Abstract:Fine-tuning large language models with LoRA requires choosing a rank r before training starts. Existing approaches either extract rank-1 components sequentially, freezing each component's error permanently into every subsequent residual, or optimize the full low-rank factorization jointly with guarantees that describe only the joint update, not individual rank-1 directions. We present AdaPaD (Adaptive Parallel Deflation), which trains all rank-1 components simultaneously: each worker refines its component against a deflation target built from the latest estimates of all predecessors, and as those estimates improve, the targets improve too. We call this property self-correction: deflation errors converge to zero over rounds rather than persisting as fixed residuals. On top of this backbone, AdaPaD adds advance learning (private pre-training before activation) and per-module dynamic rank discovery (importance-based growth until a shared budget is exhausted), making the rank distribution an output rather than an input. We prove that every component's error decays exponentially after a warm-up period, with a generalization bound that splits into a vanishing algorithmic term and an irreducible statistical floor. Empirically, AdaPaD is competitive with adaptive-rank LoRA baselines on GLUE with DeBERTaV3-base at matched parameter budgets, and competitive with fixed-rank LoRA on Qwen3-0.6B SQuAD/SQuAD v2 while deploying an adapter that is on average 30.7% smaller.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.10741 [cs.LG] |
| (or arXiv:2605.10741v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.10741 arXiv-issued DOI via DataCite (pending registration) |
From: Barbara Su [view email]
[v1]
Mon, 11 May 2026 15:44:13 UTC (145 KB)
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