Lotito Daniele, Aquaro Miriam, Marullo Chiara
Dipartimento di Informatica, Università di Pisa, 56127 Pisa, Italy.
GNFM-INdAM, Gruppo Nazionale di Fisica Matematica, Istituto Nazionale di Alta Matematica, 00185 Rome Italy
Neural Comput. 2025 Jan 21;37(2):311-343. doi: 10.1162/neco_a_01730.
Hebbian learning theory is rooted in Pavlov's classical conditioning While mathematical models of the former have been proposed and studied in the past decades, especially in spin glass theory, only recently has it been numerically shown that it is possible to write neural and synaptic dynamics that mirror Pavlov conditioning mechanisms and also give rise to synaptic weights that correspond to the Hebbian learning rule. In this article we show that the same dynamics can be derived with equilibrium statistical mechanics tools and basic and motivated modeling assumptions. Then we show how to study the resulting system of coupled stochastic differential equations assuming the reasonable separation of neural and synaptic timescale. In particular, we analytically demonstrate that this synaptic evolution converges to the Hebbian learning rule in various settings and compute the variance of the stochastic process. Finally, drawing from evidence on pure memory reinforcement during sleep stages, we show how the proposed model can simulate neural networks that undergo sleep-associated memory consolidation processes, thereby proving the compatibility of Pavlovian learning with dreaming mechanisms.
赫布学习理论源于巴甫洛夫的经典条件作用。虽然在过去几十年中已经提出并研究了前者的数学模型，特别是在自旋玻璃理论中，但直到最近才通过数值方法表明，有可能写出反映巴甫洛夫条件作用机制的神经和突触动力学，并且还能产生与赫布学习规则相对应的突触权重。在本文中，我们表明可以使用平衡统计力学工具以及基本且合理的建模假设来推导相同的动力学。然后，我们展示了在假设神经和突触时间尺度合理分离的情况下，如何研究由此产生的耦合随机微分方程组。特别是，我们通过分析证明了这种突触演化在各种情况下都收敛于赫布学习规则，并计算了随机过程的方差。最后，借鉴睡眠阶段纯记忆强化的证据，我们展示了所提出的模型如何模拟经历与睡眠相关的记忆巩固过程的神经网络，从而证明了巴甫洛夫学习与做梦机制的兼容性。
