Spectral criteria for generalization in unsupervised Hebbian nets (opens in new tab)

We consider an unsupervised Hebbian network where the pairwise interactions among neurons are built on noisy realizations of hidden ground-truth vectors. Unlike classical Hopfield models, designed as memory devices, this class of networks can be employed to extract latent structure and generalize beyond the "training" set. By combining random matrix theory and replica methods, we derive the asymptotic spectrum of the corresponding interaction ma...