Category Theory

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20 papers1 paper in the last four weeks, with none the four weeks before. 0.0% of all new papers.

PRISM: A Category-Theoretic Framework for Measuring and Refining Multimodal Analogies
Oct 1, 2026Mirella Zeisler, Ojas Shirekar, Mircea Licǎ +1Cross-Modal Alignment Multimodal Reasoning
Delft University of Technology
Categorical AI phenomenology: A first-person approach
Aug 19, 2026Robert PrentnerCategory Theory Machine Consciousness
Institute of Humanities, ShanghaiTech University, No. 393 Middle Huaxia Road, Shanghai, 201120, China · Association for Mathematical Consciousness Science, Geschwister-Scholl-Platz 1, Munich, 80539, Germany
To Describe or Construct Statistical Learning Models Using the Category-theoretical Language
Aug 4, 2026Congwei SongStatistical Learning Theory Category Theory
A cubical formalisation of topos causal models: intervention, forcing, and a contextuality obstruction
Jul 17, 2026Karen SargsyanCausal World Models Causal Intervention
Institute of Chemistry, Academia Sinica, Taipei, Taiwan
Learning in Infinitesimal Non-Compositional Sketches
Jul 16, 2026Sridhar MahadevanCategory Theory
Adobe Research · University of Massachusetts, Amherst
A Category Theory Account of AI Identity
Jun 30, 2026Andrea FerrarioCategory Theory
Institute of Biomedical Ethics and History of Medicine, University of Zürich, Zürich, Switzerland · SUPSI, Dalle Molle Institute for Artificial Intelligence (IDSIA), Lugano, Switzerland · ETH Zürich, Zürich, Switzerland
Compositional Dynamics in Learning and Mechanics
Jun 27, 2026David I. SpivakDynamical Systems Hamiltonian Dynamics
Infinitesimal Causality
Jun 23, 2026Sridhar MahadevanStructural Causal Models Causal Inference
Adobe Research and University of Massachusetts, Amherst
A Categorial and Sheaf-Theoretic Semantics for Autonomic Component Ensembles
Jun 17, 2026Manuel Hernández, Eduardo Sánchez-SotoFormal Verification Multi-Agent Systems
Comonadic Morphophonology: A Compositional Framework for Context-Dependent Morphological Rules in Finnish
May 27, 2026Yongseok JangMorphological Analysis Category Theory
Independent Researcher
The Cognitive Categorical Transformer: Category-Theoretic Inductive Biases for Language Modeling
May 22, 2026Al KariDecoder-Only Language Models Message Passing Neural Networks
Manceps Inc.
A Dynamical Framework for Cognitive Processes Based on Transformations and Semantic Equivalence
Apr 29, 2026Carlo Cattani, Dioneia Motta Monte-SerratDynamical Systems Cognitive Modeling
Engineering School, DEIM, University of Tuscia, (VT), 01100, Italy · Department of Physics, University of Sao Paulo, USP; Department of Law, University of Ribeirao Preto, Unaerp, Brazil.
Working Paper: Towards Schema-based Learning from a Category-Theoretic Perspective
Apr 12, 2026Pablo de los Riscos, Fernando J. Corbacho, Michael A. ArbibCategory Theory Cognitive Architectures for AI Agents
Cognodata I+D & Universidad Autonoma de Madrid · University of California San Diego
Working Paper: Towards a Category-theoretic Comparative Framework for Artificial General Intelligence
Mar 30, 2026Pablo de los Riscos, Fernando J. Corbacho, Michael A. ArbibCategory Theory Artificial General Intelligence
Cognodata R+D & Universidad Autonoma de Madrid · University of California San Diego
From Intent to Evidence: A Categorical Approach for Structural Evaluation of Deep Research Agents
Mar 26, 2026Shuoling Liu, Zhiquan Tan, Kun Yi +6Category Theory Deep Research Agents
The Hong Kong University of Science and Technology · E Fund Management Co., Ltd. · The Hong Kong Polytechnic University
Coalgebras for categorical deep learning: Representability and universal approximation
Mar 3, 2026Dragan MašulovićEquivariant Representation Learning Invariant Representation Learning
University of Novi Sad, Faculty of Sciences Department of Mathematics and Informatics Trg Dositeja Obradovića 3, 21000 Novi Sad, Serbia
The Theory behind UMAP?
Mar 2, 2026David WegmannCategory Theory Dimensionality Reduction
University of Erlangen-Nuremberg
Interactions that reshape the interfaces of the interacting parties
Feb 20, 2026David I. SpivakCategory Theory
Causal and Compositional Abstraction
Feb 18, 2026Robin Lorenz, Sean TullCategory Theory Causal Abstraction
Quantinuum, London, United Kingdom
Unraveling the iterative CHAD
May 21, 2025Fernando Lucatelli Nunes, Gordon Plotkin, Matthijs VákárDifferentiable Programming Category Theory
Department of Information and Computing Sciences, Utrecht University, Netherlands · Google DeepMind, Google DeepMind, USA

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PRISM: A Category-Theoretic Framework for Measuring and Refining Multimodal Analogies

Mirella Zeisler, Ojas Shirekar, Mircea Licǎ, Chirag Raman

Delft University of Technology

Cross-Modal Alignment Multimodal Reasoning Category Theory

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Analogical reasoning involves identifying and preserving relational structures across domains. However, existing approaches to AI-driven multimodal analogy generation lack an interpretable measure of whether this structure is understood and maintained in the generated output. We address this gap with Pullback Refinement via Interpretable Structural Mapping (PRISM), a modality-agnostic framework for measuring and improving relational alignment in multimodal analogies, evaluated on visual metaphor generation. PRISM represents analogies as explicit relational mappings grounded in category theory and uses VLMs to instantiate these structures across modalities. Its first component, the pullback score, quantifies relational alignment from the resulting graph representation. On the AnaloBench benchmark, selecting the correct analogy purely by pullback score achieves 82.5% accuracy, demonstrating that the score captures meaningful relational information. PRISM's second component is an iterative refinement loop that uses the pullback score as an in-context feedback signal to iteratively revise the generated image towards greater relational depth. VLM-as-a-judge and human evaluations show that PRISM consistently improves metaphor consistency and analogy appropriateness over zero- shot generation, with human participants preferring the refined output in 57.65% of pairwise comparisons. However, a qualitative analysis reveals that refinement can favour visually crowded compositions rather than genuinely deeper relational correspondences.