mlsanityData to 7 Oct 2026

Category Theory in Machine Learning

arXiv 2106.07032 ↗First posted 13 Jun 2021cs.LGcited by 36

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Abstract (arXiv)

Over the past two decades machine learning has permeated almost every realm of technology. At the same time, many researchers have begun using category theory as a unifying language, facilitating communication between different scientific disciplines. It is therefore unsurprising that there is a burgeoning interest in applying category theory to machine learning. We aim to document the motivations, goals and common themes across these applications. We touch on gradient-based learning, probability, and equivariant learning.

Key facts. Cited by 36 papers in the map (data through 7 Oct 2026). Builds on 38 of its 108 references that are in the map. First posted on arXiv 13 Jun 2021.

Builds on

38 of 108 references.

References · 38

  1. 2020Language Models are Few-Shot Learnerscited by 32,199
  2. 2018UMAP: Uniform Manifold Approximation and Projection for Dimension Reductioncited by 2,841
  3. 2016Group Equivariant Convolutional Networkscited by 1,154
  4. 2016Geometric deep learning: going beyond Euclidean datacited by 1,042
  5. 2016An overview of gradient descent optimization algorithmscited by 1,021
  6. 2018Spherical CNNscited by 452
  7. 2018Invariant and Equivariant Graph Networkscited by 339
  8. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 296
  9. 2019Gauge Equivariant Convolutional Networks and the Icosahedral CNNcited by 262
  10. 2021Graph Neural Network for Traffic Forecasting: A Surveycited by 260
  11. 2018A General Theory of Equivariant CNNs on Homogeneous Spacescited by 223
  12. 2017An introduction to Topological Data Analysis: fundamental and practical aspects for data scientistscited by 171
26 more
  1. 2019A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statisticscited by 55
  2. 2017Backprop as Functor: A compositional perspective on supervised learningcited by 44
  3. 2021Categorical Foundations of Gradient-Based Learningcited by 44
  4. 2017Disintegration and Bayesian Inversion via String Diagramscited by 32
  5. 2018The simple essence of automatic differentiationcited by 22
  6. 2015Interactive Visualization of 2-D Persistence Modulescited by 18
  7. 2019Reverse derivative categoriescited by 15
  8. 2017A Convenient Category for Higher-Order Probability Theorycited by 14
  9. 2019Lenses and Learnerscited by 11
  10. 2020Representable Markov Categories and Comparison of Statistical Experiments in Categorical Probabilitycited by 11
  11. 2021Reverse Derivative Ascent: A Categorical Approach to Learning Boolean Circuitscited by 10
  12. 2019On Universal Approximation by Neural Networks with Uniform Guarantees on Approximation of Infinite Dimensional Mapscited by 8
  13. 2019Compositional Deep Learningcited by 7
  14. 2017A Channel-Based Perspective on Conjugate Priorscited by 6
  15. 2020Categorical Stochastic Processes and Likelihoodcited by 6
  16. 2020Learning Functors using Gradient Descentcited by 6
  17. 2019Differentiable Causal Computations via Delayed Tracecited by 5
  18. 2018Limits of bimorphic lensescited by 4
  19. 2018Fighting Redundancy and Model Decay with Embeddingscited by 3
  20. 2019Characterizing the invariances of learning algorithms using category theorycited by 3
  21. 2020Open Diagrams via Coend Calculuscited by 3
  22. 2020Functorial Manifold Learningcited by 3
  23. 2016Consistency constraints for overlapping data clusteringcited by 2
  24. 2021Flattening Multiparameter Hierarchical Clustering Functorscited by 2
  25. 2016Functorial Hierarchical Clustering with Overlapscited by 1
  26. 2018Categorical Aspects of Parameter Learningcited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 3; 2023: 12; 2024: 7; 2025: 8; 2026: 5.

36 papers.

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  1. 2022On the Power of Foundation Modelscited by 37
  2. 2023Causal models in string diagramscited by 14
  3. 2023Going Beyond Neural Network Feature Similarity: The Network Feature Complexity and Its Interpretation Using Category Theorycited by 12
  4. 2021Compositionality as we see it, everywhere around uscited by 11
  5. 2024Towards Compositional Interpretability for XAIcited by 10
  6. 2024Neural Circuit Diagrams: Robust Diagrams for the Communication, Implementation, and Analysis of Deep Learning Architecturescited by 8
  7. 2026Position: LLMs Must Use Functor-Based and RAG-Driven Bias Mitigation for Fairnesscited by 8
  8. 2023Categorical Foundations of Explainable AI: A Unifying Theorycited by 7
  9. 2023On Meta-Promptingcited by 6
  10. 2026CatRAG: Functor-Guided Structural Debiasing with Retrieval Augmentation for Fair LLMscited by 6
  11. 2022Kan Extensions in Data Science and Machine Learningcited by 3
  12. 2023A Category-theoretical Meta-analysis of Definitions of Disentanglementcited by 3
24 more
  1. 2023Active Inference in String Diagrams: A Categorical Account of Predictive Processing and Free Energycited by 3
  2. 2023From Conceptual Spaces to Quantum Concepts: Formalising and Learning Structured Conceptual Modelscited by 3
  3. 2024Pooling Image Datasets With Multiple Covariate Shift and Imbalancecited by 3
  4. 2023Categorification of Group Equivariant Neural Networkscited by 2
  5. 2023Enriching Disentanglement: From Logical Definitions to Quantitative Metricscited by 2
  6. 2024Transport of Algebraic Structure to Latent Embeddingscited by 2
  7. 2024Towards a Categorical Foundation of Deep Learning: A Surveycited by 2
  8. 2023Computing with Categories in Machine Learningcited by 1
  9. 2025An Algebraic Approach to Moralisation and Triangulation of Probabilistic Graphical Modelscited by 1
  10. 2025Logic Explanation of AI Classifiers by Categorical Explaining Functorscited by 1
  11. 2026From Mechanistic to Compositional Interpretabilitycited by 1
  12. 2022A Probabilistic Generative Model of Free Categoriescited by 0
  13. 2023Formalising and Learning a Quantum Model of Conceptscited by 0
  14. 2023Algebraic Dynamical Systems in Machine Learningcited by 0
  15. 2024Towards an Algebraic Framework For Approximating Functions Using Neural Network Polynomialscited by 0
  16. 2024Symmetry-Enriched Learning: A Category-Theoretic Framework for Robust Machine Learning Modelscited by 0
  17. 2025Developing a Foundation of Vector Symbolic Architectures Using Category Theorycited by 0
  18. 2025The Gauss-Markov Adjunction Provides Categorical Semantics of Residuals in Supervised Learningcited by 0
  19. 2025A document is worth a structured record: Principled inductive bias design for document recognitioncited by 0
  20. 2025Higher Gauge Flow Modelscited by 0
  21. 2025Disentangling Hyperedges through the Lens of Category Theorycited by 0
  22. 2025Bayesian Networks, Markov Networks, Moralisation, Triangulation: a Categorical Perspectivecited by 0
  23. 2026From Intent to Evidence: A Categorical Approach for Structural Evaluation of Deep Research Agentscited by 0
  24. 2026Weaves, Wires, and Morphisms: Formalizing and Implementing the Algebra of Deep Learningcited by 0