Date: November 21, 2025

Time: 11:00 AM – 1:00 PM EST

Location: Zoom link

Title: The Linchpins of Directed Acyclic Graphs — with Applications in Biological and Artificial Neural Networks

Abstract:

This thesis investigates how to identify key components and changes in neural networks by modeling their feed-forward dynamics as directed acyclic graphs (DAGs). It focuses on how structural properties shape functional behavior. The work is organized into three parts, each addressing a different aspect of the structure–function relationship in biological and artificial systems. First, a weighted hourglass analysis framework is introduced to identify small sets of core nodes that mediate information flow between inputs and outputs. Applied to the C. elegans connectome, this method highlights central neurons and uncovers sex-specific organizational differences in neuronal cores. Second, the TRACED algorithm is developed to perform root-cause analysis of activation cascade differences between networks. Applied to brain networks from individuals with major depressive disorder, TRACED identifies key connectivity changes that explain functional alterations beyond what traditional structural comparisons reveal. Third, a novel growth-based method for artificial neural networks is proposed, leveraging topological insights to expand sparse architectures into efficient subnetworks that match the performance of dense models at significantly reduced computational cost. Collectively, this thesis contributes new theoretical and computational tools for identifying linchpin components in neural networks—whether essential for sustaining function, responsible for pathological change, or critical for optimizing performance.

Committee:

Dr. Constantine Dovrolis

Dr. B. Aditya Prakash

Dr. Nabil Imam

Dr. Apurva Ratan Murty

Dr. Sashank Varma

Dr. Dániel Barabási