无序神经模型中稳定吸引子的多重性
Multiplicity of Stable Attractors in Disordered Neural Models
浏览论文内容
中文总结 AI 辅助
研究无序神经模型中稳定吸引子多重性，利用大偏差统计和微扰方法，结果表明不太大耦合强度下对称与非对称情况无定性差异，该方法有望扩展到其他多自由度动力学模型。
中文摘要 AI 辅助
我们展示了大偏差统计如何使人们能够可靠地估计先前用于计算任务的神经常微分方程模型中稳定不动点的多重性。通过在无序幅度中开发一种合适的微扰方法得到了该结果。结果表明，对于不太大的耦合强度，当动力学是纯梯度演化的对称情况和原则上可能出现极限环和混沌的非对称情况之间没有定性差异。选择这个特定模型是出于教学原因，但我们相信该方法可以扩展到其他由不同类随机耦合矩阵表征的多自由度动力学模型。
英文摘要
We show how large-deviation statistics allows one to obtain reliable estimates of the multiplicity of stable fixed-points in a model of neural ordinary differential equations previously employed in computational tasks. The result is obtained by developing a suitable perturbative method in the amplitude of the disorder. It turns out that for not-too-large coupling strengths there are no qualitative differences between the symmetric case, when the dynamics is a purely gradient evolution, and the asymmetric case, when limit cycles and chaos can, in principle, arise. The selection of this specific model is dictated by pedagogical reasons, but we are confident that the approach can be extended to other many-degree-of-freedom dynamical models characterized by different classes of random coupling matrices.
发表机构
- Butterfly Decisions srl（Butterfly Decisions 公司）
- University of Florence（佛罗伦萨大学）
- Istituto dei Sistemi Complessi, CNR（复杂系统研究所，CNR）
- Institute of Pure and Applied Mathematics, Department of Physics, University of Aberdeen（纯数学与应用数学研究所，物理系，阿伯丁大学）
机构由 AI 辅助整理，请以论文原文为准。
