Higher Structures in Deep Learning
cs.LG, cs.AI
Submitted: 2026-08-31
Updated: 2026-08-31
Comments: 20 pages, 10 figures
License: http://creativecommons.org/licenses/by/4.0/
The gist: We provide an expository introduction on the importance of higher-arity tensor operations to deep learning.
Terminology
Abstract
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.
Sources
- Pregeometric Spaces from Wolfram Model Rewriting Systems as Homotopy Types
- Remarks to Glazek's results on n-ary groups
- A combinatorial approach to the algebra of hypermatrices
- Distilling the Knowledge in a Neural Network
- Biunit pairs in semiheaps and associated semigroups
- Understanding Deep Representation Learning via Layerwise Feature Compression and Discrimination
- Heaps of Fish: arrays, generalized associativity and heapoids
Related papers
- Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation
- AIRL-S: Unifying Reinforcement Learning and Search-Based Test-Time Scaling via Adversarial Inverse Reinforcement Learning
- Transformers as Bayesian In-Context Experimenters: Smoothness-Adaptive Efficient ATE Estimation
- Convergence issues in Relational Concept Analysis based on AOC-posets
- Beliefs Beyond Posteriors: Local-Consistency Optimisation for Bayesian Neural Networks
- Understanding Diffusion Models via Ratio-Based Function Approximation with SignReLU Networks