Predictive Coding for Cognitive Mapping

Author: Gornet, James Andrew

Year: 2027

Degree: Dissertation (Ph.D.)

Advisor: Thomson, Matthew

Committee Members: Siapas, Athanassios G.; Marcolli, Matilde; Winfree, Erik; Thomson, Matthew

Option: Computation and Neural Systems

DOI: 10.7907/rmb1-7w43

Abstract

Paths within a given space are constrained by the space's geometry. Any data generated by a path must then reflect the path's base space. A path's data constrained by the base space's geometry—which we call the lifting property—is the fundamental relation this thesis explores. Specifically, this thesis examines how mathematical functions—and statistical algorithms—that generate a path's data recover the base space's geometry—termed predictive coding for cognitive mapping.

It is shown that mathematical functions that generate a path's data recover the base space's geometry. We show that statistical estimators that generate a path's data can also recover the base space's geometry in a simulated natural environment. We also shown that mathematical functions recover a dynamical system if the function generates observations on a dynamical system's trajectory. We demonstrate applications of this principle to a bipedal robot's kinematics. Finally, we extend predictive coding for mapping—predicting future observations from past observations to build an environmental map—to plan and explore within the environment.

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