Publication Date

Spring 5-13-2024

Abstract

This dissertation seeks to understand how different formulations of the neurally inspired Locally Competitive Algorithm (LCA) represent and solve optimization problems. By studying these networks mathematically through the lens of dynamical and gradient systems, the goal is to discern how neural computations converge and link this knowledge to theoretical neuroscience and artificial intelligence (AI). Both classical computers and advanced emerging hardware are employed in this study. The contributions of this work include:

1. Theoretical Work: A comprehensive convergence analysis for networks using both generic Rectified Linear Unit (ReLU) and Rectified Sigmoid activation functions. Exploration of techniques to address the binary sparse optimization problem, especially when the problem landscape is non-convex. Non-autonomous systems with time-varying sigmoid activation that approaches the step function have been proposed due to the challenge of proving step function convergence.

2. Computational Work: Numerical tests on classical computers confirm the theoretical analysis. In mapping the problem to the spiking domain, it is shown spike rates can represent continuous valued neuron activations. The binary sparse optimization problem is reformulated into a Quadratic Unconstrained Binary Optimization (QUBO) problem. Solutions are then sought using quantum annealing and spiking neuromorphic devices.

Degree Name

Mathematics

Level of Degree

Doctoral

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Mohammad Motamed

Second Committee Member

Frank Gilfeather

Third Committee Member

Ben Migliori

Fourth Committee Member

Andrew Sornborger

Fifth Committee Member

Jacob Schroder

Sixth Committee Member

Robyn Miller

Project Sponsors

Los Alamos National Laboratory

Language

English

Keywords

Mathematics, Physics, Neuromorphic, Quantum, Neuroscience

Document Type

Dissertation

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