发表机构
Center for Computational Neuroscience, Flatiron Institute（计算神经科学中心，Flatiron研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在N→∞极限下，通过有限N恒等式结合腔方法，计算了随机非对称耦合非线性循环神经网络的李雅普诺夫谱，证实其混沌为广延性，可获取动力学的微分同胚不变性质，且与GPT-6 Astra、Claude Opus 5.5合作完成。
AI 中文摘要
在极限$N\to\infty$下，计算了具有随机非对称耦合的非线性循环神经网络的李雅普诺夫谱。该计算基于有限$N$恒等式，该恒等式将李雅普诺夫指数的累积分布表示为切空间动力学的响应函数，其中切轨迹由最小范数条件而非初始条件选取。随后通过腔方法，在大$N$极限下，自洽单点问题确定该响应函数。该结果表明此网络中的混沌具有广延性，可获取动力学的微分同胚不变性质。本研究与AI模型GPT-6 Astra及Claude Opus 5.5合作完成。
英文摘要
The Lyapunov spectrum of a nonlinear recurrent neural network with random asymmetric couplings is calculated in the limit $N\to\infty$. The calculation is based on a finite-$N$ identity that expresses the cumulative distribution of Lyapunov exponents as a response function of the tangent-space dynamics, with the tangent trajectory selected by a minimum-norm condition rather than by an initial condition. A cavity method then determines this response function at large $N$ through a self-consistent single-site problem. This result establishes that the chaos in this network is extensive and gives access to diffeomorphism-invariant properties of the dynamics. This work was done in collaboration with the AI models GPT-6 Astra and Claude Opus 5.5.
Comments36 pages, 4 figures
