发表机构
BCAM – Basque Center for Applied Mathematics; IKERBASQUE, Basque Foundation for Science; Biofisika Institute (CSIC, EHU)（巴斯克应用数学中心; 伊克尔巴斯基克科学基金会; 生物物理研究所（西班牙国家研究委员会、巴斯克大学））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出非互易联想网络的动力学平均场理论，发现耦合矩阵特征值退相干可抵消噪声，从而大幅提升极限环和混沌吸引子的存储容量。
AI 中文摘要
我们为非互易联想网络发展了一种动力学平均场理论，该网络存储了从极限环到奇异吸引子的广泛动力学吸引子。在淬火无序条件下，利用路径积分计算，我们推导出模式重叠、自相关和响应函数的自洽动力学平均场方程。记忆检索能力由编码存储模式的耦合矩阵的谱结构决定。当其特征值相干对齐时，延迟自相互作用和淬火噪声会破坏性地反馈：在零特征相位（不动点吸引子）时，恢复经典平衡容量界限，而对于极限环，检索能力远低于该界限。相反，对于均匀分布的特征相位，延迟自相互作用和大部分淬火噪声相互抵消，将动力学简化为有效的单自旋过程，并大幅提高容量。我们针对极限环和混沌吸引子，通过微观模拟验证了该理论，并确定特征值退相干是增强动力学记忆存储的机制。
英文摘要
We develop a dynamical mean-field theory for nonreciprocal associative networks that store an extensive number of dynamical attractors, from limit cycles to strange attractors. Using a path integral calculation under quenched disorder, we derive self-consistent dynamical mean-field equations for pattern overlaps, autocorrelations and response functions. Memory retrieval capacity is governed by the spectral structure of the coupling matrices encoding stored patterns. When their eigenvalues are coherently aligned, retarded self-interactions and quenched noise feed back destructively: at zero eigenphase (fixed point attractors) the classical equilibrium capacity bound is recovered, while for limit cycles retrieval collapses far below it. In contrast, for uniformly distributed eigenphases, retarded self-interactions and much of the quenched noise cancels, reducing the dynamics to an effective single-spin process and amplifying capacity substantially. We validate the theory against microscopic simulations for limit-cycle and chaotic attractors, identifying eigenvalue decoherence as the mechanism enabling enhanced storage of dynamical memories.
