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Source note3 min read

Statistical Inference for Rank Allocation in Low-Rank Adaptation

Source

arXiv

arxiv.org/abs/2607.20205v1

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Plain-Language Brief

In this paper, the authors propose StatLoRA, a statistical inference-based rank allocation method for low-rank adaptation (LoRA) in large language models. The proposed method uses estimated p-values to determine which LoRA components should be retained or pruned under a prescribed rank budget. They establish asymptotic normality for various optimizers used in deep learning, including AdamW, and evaluate StatLoRA on DeBERTaV3-base, BART-Large, and Qwen2.5-7B models across different tasks.

What the Document Says

  • Low-rank adaptation (LoRA) is a parameter-efficient fine-tuning method for large language models.
  • The authors propose StatLoRA, a statistical inference-based rank allocation method for LoRA.
  • StatLoRA associates each LoRA component with a test statistic and uses estimated p-values to determine which components to retain or prune under a prescribed rank budget.
  • The proposed testing procedure is supported by central limit theory for stochastic optimizer trajectories.
  • Asymptotic normality is established for a broad class of commonly used optimizers in deep learning, including AdamW.
  • The authors derive the corresponding asymptotic distributions for the proposed component scores used in hypothesis testing.
  • Experiments are conducted on LoRA fine-tuning of DeBERTaV3-base, BART-Large, and Qwen2.5-7B models across various tasks.
  • StatLoRA achieves comparable or better performance than vanilla LoRA, AdaLoRA, and IGU-LoRA under matched rank budgets.

Key Concepts Mentioned

  • Low-rank adaptation
  • parameter-efficient fine-tuning
  • statistical inference
  • hypothesis testing
  • test statistic
  • p-value
  • rank allocation
  • asymptotic normality
  • AdamW
  • deep learning
  • optimizer trajectories

Claims Made by the Document

  • StatLoRA outperforms or performs as well as vanilla LoRA, AdaLoRA, and IGU-LoRA under matched rank budgets.
  • The proposed testing procedure is supported by central limit theory for stochastic optimizer trajectories.

Evidence Used

  • Experiments conducted on DeBERTaV3-base, BART-Large, and Qwen2.5-7B models across various tasks.
  • Theoretical proofs of asymptotic normality for the proposed component scores used in hypothesis testing.

Methods / Approach

UNKNOWN

Limitations Stated by the Authors

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Limitations Noted by the Agent

Agent interpretation — not from the source.

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Open Questions

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Notes for Future Q&A

May include interpretation. Labeled where it does.

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Raw Abstract / Excerpt

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.