用大偏差方法估算神经网络中稳定吸引子的数量。
Multiplicity of Stable Attractors in Disordered Neural Models
- 基于扰动法分析无序耦合下的稳定固定点
- 弱耦合时对称与非对称系统无质的区别
- 适用于多自由度随机耦合动力系统
我们展示如何利用大偏差统计方法，对先前用于计算任务的神经微分方程模型中的稳定不动点多重性进行可靠估计。该结果通过在无序幅度上发展合适的微扰方法获得。研究发现，在非过强的耦合强度下，纯梯度演化的情形（对称）与可能产生极限环和混沌的情形（非对称）之间没有定性差异。选择此特定模型出于教学目的，但我们相信该方法可推广至具有不同类随机耦合矩阵的其他多自由度动力学模型。
原文摘要 · Abstract (English)
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.
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