Many-body approach to the dynamics of batch learning

Abstract

Using the cavity method and diagrammatic methods, we model the dynamics of batch learning of restricted sets of examples, widely applicable to general learning cost functions, and fully taking into account the temporal correlations introduced by the recycling of the examples. The approach is illustrated using the Adaline rule learning teacher-generated or random examples.

Relationship between Pyroelectric Properties and Electrode Sizes in (Pb, La)(Zr, Ti)O3 (PLZT) Thin Films

“…G tt = G( (t − t )) for t t . The on-line response found here for linear learning rules agrees with the batch results found for the linear rule in [5] and the adaline rule in [17]. The Fourier transform of the previous relation reads…”

“…The generating functional technique was used to study the dynamics of Gibbs learning in a perceptron with binary weights in [14,15]. A dynamical version of the cavity method was employed in [16][17][18] to study gradient-descent batch learning and the methods of dynamical replica theory were applied to the problem of on-line learning in [19][20][21][22]. The on-line learning scenario in this last sequence of papers is the one that we study here, but in the present paper we adapt the generating functional methodà la De Dominicis to deal with on-line learning.…”

Dynamical and stationary properties of on-line learning from finite training sets

“…This equation of the sequence-averaged activation is the same as that of the self-consistent equation of the activation in batch learning, after rescaling the time and weight decay [4].…”

“…is determined by the magnitude of the student vector C(t, t) and its correlation with the teacher vector R(t) [4], that is,…”

“…It enables us to understand the properties of a system by focusing on the response of the system to a single element added to it. It was later generalized to study learning in neural networks with the advantages of a clear physical picture and microscopic insights to both their equilibrium and dynamical properties [4,5,17]. The cavity method was subsequently applied to analyse the dynamics of batch learning, in which the entire set of examples is provided for each learning step [4], It provides dynamical equations and obtains important results on the overtraining, early stopping, noise effects and average learning strategy.…”