Odyssey framework uses category theory to build verifiable, truth-preserving AI foundation models

Researchers have long struggled with ensuring that large AI models produce outputs that are both truthful and verifiable, especially when handling diverse sources of information. Odyssey, a new framework by Sridhar Mahadevan, tackles this head-on by applying category theory—specifically sheaf theory—to model building. The core idea is to break down knowledge into small, verifiable 'foundries' (local contexts) that can be composed using strict rules for consistency. This approach prevents false information from being introduced when combining different data sources, effectively creating a mathematical guarantee that the final model's outputs preserve local truths as they are scaled up.

Odyssey is not just theoretical. It comes with a full implementation and has been tested across multiple domains, including evidence/argument, operational decision, and scientific challenge foundries. Universal Foundry Learning (UFL) formalizes the construction process using left and right Kan extensions—a technique from category theory that rolls local artifacts into candidate models while enforcing restrictions and gluing rules. Foundry SQL provides a query interface for slicing maintained artifacts, and the TICKET certification system ensures that external or pre-built models can be admitted into Odyssey's durable state only after passing causal-claim extraction and argumentation checks. The framework is being presented as a 2.5-hour tutorial at ICML 2026, signaling its potential to become a standard for building trustworthy AI systems.