High-Dimensional Theory of LoRA Fine-Tuning in a Solvable Attention Model
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Computer Science > Machine Learning
Title:High-Dimensional Theory of LoRA Fine-Tuning in a Solvable Attention Model
Abstract:We develop a high-dimensional statistical theory of low-rank adaptation (LoRA) in attention models, capturing the interplay between pre-training and fine-tuning. We introduce a solvable framework in which a single-head attention layer is first pre-trained on a data-abundant task and subsequently adapted via a rank-one LoRA update on limited data. In the high-dimensional limit, both stages admit a sharp asymptotic characterization in terms of a finite set of order parameters, yielding explicit predictions for test errors and representation alignment. Our analysis shows that the impact of pre-training on LoRA is summarized by an effective noise term, from which we derive prescriptions for the optimal pre-training procedure. We also demonstrate a regime with a mismatch between the value of the test error and representation quality, and propose an application of our theory to active fine-tuning.
| Subjects: | Machine Learning (cs.LG); Disordered Systems and Neural Networks (cond-mat.dis-nn) |
| Cite as: | arXiv:2606.05899 [cs.LG] |
| (or arXiv:2606.05899v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2606.05899
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