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This research applies large-deviation statistics to estimate stable fixed-points in disordered neural ordinary differential equations, offering a perturbative method applicable to complex dynamical models with random coupling matrices. The study finds that for moderate coupling strengths, the system's behavior remains qualitatively similar whether dynamics are purely gradient-based or allow for limit cycles and chaos.
Multiplicity of Stable Attractors in Disordered Neural Models
arXiv:2607.22047v1 Announce Type: cross Abstract: 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.
Abstract: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.
Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Artificial Intelligence (cs.AI); Chaotic Dynamics (nlin.CD)
arXiv:2607.22047 [cond-mat.dis-nn]
(or arXiv:2607.22047v1 [cond-mat.dis-nn] for this version)
https://doi.org/10.48550/arXiv.2607.22047 arXiv-issued DOI via DataCite (pending registration)
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