Weaves, Wires, and Morphisms: Formalizing and Implementing the Algebra of Deep Learning
Despite deep learning models running well-defined mathematical functions, we lack a formal mathematical framework for describing model architectures. Ad-hoc notation, diagrams, and pseudocode poorly handle nonlinear broadcasting and the relationship between individual components and composed models. This paper introduces a categorical framework for deep learning models that formalizes broadcasting through the novel axis-stride and array-broadcasted categories. This allows the mathematical function underlying architectures to be precisely expressed and manipulated in a compositional manner. These mathematical definitions are translated into human manageable diagrams and machine manageable ...
| Authors | Vincent Abbott, Gioele Zardini |
|---|---|
| Primary category | cs.LG |
| Published | 8 April 2026 |
| Last updated at source | 12 August 2026 |
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