Dr. Clark derives full Lyapunov spectrum for chaotic neural networks

Sommers: Sommers is a physicist who collaborated on the 1988 Physical Review Letters paper introducing the cornerstone chaotic neural network model. The study linked the largest Lyapunov exponent to a ground-state energy problem and highlighted the broader spectrum as unsolved. The model has influenced both spontaneous activity studies and recurrent network training. Crisanti: Crisanti is a theoretical physicist who co-developed the seminal nonlinear recurrent-network model of chaotic neurons in 1988. The work established the transition to chaos above a critical coupling strength and posed the full Lyapunov spectrum as an open analytical challenge. It continues to serve as a benchmark for theoretical neuroscience. Dr. Clark: Dr. Clark is a researcher in theoretical neuroscience focused on high-dimensional dynamical systems and chaotic neural networks. In this work, he derived an analytical solution for the full Lyapunov spectrum of the Sompolinsky-Crisanti-Sommers model after initial assistance from AI models. He emphasizes applying similar methods to trained networks and other complex systems. Sompolinsky: Sompolinsky is a theoretical physicist and neuroscientist known for foundational models of chaotic neural dynamics. Along with collaborators, he co-authored the 1988 paper that introduced the randomly coupled neuron network and derived the largest Lyapunov exponent via a Schrödinger equation analogy. The model has remained central to understanding cortical spontaneous activity. Engelken et al.: Engelken et al. are researchers who performed a numerical computation of the full Lyapunov spectrum for the chaotic recurrent network model. Their 2023 study provided key numerical benchmarks that the new analytical theory now matches closely. This work built directly on the original 1988 formulation of the model. AI Collaboration: AI models assisted in generating the initial derivation of the self-consistent single-site problem for the Lyapunov spectrum. Model Significance: The Sompolinsky-Crisanti-Sommers network serves as a foundational model for both spontaneous cortical activity and the starting point for training recurrent networks on tasks. Broader Implications: The analytical approach opens pathways for understanding high-dimensional nonlinear systems in theoretical neuroscience and AI models themselves.