# Characterizing the invariances of learning algorithms using category theory

@article{Harris2019CharacterizingTI, title={Characterizing the invariances of learning algorithms using category theory}, author={Kenneth D. Harris}, journal={ArXiv}, year={2019}, volume={abs/1905.02072} }

Many learning algorithms have invariances: when their training data is transformed in certain ways, the function they learn transforms in a predictable manner. Here we formalize this notion using concepts from the mathematical field of category theory. The invariances that a supervised learning algorithm possesses are formalized by categories of predictor and target spaces, whose morphisms represent the algorithm's invariances, and an index category whose morphisms represent permutations of the…

## 2 Citations

Compositional Deep Learning

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This thesis builds a category-theoretic formalism around a class of neural networks exemplified by CycleGAN, and uses the framework to conceive a novel neural network architecture whose goal is to learn the task of object insertion and object deletion in images with unpaired data.

Category Theory in Machine Learning

- Computer ScienceArXiv
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This work aims to document the motivations, goals and common themes across these applications of category theory in machine learning, touching on gradient-based learning, probability, and equivariant learning.

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