/) (2018)
- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [The physics of higher-order interactions in complex systems](https://mlsanity.com/paper/2110.06023/) (2021)
- [Convolutional Rectifier Networks as Generalized Tensor Decompositions](https://mlsanity.com/paper/1603.00162/) (2016)
- [Understanding Deep Representation Learning via Layerwise Feature Compression and Discrimination](https://mlsanity.com/paper/2311.02960/) (2023)
- [Position: Categorical Deep Learning is an Algebraic Theory of All Architectures](https://mlsanity.com/paper/2402.15332/) (2024)
- [Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry](https://mlsanity.com/paper/2501.18915/) (2025)
- [Topological Generalization Bounds for Discrete-Time Stochastic Optimization Algorithms](https://mlsanity.com/paper/2407.08723/) (2024)
- [Copresheaf Topological Neural Networks: A Generalized Deep Learning Framework](https://mlsanity.com/paper/2505.21251/) (2025)
- [Relating Regularization and Generalization through the Intrinsic Dimension of Activations](https://mlsanity.com/paper/2211.13239/) (2022)
- [Homotopies in Multiway (Non-Deterministic) Rewriting Systems as n-Fold Categories](https://mlsanity.com/paper/2105.10822/) (2021)
- [Pregeometric Spaces from Wolfram Model Rewriting Systems as Homotopy Types](https://mlsanity.com/paper/2111.03460/) (2021)
- [On the Architectural Complexity of Neural Networks](https://mlsanity.com/paper/2605.04325/) (2026)

## Abstract (arXiv)

We provide an expository introduction on the importance of higher-arity tensor operations to deep learning. Then, we conduct a novel empirical investigation of higher-arity phenomenon in trained neural networks, introduce a hypergraphical generalization of the multilayer perceptron, and explore connections to evolutionary algorithms. We conclude with a discussion of promising directions for future research.