Learning in Associative Networks through Pavlovian Dynamics

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 it has 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 paper, 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.