RI: Principles of Robust and Flexible Computation Under Resource Constraints

Intelligent systems, whether living brains or artificial networks, must hold information in mind long enough to guide action while still adapting to new evidence and changing conditions. Striking this balance is difficult when energy and physical resources are limited, as they always are in biological tissue. This project develops a mathematical theory of how the brain sustains stable yet flexible memory by coordinating fast electrical activity with slower processes that distribute a finite supply of cellular resources across the network, a role played in part by support cells called astrocytes. The project's novelties are treating these resource supplies not as fixed background conditions but as active participants that store information and shape what the system remembers and forgets. The project's broader significance and importance are a clearer account of when memory stays reliable, when it fails, and how the same principles might guide the design of more energy-efficient and adaptive artificial intelligence. The research uses continuous models of brain tissue in which patterns of activity represent remembered quantities. Because these patterns drift under noise, the work analyzes how a diffusing pool of shared resources stabilizes them, suppresses error accumulation, and sets limits on how long memories endure. Mathematical tools that separate fast and slow timescales reduce the full system to simple, interpretable equations describing memory accuracy and failure. A second component examines how slow redistribution of resources learns the statistical structure of an environment, embedding biases that improve recall. A third identifies control rules that adjust resource transport over very long timescales, placing stabilizing capacity where demand is greatest. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.