Gibbs Nwemadji

Gibbs Nwemadji, Bruno Loureiro, Jean Barbier

Pre-training on a source task is usually expected to facilitate fine-tuning on similar downstream problems. In this work, we mathematically show that this naive intuition is not always true: excessive pre-training can computationally slow down fine-tuning optimization. We study this phenomenon for low-rank adaptation (LoRA) fine-tuning on single-index models trained under one-pass SGD. Leveraging a summary statistics description of the fine-tuning dynamics, we precisely characterize how the convergence rate depends on the initial fine-tuning alignment and the degree of non-linearity of the target task. The key take away is that even when the pre-training and down- stream tasks are well aligned, strong pre-training can induce a prolonged search phase and hinder convergence. Our theory thus provides a unified picture of how pre-training strength and task difficulty jointly shape the dynamics and limitations of LoRA fine-tuning in a nontrivial tractable model.

Jean Barbier, Federica Gerace, Alessandro Ingrosso et al.

Understanding the generalization abilities of neural networks for simple input-output distributions is crucial to account for their learning performance on real datasets. The classical teacher-student setting, where a network is trained from data obtained thanks to a label-generating teacher model, serves as a perfect theoretical test bed. In this context, a complete theoretical account of the performance of fully connected one-hidden layer networks in the presence of generic activation functions is lacking. In this work, we develop such a general theory for narrow networks, i.e. networks with a large number of hidden units, yet much smaller than the input dimension. Using methods from statistical physics, we provide closed-form expressions for the typical performance of both finite temperature (Bayesian) and empirical risk minimization estimators, in terms of a small number of weight statistics. In doing so, we highlight the presence of a transition where hidden neurons specialize when the number of samples is sufficiently large and proportional to the number of parameters of the network. Our theory accurately predicts the generalization error of neural networks trained on regression or classification tasks with either noisy full-batch gradient descent (Langevin dynamics) or full-batch gradient descent.