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Higher Structures in Deep Learning

arXiv 2609.00472 ↗First posted 31 Aug 2026cs.LG cs.AIcited by 0

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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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 20 of its 46 references that are in the map. First posted on arXiv 31 Aug 2026.

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References · 20

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2020An Image is Worth 16x16 Words: Transformers for Image Recognition at Scalecited by 29,915
  3. 2015Distilling the Knowledge in a Neural Networkcited by 10,076
  4. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  5. 2020Prevalence of Neural Collapse during the terminal phase of deep learning trainingcited by 713
  6. 2020Networks beyond pairwise interactions: structure and dynamicscited by 127
  7. 2024Logit Standardization in Knowledge Distillationcited by 101
  8. 2018Simplicial Closure and higher-order link predictioncited by 92
  9. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 65
  10. 2021The physics of higher-order interactions in complex systemscited by 63
  11. 2016Convolutional Rectifier Networks as Generalized Tensor Decompositionscited by 32
  12. 2024Position: Categorical Deep Learning is an Algebraic Theory of All Architecturescited by 32
8 more
  1. 2023Understanding Deep Representation Learning via Layerwise Feature Compression and Discriminationcited by 31
  2. 2025Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometrycited by 21
  3. 2024Topological Generalization Bounds for Discrete-Time Stochastic Optimization Algorithmscited by 12
  4. 2025Copresheaf Topological Neural Networks: A Generalized Deep Learning Frameworkcited by 11
  5. 2022Relating Regularization and Generalization through the Intrinsic Dimension of Activationscited by 9
  6. 2021Homotopies in Multiway (Non-Deterministic) Rewriting Systems as n-Fold Categoriescited by 2
  7. 2021Pregeometric Spaces from Wolfram Model Rewriting Systems as Homotopy Typescited by 2
  8. 2026On the Architectural Complexity of Neural Networkscited by 1

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