Slow Transition to Low-Dimensional Chaos in Heavy-Tailed Recurrent Neural Networks.

ABSTRACT: Growing evidence suggests that synaptic weights in the brain follow heavy-tailed distributions, yet most theoretical analyses of recurrent neural networks (RNNs) assume Gaussian connectivity. We systematically study the activity of RNNs with random weights drawn from biologically plausible Lévy alpha-stable distributions. While mean-field theory for the infinite system predicts that the quiescent state is always unstable-implying ubiquitous chaos-our finite-size analysis reveals a sharp transition between quiescent and chaotic dynamics. We theoretically predict the gain at which the finite system transitions from quiescent to chaotic dynamics, and validate it through simulations. Compared to Gaussian networks, finite heavy-tailed RNNs exhibit a broader gain regime near the edge of chaos, n

SUBMITTER: Xie EY 

PROVIDER: S-EPMC12633207 | biostudies-literature | 2025 Oct

REPOSITORIES: biostudies-literature