Jim Crutchfield | Computational Mechanics | Dynamics of Learning | Evolving Cellular Automata | Evolutionary Dynamics



Research Themes


Research Communications


Tools and Resources

Learning in Autonomous Robot Collectives


About the Project...

The Dynamics of Learning project is a Complexity Sciences Center research initiative that seeks to understand the process of learning using techniques from statistical mechanics, dynamical systems, and computation theory.

The Dynamics of Learning project is headed by Professor Jim Crutchfield and sponsored by DARPA through its TASK program. Like much of the work associated with complex systems research, the Dynamics of Learning project is agent-based, but not in the usual way. Most agent-based research designs agents for a particular task, or for simulating a particular model; some focus on building general simulation systems for agent-design. While these efforts have been valuable and (mostly) successful, they haven't given us a theory of agents or their collective behavior. This is the gap Crutchfield hopes to fill. The goal is a general, quantitative, predictive theory of cognitive agents and of agent collectives, applying both to natural systems (e.g., the immune system, or insect swarms) and artificial ones (e.g., a group of autonomous robots). The theory would be analytical, predicting what a given system would do, rather than synthetic, saying how to design a system with some desired behaviors, but the analytical methods ought to be useful to designers.

The Dynamics of Learning work builds on computational mechanics, a theory developed by Crutchfield and his co-workers over the last decade, combining elements of dynamics, computation and information theory. The main result of computational mechanics is an automatic method for pattern discovery from observational data. The method will find all the patterns in the data, and represent them in the simplest possible way, even when we know little about the underlying data-generating process. Since any kind of learning agent is effectively doing some kind of pattern discovery, computational mechanics puts limits on how well an agent can predict or learn its environment.

The Dynamics of Learning project takes computational mechanics in a new direction. Anything people are willing to call an agent has inputs and outputs. In organisms, the inputs are all the senses, and the outputs all the motions of the animal. In machines (e.g., a mobile robot), the inputs would come from sensors (e.g., cameras, heat detectors, wireless links) and the outputs would go to ''effectors'' (e.g., motors in wheels and wireless links). Some mechanism connects them, making an agent into what computer science calls a transducer or a channel with memory. Computational mechanics now has the tools to discover the patterns of intrinsic computation going on in a transducer, including the way it changes its own organization in response to inputs. These tools work even when the transducer is a ''learning channel'' and works by building a model of its input — in principle, one can do pattern discovery on pattern discoverers! Using these methods, Crutchfield and his former student Dave Feldman have already calculated how much internal complexity an agent must have in order to adequately model its environment. Excessively simple agents can't grasp all the structure in the environment, and see it as more random than it really is — and the amount of excess randomness depends on the mismatch between the agent's cognitive complexity and the environment's structural complexity.

The next stage of the project will go beyond single-agent learning, to learning and adaptation in multi-agent systems. A collective of agents is like a network of interconnected transducers. Computational mechanics can show how the local behavior of the agents builds up into the global behavior of the network and can identify the intrinsic computation the collective performs. Given that, the group will begin seeing when the collective can do things that individuals cannot — how an adaptation can be distributed, just as a computation can be. The ultimate goal of the project is to understand collective cognition, the way groups can sometimes solve problems and learn things better than any of their members could. It's only fitting that what amounts to a quantitative sociology of science be initiated at SFI.

(Modified from a piece in the SFI Bulletin (vol. 16, no. 1) by C. R. Shalizi)