Title: Fractal Basins in Reasoning Dynamics

Speaker: William Gilpin, University of Texas Austin

Abstract: Both biological and artificial intelligence perform reasoning, in which a system repeatedly revisits and revises its solution to a problem. We frame reasoning as a search process executed by high-dimensional dynamical systems. We use this framework to show that many leading artificial intelligence models produce transient chaos and fractal basins when they encounter hard algorithmic tasks like solving mazes, Sudoku, or mathematical puzzles. These phenomena emerge due to reasoning becoming trapped for extended durations near saddle points, which we show correspond to nearly-correct attempted solutions of the underlying problem. We thus find that transient chaos is a general consequence of problem hardness when modern artificial intelligence models represent tasks as dynamical systems. Our findings have broader implications for understanding biological networks and other analogue systems that perform computation.

Bio: William Gilpin is an assistant professor of physics at UT Austin. His group studies computational nonlinear dynamics, with particular applications to systems biology and fluid dynamics. After completing his undergraduate degree in physics at Princeton, he received his Ph.D. in applied physics from Stanford, followed by a postdoctoral fellowship at Harvard's quantitative biology initiative. His work is currently supported by an NSF CAREER award, a Cottrell Scholarship, and the Chan-Zuckerberg Initiative.

Zoom: https://northwestern.zoom.us/j/98191770704

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