# Discontinuous transition to chaos in a canonical random neural network

arXiv: https://arxiv.org/abs/2405.14607 · HTML: https://mlsanity.com/paper/2405.14607/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2024.

## Built on by (most cited first, 1 of 1)

- [Leveraging chaotic transients in the training of artificial neural networks](https://mlsanity.com/paper/2506.08523/) (2025)

## Abstract (arXiv)

We study a paradigmatic random recurrent neural network introduced by Sompolinsky, Crisanti, and Sommers (SCS). In the infinite size limit, this system exhibits a direct transition from a homogeneous rest state to chaotic behavior, with the Lyapunov exponent gradually increasing from zero. We generalize the SCS model considering odd saturating nonlinear transfer functions, beyond the usual choice φ(x)=tanh x. A discontinuous transition to chaos occurs whenever the slope of φ at 0 is a local minimum (i.e., for φ'''(0)>0). Chaos appears out of the blue, by an attractor-repeller fold. Accordingly, the Lyapunov exponent stays away from zero at the birth of chaos.