Category Theoretic Approaches to Machine Learning

Many of papers are in multiple fields and some of these fields overlap. Let me know what's missing! (preferably by creating a pull request)

Survey papers

• Category Theory in Machine Learning

Deep Learning

• Categorical Foundations of Gradient-Based Learning
• Backprop as Functor
• Lenses and Learners
• Reverse Derivative Ascent
• Dioptics
• Learning Functors using Gradient Descent (longer version here)
• Compositionality for Recursive Neural Networks
• Deep neural networks as nested dynamical systems
• Neural network layers as parametric spans

Differentiable programming / automatic differentiation

• Differentiable Causal Computations via Delayed Trace
• Simple Essence of Automatic Differentiation
• Reverse Derivative Categories
• Towards formalizing and extending differential programming using tangent categories

Probability theory

• Markov categories
• Infinite products and zero-one laws in categorical probability
• A Convenient Category for Higher-Order Probability Theory
• Bimonoidal Structure of Probability Monads
• Representable Markov Categories and Comparison of Statistical Experiments in Categorical Probability

Bayesian/Causal inference

• A category theory framework for Bayesian Learning
• Causal Theories: A Categorical Perspective on Bayesian Networks
• Bayesian machine learning via category theory
• A Categorical Foundation for Bayesian probability
• Bayesian Open Games
• Causal Inference by String Diagram Surgery
• Disintegration and Bayesian Inversion via String Diagrams
• Categorical Stochastic Processes and Likelihood
• Bayesian Updates Compose Optically
• Automatic Backward Filtering Forward Guiding for Markov processes and graphical models
• A Channel-Based Perspective on Conjugate Priors

Topological Data Analysis

• On Characterizing the Capacity of Neural Networks using Algebraic Topology
• Persistent-Homology-based Machine Learning and its Applications - A Survey
• Topological Expresivenss of Neural Networks

Metric space magnitude

• Approximating the convex hull via metric space magnitude
• Practical applications of metric space magnitude and weighting vectors
• Weighting vectors for machine learning: numerical harmonic analysis applied to boundary detection
• The magnitude vector of images

Blog posts

• Neural Networks, Types, and Functional Programming
• Towards Categorical Foundations of Learning

Automata Learning

• Automata Learning: A Categorical Perspective
• A Categorical Framework for Learning Generalised Tree Automata

Misc

• Graph Neural Networks are Dynamic Programmers
• Generalized Convolution and Efficient Language Recognition
• Learning as Change Propagation with Delta Lenses
• From Open Learners to Open Games
• Learners Languages
• A Constructive, Type-Theoretic Approach to Regression via Global Optimisation
• Natural Graph Networks
• Local Permutation Equivariance For Graph Neural Networks
• Characterizing the invariances of learning algorithms using category theory
• Functorial Manifold Learning
• Sheaf Neural Networks
• Sheaf Neural Networks with Connection Laplacians
• Diegetic representation of feedback in open games
• Assessing the Unitary RNN as an End-to-End Compositional Model of Syntax