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This article explains Tambara modules in category theory, their relation to monoidal functors and profunctor optics, and illustrates the concepts using Haskell code, drawing from a recent paper by Mateusz Stroiński.
An article explaining the concept of actegories in category theory and their role in programming optics such as lenses and prisms, with Haskell implementations.
This article delves into transfer learning from the perspective of category theory, proposing deep manifold theory. It argues that neural networks learn relational structures through attribute-free numerical computation, thereby enabling cross-domain transfer, and explains the internal logic of classification.
This paper develops a typed interface correspondence between Gene Regulatory Networks and agentic software systems using polynomial functors and wiring diagrams, mapping five biological motifs to composable software design patterns to address reliability and security challenges in autonomous AI agents.
A tweet shares a personal anecdote about explaining object-oriented programming to a humanities student, who insightfully summarized it as 'classification', leading the author to discover applied category theory and a related course.
An online course on applied category theory taught by John Baez, based on the book 'Seven Sketches in Compositionality', covering ordered sets, resource theories, and databases through a series of lecture notes.
This paper introduces a categorical framework for transfer learning using Kan extensions, defining a transfer discrepancy that compares target invariants against those forced by a prescribed task transformation. It proves finite cokernel formulas for chain complexes and persistence modules and validates the approach on neural latent point clouds.
This paper introduces a categorical framework for distinguishing genuine scientific discovery from mere retrieval or search in self-improving AI agents, using category theory to formalize regime transitions. The authors demonstrate the framework with a protein mechanics example where an agent's accuracy drops as it tackles harder problems, but its theory compresses more data, indicating real discovery.
An introductory literate Haskell document exploring the relationship between coalgebras and automata, demonstrating how state machines can be modeled using fold and unfold operations within category theory.
CQL is an open-source tool that uses category theory to perform database operations such as querying, migrating, and integrating data with built-in correctness guarantees through theorem proving.
The Cognitive Categorical Transformer (CCT) augments GPT-2 Small with category-theoretic components, achieving a 12% relative perplexity reduction on WikiText-103 under matched training conditions, with simplicial message passing responsible for 84% of the improvement.
This paper proposes a structural and dynamical framework for modeling cognitive processes using iterative state transformations and semantic equivalence, integrating dynamical systems, category theory, and feedback mechanisms to model cognition as a process evolving toward stable interpretations.
A deep dive into the theoretical foundations of Church encoding, connecting it with parametricity and the Yoneda lemma in the context of System F and polymorphic lambda calculus.
This blog post provides a toy Haskell implementation of profunctor equipment, including natural transformations and composition, to make category-theoretic concepts accessible to programmers.
This article announces a working draft book 'Category Theory for Tiny ML in Rust' and a public workshop introducing a tiny ML pipeline using Rust and category theory, aimed at making machine learning structure explicit through typed transformations.