5/ ‼️Result 3: However, this robustness of slow transition comes with a tradeoff ↔️: heavier tails reduce the Lyapunov dimension of the network attractor, indicating lower effective dimensionality.

3/ 🔎Result 2: Compared to Gaussian networks, we found finite heavy-tailed RNNs exhibit a broader gain regime near the edge of chaos: a *slow* transition to chaos. 🐢

2/ 🔎Result 1: While mean-field theory for the infinite system predicts ubiquitous chaos, our analysis reveals *finite-size* RNNs have a sharp transition between quiescent & chaotic dynamics. 

We theoretically predict the gain of transition and validated it through simulations.

Connectome suggests brain’s synaptic weights follow heavy-tailed distributions, yet most analyses of RNNs assume Gaussian connectivity. 

🧵⬇️ Our @alleninstitute.org #NeurIPS2025 paper shows heavy-tailed weights can strongly affect dynamics, trade off robustness + attractor dimension.