Pavlov Learning Machines

TL;DR

This paper models the connection between Pavlovian classical conditioning and Hebbian learning using stochastic processes, demonstrating how Pavlovian mechanisms can naturally lead to Hebbian synaptic weights under certain conditions.

Contribution

It introduces a novel mathematical framework linking Pavlovian and Hebbian learning through Langevin equations, bridging a longstanding gap in neural modeling.

Findings

Pavlovian conditioning emerges from neural and synaptic dynamics.

Synaptic weights recover Hebbian kernels under specific timescale conditions.

The model provides a unified view of associative learning mechanisms.

Abstract

As well known, Hebb's learning traces its origin in Pavlov's Classical Conditioning, however, while the former has been extensively modelled in the past decades (e.g., by Hopfield model and countless variations on theme), as for the latter modelling has remained largely unaddressed so far; further, a bridge between these two pillars is totally lacking. The main difficulty towards this goal lays in the intrinsically different scales of the information involved: Pavlov's theory is about correlations among \emph{concepts} that are (dynamically) stored in the synaptic matrix as exemplified by the celebrated experiment starring a dog and a ring bell; conversely, Hebb's theory is about correlations among pairs of adjacent neurons as summarized by the famous statement {\em neurons that fire together wire together}. In this paper we rely on stochastic-process theory and model neural and synaptic dynamics via Langevin equations, to prove that -- as long as we keep neurons' and synapses' timescales largely split -- Pavlov mechanism spontaneously takes place and ultimately gives rise to synaptic weights that recover the Hebbian kernel.