Don't Forget the Nonlinearity: Unlocking Activation Functions in Efficient Fine-Tuning

• URL: http://arxiv.org/abs/2509.13240v2
• Date: Thu, 18 Sep 2025 04:46:37 GMT
• Title: Don't Forget the Nonlinearity: Unlocking Activation Functions in Efficient Fine-Tuning
• Authors: Bo Yin, Xingyi Yang, Xinchao Wang,
• Abstract summary: NoRA replaces fixed activations with learnable rational functions and applies structured low-rank updates to numerator and denominator coefficients.<n>On vision transformers trained on CIFAR-10 and CIFAR-100, NoRA matches or exceeds full fine-tuning while updating only 0.4% of parameters.<n>NoRA constrains adaptation to a low-dimensional functional subspace, implicitly regularizing update magnitude and direction.
• Score: 82.16625951603315
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Existing parameter-efficient fine-tuning (PEFT) methods primarily adapt weight matrices while keeping activation functions fixed. We introduce \textbf{NoRA}, the first PEFT framework that directly adapts nonlinear activation functions in pretrained transformer-based models. NoRA replaces fixed activations with learnable rational functions and applies structured low-rank updates to numerator and denominator coefficients, with a group-wise design that localizes adaptation and improves stability at minimal cost. On vision transformers trained on CIFAR-10 and CIFAR-100, NoRA matches or exceeds full fine-tuning while updating only 0.4\% of parameters (0.02M), achieving accuracy gains of +0.17\% and +0.27\%. When combined with LoRA (\textbf{NoRA++}), it outperforms LoRA and DoRA under matched training budgets by adding fewer trainable parameters. On LLaMA3-8B instruction tuning, NoRA++ consistently improves generation quality, yielding average MMLU gains of +0.3\%--0.8\%, including +1.6\% on STEM (Alpaca) and +1.3\% on OpenOrca. We further show that NoRA constrains adaptation to a low-dimensional functional subspace, implicitly regularizing update magnitude and direction. These results establish activation-space tuning as a complementary and highly parameter-efficient alternative to weight-based PEFT, positioning activation functions as first-class objects for model adaptation.

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