Unifying Dynamical Systems and Graph Theory to Mechanistically Understand Computation in Neural Networks
Researchers demonstrate that recurrent neural networks implement computation through multi-hop pathways across graph structures rather than direct connections alone. They introduce resolvent-RNNs (R-RNNs) that constrain these pathways to achieve better temporal sparsity and robustness than traditional L1 regularization, revealing fundamental principles about how neural networks process information.