Optimal generalisation and learning transition in extensive-width shallow neural networks near interpolation

תקציר מקורי באנגליתarXiv:2501.18530v3 Announce Type: replace-cross Abstract: We consider a teacher-student model of supervised learning with a fully-trained two-layer neural network whose width $k$ and input dimension $d$ are large and proportional. We provide an effective theory for approximating the Bayes-optimal generalisation error of the network for any activation function in the regime of sample size $n$ scaling quadratically with the input dimension, i.e., around the interpolation threshold where the number of trainable parameters $kd+k$ and of data $n$ are comparable. Our analysis tackles generic weight distributions. We uncover a discontinuous phase transition separating a "universal" phase from a "specialisation" phase. In the first, the generalisation error is independent of the weight distributio