Two-Timescale Fine-tuning Provably Learns New Features for Two-Layer ReLU Networks
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 $\mathcal{...
| Authors | Etienne Boursier, Nicolas Flammarion |
|---|---|
| Primary category | stat.ML |
| Published | 28 September 2026 |
| Last updated at source | 28 September 2026 |
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