Abstract
Parameter-efficient fine-tuning enables large language models to adapt to downstream tasks with substantially lower computational and storage cost, and Low-Rank Adaptation (LoRA) is among its most widely used techniques. However, vanilla LoRA assigns a uniform rank to all adapted modules, while existing adaptive methods either incur additional optimization overhead or rely on static weights and local gradients that do not capture task-conditioned representation changes. We propose RSRA, a training-free rank allocator that estimates where adaptation capacity is most needed through forward-only representation sensitivity probing on a small calibration set. Specifically, RSRA uses Spectral Effective Rank to allocate capacity across layers, measures module-wise hidden-state displacement under standardized virtual low-rank updates with the Frechet Distance, and combines both signals through hierarchical normalization to produce a task-aware rank configuration before fine-tuning. Across commonsense reasoning and natural language understanding benchmarks with Qwen3-4B and Mistral-7B, RSRA achieves the highest average performance in all three reported model-benchmark settings and a 1.48x-1.93x speedup in allocation time over the fastest competing pre-allocation method. When integrated with DoRA, LoRA-FA, and PiSSA, RSRA improves 15 of the 18 evaluated combinations and increases the average performance of all three PEFT methods.