Functional connectomes of neural networks
Tananun Songdechakraiwut, Yutong Wu
TL;DR
This work proposes a brain-inspired framework for analyzing neural networks via functional connectomes and persistent graph homology, avoiding thresholding and enabling scalable topology statistics. It introduces closed-form Wasserstein distances and barycenters on persistence summaries, enabling a centroid-based clustering method (Top) that outperforms baselines on MNIST, Fashion-MNIST, and CIFAR-10. The approach yields interpretable topological signatures of how regularization and stimuli shape information flow, with runtime analysis showing scalability to large networks. The results suggest a principled, scalable path to bridging brain-connectomics and deep learning for improved interpretability and analysis.
Abstract
The human brain is a complex system, and understanding its mechanisms has been a long-standing challenge in neuroscience. The study of the functional connectome, which maps the functional connections between different brain regions, has provided valuable insights through various advanced analysis techniques developed over the years. Similarly, neural networks, inspired by the brain's architecture, have achieved notable success in diverse applications but are often noted for their lack of interpretability. In this paper, we propose a novel approach that bridges neural networks and human brain functions by leveraging brain-inspired techniques. Our approach, grounded in the insights from the functional connectome, offers scalable ways to characterize topology of large neural networks using stable statistical and machine learning techniques. Our empirical analysis demonstrates its capability to enhance the interpretability of neural networks, providing a deeper understanding of their underlying mechanisms.