cs.LG · 2609.00472 Copy arXiv ID · Aug 31, 2026 Save Higher Structures in Deep Learning Authors: Michael L. Roberts , Carlos Zapata Carratalá. Nicholas J. Cooper , Lijun Chen , François G. Meyer , Danna Gurari
Organizations: Combinatorial Labs · SEMF/Independent Researcher · University of Colorado Boulder
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.
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May 5, 2026 · cs.LG J/K move · Enter open · S save
Nicholas J. Cooper, François G. Meyer, Michael L. Roberts, Carlos Zapata-Carratalá +2
Combinatorial Labs · University of Colorado Boulder · SEMF/Independent Researcher
We introduce a unified theoretical framework for the rigorous analysis and systematic construction of deep neural networks (DNNs). This framework addresses a gap in existing theory by explicitly modeling the structure of tensor operations -- lower level information that is often abstracted. Our framework enables two novel objectives: (1) analysis of the evolution of architectural complexity over deep learning history, and (2) automatic construction of novel architectures based on new types of tensor operations. Our study of DNNs introduced over the past 40 years reveals a connection between groundbreaking architectures and increases in different types of architectural complexity. Moreover, we identify several large classes of higher complexity architectures that have not yet been explored. We then collect a dataset of 3,000+ higher complexity architectures, which we publicly release at: https://github.com/combinatoriallabs/ArchitecturalComplexity.