Two-Timescale Fine-tuning Provably Learns New Features for Two-Layer ReLU Networks
Abstract
Fine-tuning pre-trained models on specialized tasks with scarce data is central to modern deep learning. Despite its empirical success, theoretical understanding of fine-tuning remains limited. We introduce a Gaussian multi-index setting to study fine-tuning from pre-trained weights, where the teacher network has m+1 features, m of which are learned during pre-training and one of which must be learned during fine-tuning. For two-layer ReLU networks, we show that two-timescale training, i.e., updating the outer weights infinitely faster than the hidden ones, learns the new task-specific feature while preserving the pre-trained ones in the model representation. Moreover, only 𝒪(d) fine-tuning samples are required for this recovery, independently of the number of pre-trained features. In contrast, with random initialization, the same number of samples is insufficient to recover the target parameters. Our results therefore demonstrate that pre-training can induce an implicit bias with a clear statistical advantage over random initialization, enabling feature learning from scarce fine-tuning data.
Related
- One-Layer Transformer Provably Learns Multiclass One-Nearest Neighbor in Context
- Statistical Benefits of Fine-Tuning from Pretrained Initialization in Diagonal Linear Networks
- Phase Transition from Random Features to Fully Trainable Networks
- Muon Learns Facts Better: Understanding the Role of Spectral Orthogonalization
- Orientation Diversity Provably Increases the Angular-Domain Rank of 3D MIMO Arrays
BibTeX
@misc{boursier2026twotimescale,
title = {{Two-Timescale Fine-tuning Provably Learns New Features for Two-Layer ReLU Networks}},
author = {Etienne Boursier and Nicolas Flammarion},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34667},
eprint = {2609.34667},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34667},
}
RIS
TY - UNPB
TI - Two-Timescale Fine-tuning Provably Learns New Features for Two-Layer ReLU Networks
AU - Etienne Boursier
AU - Nicolas Flammarion
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34667
UR - https://arxiv.org/abs/2609.34667
AB - Fine-tuning pre-trained models on specialized tasks with scarce data is central to modern deep learning. Despite its empirical success, theoretical understanding of fine-tuning remains limited. We introduce a Gaussian multi-index setting to study fine-tuning from pre-trained weights, where the teacher network has m+1 features, m of which are learned during pre-training and one of which must be learned during fine-tuning. For two-layer ReLU networks, we show that two-timescale training, i.e., updating the outer weights infinitely faster than the hidden ones, learns the new task-specific feature while preserving the pre-trained ones in the model representation. Moreover, only 𝒪(d) fine-tuning samples are required for this recovery, independently of the number of pre-trained features. In contrast, with random initialization, the same number of samples is insufficient to recover the target parameters. Our results therefore demonstrate that pre-training can induce an implicit bias with a clear statistical advantage over random initialization, enabling feature learning from scarce fine-tuning data.
ER -