Neural Network Computation Explained via Graph Theory and Multi-Hop Pathways

A recent study published on arXiv (2605.03598) reveals that recurrent neural networks (RNNs) trained on tasks with a hierarchical modular structure can be analyzed by representing the network as a graph and examining the multi-hop connections between input and output units. By breaking down these connections according to hop length, the research uncovers how the network manages information over time, providing insights into its computational mechanisms based on connectivity. This approach reinterprets regularization; since functionality depends on multi-hop communication, traditional penalties like L1 regularization, which focus solely on individual weights, limit single-hop structures instead of the multi-hop pathways essential for computation. The study integrates concepts from dynamical systems and graph theory to tackle a key issue in both neuroscience and machine learning.