Artificial intelligence · Machine learning · Category theory

Exploring the Compositional Structure of Intelligence.

Over four decades, my work has moved from learning apprentices and autonomous agents to representation discovery, causal inference, categorical AI, and computational creativity. This UMass page preserves that academic trajectory and points toward the questions still unfolding.

Visit the permanent research portal Follow the research arc ↓

Intelligence is not only the minimization of a loss. It is the capacity to build a theory, recognize where that theory fails, and revise the structure through which the world is understood.

A research life in four movements

One question, repeatedly reframed.

The methods have changed. The search for learnable structure has remained.

01
1980s–1990s
Learning from explanation
Learning apprentices, explanation-based learning, and the question that has endured throughout my work: how can an intelligent system acquire structure rather than merely fit observations?
02
1990s–2000s
Agents that learn to act
Reinforcement learning, hierarchical decision-making, multi-agent systems, robot learning, and autonomous agents operating under uncertainty.
03
2000s–2010s
Discovering representation
Spectral methods, proto-value functions, manifold learning, transfer, optimization, and the geometry hidden inside high-dimensional decision problems.
04
2020s–
A categorical research program for AI
Categories, causality, trustworthy foundation models, learning from failures of compositionality, infinitesimal creativity, and the discovery of compositional worlds.

Research atlas

From appearances to compositional structure.

My current program asks how explicit mathematical structure can make learning systems more diagnosable, intervenable, and capable of controlled theory change.

Representation

How intelligent systems construct useful coordinates, abstractions, and invariants.

Decision

How agents learn, plan, and act in uncertain and changing worlds.

Causality

How models support intervention, verification, and trustworthy inference.

Creativity

How a system might diagnose the limits of a theory and construct an admissible extension.

The categorical AI tetralogy

Four books. One categorical research program.

A four-volume arc from the functorial language of cognition and learning by structural repair to infinitesimal creativity and the discovery of compositional worlds.