Regularization, early-stopping and dreaming: a Hopfield-like setup to address generalization and overfitting

In this work we approach attractor neural networks from a machine learning perspective: we look for optimal network parameters by applying a gradient descent over a regularized loss function. Within this framework, the optimal neuron-interaction matrices turn out to be a class of matrices which correspond to Hebbian kernels revised by iteratively applying some unlearning protocols. Remarkably, the number of unlearning steps is proved to be related to the regularization hyperparameters of the loss function and to the training time. Thus, we can design strategies to avoid overfitting that are formulated in terms of the algebraic properties of the interaction matrix, or, equivalently, in terms of regularization tuning and early-stopping strategies. The generalization capabilities of these attractor networks are also investigated: analytical results are obtained for random synthetic datasets, next, the emerging picture is corroborated by numerical experiments that highlight the existence of several regimes (i.e., overfitting, failure and success) as the dataset parameters are varied.