Lyapunov spectrum of random neural networks

arXiv:2610.12426 · cond-mat.dis-nn, q-bio.NC · Submitted 2026-10-08 · Read on arXiv

cond-mat.dis-nn, q-bio.NC

Submitted: 2026-10-08

Updated: 2026-10-08

Comments: 36 pages, 4 figures

Code: https://github.com/davidclark1/rnn-lyapunov

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Regularization — 7× in this paper · explained in 3 episodes
• Trace — 5× in this paper · explained in 2 episodes
• Transformer — 4× in this paper · explained in 2 episodes
• Adam — 2× in this paper · explained in 2 episodes
• Computational Biology — 2× in this paper · explained in 2 episodes
• Consistency — 2× in this paper · explained in 3 episodes
• Self-consistency — 2× in this paper · explained in 2 episodes
• Chaotic Dynamics — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Interpretability — 1× in this paper · explained in 15 episodes
• Latent Reasoning — 1× in this paper · explained in 2 episodes
• Sampling Biases — 1× in this paper · explained in 2 episodes

Sources

• Stationary covariance spectra of discrete-time non-normal random recurrent dynamics
• Covariance spectrum in nonlinear recurrent neural networks
• Solution of a chaotic neural network at fixed connectivity
• Linear equivalence of nonlinear recurrent neural networks
• Sparse chaos in cortical circuits
• Fractal basins trap latent reasoning
• Determinants on von Neumann algebras, Mahler measures and Ljapunov exponents

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