Slow Transition to Low-Dimensional Chaos in Heavy-Tailed Recurrent Neural Networks
chaotic dynamicsedge of chaoseffective dimensionalityfinite-size analysisgain transitionheavy-tailed distributionsheavy-tailed neural circuitslyapunov dimensionlévy alpha-stable distributionsmean-field theoryneural activityquiescent staterecurrent neural networkssimulationssynaptic weightstransition point
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