001 A cubical formalisation of topos causal models: intervention, sheaf gluing, and the intuitionistic do-calculus arXiv Paper Karen Sargsyan Jul 17 002 Learning in Infinitesimal Non-Compositional Sketches arXiv Paper Sridhar Mahadevan Jul 16 003 CAS I: A Geometric Coding Theorem arXiv Paper Romie Banerjee Jul 15 004 Agentic Skill Optimization over Lie Algebroids arXiv Paper Sridhar Mahadevan Jul 13 005 A Category Theory Account of AI Identity arXiv Paper Andrea Ferrario Jun 30 006 Compositional Dynamics in Learning and Mechanics arXiv Paper David I. Spivak Jun 27 007 Reduction of Probabilistic Chemical Reaction Networks arXiv Paper Mauricio Montes, Grégoire Sergeant-Perthuis Jun 26 008 Compositional Behavioral Semantics for State Abstraction in Reinforcement Learning arXiv Paper Yivan Zhang, Ziyan Luo et al. Jun 24 009 Infinitesimal Causality arXiv Paper Sridhar Mahadevan Jun 23 010 NeSyCat Torch: A Differentiable Tensor Implementation of Categorical Semantics for Neurosymbolic Learning arXiv Paper D. Schellhorn, Till Mossakowski et al. Jun 17 011 Operads for compositional reasoning in LLMs arXiv Paper Nathaniel Bottman, Kyle Richardson Jun 11 012 Theoretical Aspects of Lie Groupoid and Lie Algebroid Equivariant Convolutional Neural Networks arXiv Paper Michael Astwood Jun 1 013 Self-Revising Discovery Systems for Science: A Categorical Framework for Agentic Artificial Intelligence arXiv Paper F. Y. Wang, M. J. Buehler May 31 014 Learning Transfers: Kan Extensions for Neural Invariants arXiv Paper Luciano Melodia May 30 015 Graphical einops: bridging tensor networks and computation graphs arXiv Paper Vincent Wang-Mascianica, Nikhil Khatri May 29 016 Gaussian Sheaf Neural Networks arXiv Paper Antônio H. Ribeiro, Ana Luiza Tenorio et al. May 20 017 Harness Engineering as Categorical Architecture arXiv Paper B. Banu May 12 018 NeSyCat: A Monad-Based Categorical Semantics of the Neurosymbolic ULLER Framework arXiv Paper D. Schellhorn, Till Mossakowski Apr 27 019 Weaves, Wires, and Morphisms: Formalizing and Implementing the Algebra of Deep Learning arXiv Paper Vincent Abbott, Gioele Zardini Apr 8 020 From Torsors to Topoi: An Introduction with a View Toward $Σ$-Protocols in Cryptography arXiv Paper Takao Inou'e Mar 17 021 Functorial Neural Architectures from Higher Inductive Types arXiv Paper Karen Sargsyan Mar 17 022 The Theory behind UMAP? arXiv Paper David Wegmann Mar 2 023 Interactions that reshape the interfaces of the interacting parties arXiv Paper David I. Spivak Feb 20 024 Causal and Compositional Abstraction arXiv Paper Robin Lorenz et al. Feb 18 025 Can a Lightweight Automated AI Pipeline Solve Research-Level Mathematical Problems? arXiv Paper Lve Meng et al. Feb 14 026 Weisfeiler and Lehman Go Categorical arXiv Paper Seongjin Choi et al. Feb 6 027 Identifiable Equivariant Networks are Layerwise Equivariant arXiv Paper Vahid Shahverdi et al. Jan 29 028 Categorical Belief Propagation: Sheaf-Theoretic Inference via Descent and Holonomy arXiv Paper Enrique ter Horst et al. Jan 8 029 LeanCat: A Benchmark Suite for Formal Category Theory in Lean (Part I: 1-Categories) arXiv Paper Rongge Xu et al. Dec 31, 2025 030 Bayesian Networks, Markov Networks, Moralisation, Triangulation: a Categorical Perspective arXiv Paper A. Lorenzin, Fabio Zanasi Dec 10, 2025 031 Categorical Framework for Quantum-Resistant Zero-Trust AI Security arXiv Paper I. Cherkaoui et al. Nov 25, 2025 032 Internalizing Tools as Morphisms in Graded Transformers arXiv Paper