BoostLoRA: Growing Effective Rank by Boosting Adapters

Parameter-efficient fine-tuning (PEFT) methods face a tradeoff between adapter size and expressivity: ultra-low-parameter adapters are confined to fixed low-rank subspaces, capping performance even with extended training. We propose BoostLoRA, a gradient-boosting framework that overcomes this limit by iteratively training and merging minimal adapters on the examples the current model gets wrong. A ROTATE SVD basis strategy assigns each round to an orthogonal subspace, so cumulative effective rank grows linearly with the number of rounds while each adapter remains ultra-low-rank. After merging, adapters are discarded, leaving zero inference overhead. On Qwen2.5-3B, BoostLoRA reaches 89.1% on GSM8K and 68.8% on MATH-500, surpassing both the best single-shot ultra-low-parameter adapter (TinyLoRA) and full fine-tuning; on code generation it reaches 57.2% on MBPP and 80.4% on HumanEval while full fine-tuning drops below the zero-shot baseline. We also demonstrate general applicability across domains via protein binding classification with ESM2-650M and cross-entropy training. BoostLoRA is, to our knowledge, the first ultra-low PEFT method whose effective rank grows with training, separating per-round parameter cost from total representational capacity.