COMPSCI 692CT — Category Theory for AGI
Meets Mon/Wed 5:30–6:45pm ET · Online (live & recorded) · Instructor: Sridhar Mahadevan · Zoom link TBA
What is this course about?
The world's largest AI companies are collectively spending several trillion dollars in the most expensive race in human history to build artificial general intelligence (AGI). This course will give students a detailed introduction to category theory, and how to use it to analyze today’s AGI systems, understand their limitations and how to design the next generation of AGI sytems. We’ll cover the core theoretical concepts, including categories, functors, natural transformations, the Yoneda lemma, limits & colimits, adjunctions, monads, and Kan extensions, as well as their application to building AGI systems that can reason causally, learn from their experience, plan to achieve long-term goals, interact with users in natural language, and ultimately, achieve consciousness.
Texts
- Primary: Emily Riehl, Category Theory in Context (Dover, 2016). Free PDF hosted by the author: emilyriehl.github.io/files/context.pdf
- Optional notes: Mahadevan, Artificial General Intelligence: A Categorial Formulation (draft; link TBA).
Tentative weekly outline
| Week | Category Theory Focus | AGI Modality |
|---|---|---|
| W1 | Categories & Functors | Compositional Machine Learning |
| W2 | Natural Transformations & Yoneda Lemma | Universal Imitation Games |
| W3 | Limits & Colimits | Building compositional structures(pullbacks/pushouts) |
| W4 | Adjunctions | Bridging Causal and Statistical Learning |
| W5 | Monads | Categorical Probability and Disintegration |
| W6 | Symmetric Monoidal Categories | Markov Categories and string diagrams |
| W7 | Topos Theory | New Architectures for LLMs |
| W8 | Presheaves & Internal Logic (Ω) | Reasoning in possible worlds |
| W9 | Topos Causal Models I | Interventions as Subobject Clasifiers |
| W10 | Kan Extensions | Learning to Extend Functors |
| W11 | Coalgebras & Coinduction | Universal Reinforcement Learning |
| W12 | Simplicial Sets | UMAP and manifold learning |
| W13 | Compositional Games | Equilibria via variational inequalities |
| W14 | Consciousness And Student Project Demos | Frontiers of AGI |
This outline will evolve; readings and Zoom link will appear here.
Contact
Instructor: Sridhar Mahadevan · Email: mahadeva@cs.umass.edu
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