Statistical Inference for Rank Allocation in Low-Rank Adaptation

2026-07-22

AI Summary

This work addresses the critical challenge of efficiently allocating rank resources across modules and layers in Low-Rank Adaptation (LoRA) under a fixed parameter budget to balance efficiency, expressiveness, and generalization. We propose StatLoRA, the first method to incorporate statistical hypothesis testing into LoRA rank allocation: by constructing test statistics for each LoRA component and leveraging p-values, it makes data-driven decisions on pruning or retaining components. Theoretically, we establish a central limit theorem for the trajectory of stochastic optimizers such as AdamW, deriving an asymptotic normal distribution for component scores that rigorously justifies our approach. Experiments demonstrate that StatLoRA consistently matches or surpasses vanilla LoRA, AdaLoRA, and IGU-LoRA across natural language understanding, generation, and question answering tasks on DeBERTaV3-base, BART-Large, and Qwen2.5-7B, confirming its effectiveness and stability.

Abstract

Low-rank adaptation (LoRA) has become a widely used parameter-efficient fine-tuning method for large language models. Since different modules and layers may contribute unequally to downstream adaptation, allocating rank resources under a fixed parameter budget is an important problem for balancing efficiency, expressiveness, and generalization. Existing adaptive rank methods address this problem mainly through carefully designed importance scores constructed from gradient-derived sensitivity and uncertainty measures, without an explicit statistical interpretation. In this paper, we formulate LoRA rank allocation as a statistical hypothesis testing problem and propose StatLoRA, a statistical inference-based rank allocation method. StatLoRA associates each LoRA component with a test statistic and uses estimated p-values to determine which components should be retained or pruned under a prescribed rank budget. The proposed testing procedure is supported by our central limit theory for stochastic optimizer trajectories. In particular, we establish asymptotic normality for a broad class of commonly used optimizers in deep learning, including AdamW, and derive the corresponding asymptotic distributions for the proposed component scores used in hypothesis testing. We evaluate StatLoRA on LoRA fine-tuning of DeBERTaV3-base, BART-Large, and Qwen2.5-7B across natural language understanding, natural language generation, and question answering tasks. Experiments show that StatLoRA achieves comparable or better performance than vanilla LoRA, AdaLoRA, and IGU-LoRA under matched rank budgets. Sensitivity analyses and empirical diagnostics further support the stability of the proposed hypothesis-testing-based allocation rule and provide empirical evidence for the asymptotic theory of component scores.

Problem

• rank allocation
• low-rank adaptation
• parameter-efficient fine-tuning
• statistical inference
• hypothesis testing

Innovation

• statistical inference
• low-rank adaptation
• hypothesis testing
• asymptotic normality
• parameter-efficient fine-tuning