Tony Shaska Nov 21, 2025 033 Quantum Concept Music Score from Quantum Picturalism: Musical Incarnation of a Bell-Pair under Measurements arXiv Paper Rakhat-Bi Abdyssagin et al. Oct 6, 2025 034 Transparent Semantic Spaces: A Categorical Approach to Explainable Word Embeddings arXiv Paper Ares Fabregat-Hernández, Javier Palanca et al. Aug 28, 2025 035 Macroeconomic Foundation of Monetary Accounting by Diagrams of Categorical Universals arXiv Paper Renée Menéndez et al. Aug 19, 2025 036 Modeling GRNs with a Probabilistic Categorical Framework arXiv Paper Yiyang Jia et al. Aug 16, 2025 037 Graph Lineages and Skeletal Graph Products arXiv Paper Eric Mjolsness et al. Jul 31, 2025 038 Recursive Reward Aggregation arXiv Paper Yuting Tang et al. Jul 11, 2025 039 A Category-Theoretic Analysis of Conformal Prediction arXiv Paper Michele Caprio Jul 6, 2025 040 The Gauss-Markov Adjunction Provides Categorical Semantics of Residuals in Supervised Learning arXiv Paper M. Kamiura Jul 3, 2025 041 Unraveling the iterative CHAD arXiv Paper Fernando Lucatelli Nunes et al. May 21, 2025 042 Accelerating Machine Learning Systems via Category Theory: Applications to Spherical Attention for Gene Regulatory Networks arXiv Paper Vincent Abbott, Kotaro Kamiya et al. May 14, 2025 043 Categorical and geometric methods in statistical, manifold, and machine learning arXiv Paper Hông Vân Lê, Ha Quang Minh et al. May 6, 2025 044 Aggregating time-series and image data: functors and double functors arXiv Paper Joscha Diehl Apr 7, 2025 045 An Algebraic Approach to Moralisation and Triangulation of Probabilistic Graphical Models arXiv Paper A. Lorenzin, Fabio Zanasi Mar 14, 2025 046 The Relativity of Causal Knowledge arXiv Paper Gabriele D'Acunto, C. Battiloro Mar 13, 2025 047 Learning Is a Kan Extension arXiv Paper Matthew Pugh et al. Feb 19, 2025 048 The magnitude of categories of texts enriched by language models arXiv Paper Tai-Danae Bradley, Juan Pablo Vigneaux Jan 11, 2025 049 DiagrammaticLearning: A Graphical Language for Compositional Training Regimes arXiv Paper Mason Lary, Richard Samuelson et al. Jan 2, 2025 050 Towards structure-preserving quantum encodings arXiv Paper Arthur J. Parzygnat et al. Dec 23, 2024 051 Order Theory in the Context of Machine Learning arXiv Paper Eric Dolores-Cuenca, Aldo Guzmán-Sáenz et al. Dec 8, 2024 052 Variational methods for Learning Multilevel Genetic Algorithms using the Kantorovich Monad arXiv Paper Jonathan Warrell, Francesco Alesiani et al. Nov 14, 2024 053 Why quantum state verification cannot be both efficient and secure: a categorical approach arXiv Paper Fabian Wiesner et al. Nov 7, 2024 054 Towards a Categorical Foundation of Deep Learning: A Survey arXiv Paper Francesco Riccardo Crescenzi Oct 7, 2024 055 Reduce, Reuse, Recycle: Categories for Compositional Reinforcement Learning arXiv Paper Georgios Bakirtzis, M. Savvas et al. Aug 23, 2024 056 IsUMap: Manifold Learning and Data Visualization leveraging Vietoris-Rips filtrations arXiv Paper Lukas Silvester Barth, Fatemeh Fahimi et al. Jul 25, 2024 057 A Pattern Language for Machine Learning Tasks arXiv Paper Benjamin Rodatz, Ian Fan et al. Jul 2, 2024 058 On the Anatomy of Attention arXiv Paper Nikhil Khatri et al. Jul 2, 2024 059 Towards Compositional Interpretability for XAI arXiv Paper Sean Tull, Robin G. Lorenz et al. Jun 25, 2024 060 Automating Transfer of Robot Task Plans using Functorial Data Migrations arXiv Paper Angeline Aguinaldo, Evan Patterson et al. Jun 22, 2024