Don't Forget the Nonlinearity: Unlocking Activation Functions in Efficient Fine-Tuning
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| Format: | Preprint |
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2025
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| _version_ | 1866912591295545344 |
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| author | Yin, Bo Yang, Xingyi Wang, Xinchao |
| author_facet | Yin, Bo Yang, Xingyi Wang, Xinchao |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_13240 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Don't Forget the Nonlinearity: Unlocking Activation Functions in Efficient Fine-Tuning Yin, Bo Yang, Xingyi Wang, Xinchao Machine Learning 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. |
| title | Don't Forget the Nonlinearity: Unlocking Activation Functions in Efficient Fine-Tuning |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2509.13240 |