NormTune: Norm-Guided Parameter-Efficient Fine-Tuning for Reasoning-Intensive Tasks

Full fine-tuning has achieved remarkable success on reasoning-intensive tasks, but it often requires substantial GPU resource consumption. Parameter-efficient fine-tuning (PEFT) provides a promising alternative for reducing this cost, yet we observe a substantial performance gap on reasoning-intensive tasks. In this paper, we present three key observations showing that this gap is closely associated with norm-related under-adaptation, where PEFT produces markedly smaller weight-update norms than full fine-tuning. Based on these observations, we propose Norm-Guided Parameter-Efficient Fine-Tuning (NormTune), a simple yet effective strategy that adaptively strengthens insufficiently updated layers according to their weight-update norms. Extensive experiments show that NormTune consistently enhances multiple PEFT methods across challenging reasoning benchmarks. Specifically, when trained on S1K-1.1, integrating NormTune into rank-8 LoRA, Bone, and MoRA yields substantial average accuracy improvements of 24.24%, 11.33%, and 16.21% , respectively, across AIME 2024, MATH 500, GPQA, and AIME 2025. Moreover, NormTune-enhanced rank-256 LoRA, Bone, and MoRA surpass S1 full fine-tuning by 2.17%, 0.93%, and 3.00% on average, respectively.