# Self-Revising Discovery Systems for Science: A Categorical Framework for Agentic Artificial Intelligence

arXiv: https://arxiv.org/abs/2606.01444 · HTML: https://mlsanity.com/paper/2606.01444/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Medical and scientific domain agents, one of 16 directions in LLM agents and tool use.
- Builds on 19 of its 81 references that are in the map.
- First posted on arXiv 31 May 2026.

## Placed in

- LLM agents and tool use / [Medical and scientific domain agents](https://mlsanity.com/agents/medical-and-scientific-domain-agents/)

## Builds on (most cited first, 19 of 19)

- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [The AI Scientist: Towards Fully Automated Open-Ended Scientific Discovery](https://mlsanity.com/paper/2408.06292/) (2024)
- [The AI Scientist-v2: Workshop-Level Automated Scientific Discovery via Agentic Tree Search](https://mlsanity.com/paper/2504.08066/) (2025)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Paired Open-Ended Trailblazer (POET): Endlessly Generating Increasingly Complex and Diverse Learning Environments and Their Solutions](https://mlsanity.com/paper/1901.01753/) (2019)
- [ProtAgents: Protein discovery via large language model multi-agent collaborations combining physics and machine learning](https://mlsanity.com/paper/2402.04268/) (2024)
- [MechAgents: Large language model multi-agent collaborations can solve mechanics problems, generate new data, and integrate knowledge](https://mlsanity.com/paper/2311.08166/) (2023)
- [Backprop as Functor: A compositional perspective on supervised learning](https://mlsanity.com/paper/1711.10455/) (2017)
- [MechGPT, a language-based strategy for mechanics and materials modeling that connects knowledge across scales, disciplines and modalities](https://mlsanity.com/paper/2310.10445/) (2023)
- [AutoDiscovery: Open-ended Scientific Discovery via Bayesian Surprise](https://mlsanity.com/paper/2507.00310/) (2025)
- [Position: Categorical Deep Learning is an Algebraic Theory of All Architectures](https://mlsanity.com/paper/2402.15332/) (2024)
- [MeLM, a generative pretrained language modeling framework that solves forward and inverse mechanics problems](https://mlsanity.com/paper/2306.17525/) (2023)
- [PRefLexOR: Preference-based Recursive Language Modeling for Exploratory Optimization of Reasoning and Agentic Thinking](https://mlsanity.com/paper/2410.12375/) (2024)
- [Sparks: Multi-Agent Artificial Intelligence Model Discovers Protein Design Principles](https://mlsanity.com/paper/2504.19017/) (2025)
- [Autonomous Agents Coordinating Distributed Discovery Through Emergent Artifact Exchange](https://mlsanity.com/paper/2603.14312/) (2026)
- [GraphAgents: Knowledge Graph-Guided Agentic AI for Cross-Domain Materials Design](https://mlsanity.com/paper/2602.07491/) (2026)
- [Learners' Languages](https://mlsanity.com/paper/2103.01189/) (2021)
- [Deep Learning with Parametric Lenses](https://mlsanity.com/paper/2404.00408/) (2024)
- [Towards a Categorical Foundation of Deep Learning: A Survey](https://mlsanity.com/paper/2410.05353/) (2024)

## Built on by (most cited first, 4 of 4)

- [How Do Agents Fail on AutoResearch: End-to-End Diagnostic Evaluation on 100 Real-World Frontier Research Tasks](https://mlsanity.com/paper/2608.14905/) (2026)
- [SwarmWorld: Stigmergic technological evolution in societies of language-model agents](https://mlsanity.com/paper/2608.26081/) (2026)
- [The Calibration Turn in AI-Assisted Research: A Conceptual and Methodological Framework for Evidence-Licensed Claims](https://mlsanity.com/paper/2606.31273/) (2026)
- [Triage-PiEvo: Evidence Admission for Principle-Evolving Scientific Agents](https://mlsanity.com/paper/2610.14683/) (2026)

## Abstract (arXiv)

Scientific discovery is not only answer generation but revision of the representational regime in which evidence, artifacts, operations, and verifiers are typed. We develop a category-theoretic account of agentic discovery for materials science. In a fixed regime b with schema category Sb, the system state is a copresheaf It: Sb -> Set, and provenance is the category of elements intSb It. Fixed-regime operation is an update on such states, endofunctorial only when provenance-preserving refinements are specified and preserved. Discovery is instead a verified regime transition u: Sb -> Sb': old artifacts are preserved, transported by the left Kan extension Lanu It, and compared with the post-transition state to identify residual content beyond functorial transport. This separates retrieval, search, and discovery without subjective novelty. We instantiate the framework in two systems. In Builder/Breaker, a protein-mechanics world model is revised under a Minimum Description Length gate; the accepted law expresses within-chain flexibility as all-mode elastic compliance conditioned by slow collective-mode participation, or mode-conditioned compliance. In CategoryScienceClaw, typed skills, artifacts, open needs, workflow mutation, gates, stress tests, and public discourse become a proof-carrying knowledge-computation graph. A fiber-network example records candidate models, rejected alternatives, an AIC gate, perturbation tests, and an accepted orientation-tensor anisotropic stiffness surrogate over an isotropic fiber-count descriptor. Together, the cases show how category theory can be both a mathematical language for discovery and an engineering specification for self-revising AI discovery systems.