# Nonlinearity-Aware LoRA: Structured Gate Adaptation under Low-Rank Constraints

arXiv: https://arxiv.org/abs/2606.31717 · HTML: https://mlsanity.com/paper/2606.31717/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 34 references that are in the map.
- First posted on arXiv 30 Jun 2026.

## Builds on (most cited first, 23 of 23)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
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- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [WizardLM: Empowering large pre-trained language models to follow complex instructions](https://mlsanity.com/paper/2304.12244/) (2023)
- [Remote Sensing Image Scene Classification: Benchmark and State of the Art](https://mlsanity.com/paper/1703.00121/) (2017)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)
- [PiSSA: Principal Singular Values and Singular Vectors Adaptation of Large Language Models](https://mlsanity.com/paper/2404.02948/) (2024)
- [OpenCodeInterpreter: Integrating Code Generation with Execution and Refinement](https://mlsanity.com/paper/2402.14658/) (2024)
- [A Rank Stabilization Scaling Factor for Fine-Tuning with LoRA](https://mlsanity.com/paper/2312.03732/) (2023)
- [LoRA-GA: Low-Rank Adaptation with Gradient Approximation](https://mlsanity.com/paper/2407.05000/) (2024)
- [LoRA-Pro: Are Low-Rank Adapters Properly Optimized?](https://mlsanity.com/paper/2407.18242/) (2024)
- [AuroRA: Breaking Low-Rank Bottleneck of LoRA with Nonlinear Mapping](https://mlsanity.com/paper/2505.18738/) (2025)

## Abstract (arXiv)

Low-rank adaptation (LoRA) is commonly viewed as an update-space approximation to full fine-tuning, yet this view is incomplete for self-gated Transformer feed-forward networks. In gated FFNs, a low-rank residual can change not only projected features but also the nonlinear selection weights that determine which channels contribute to the output. We formalize this effect as selection misalignment and connect it to the local effective homogeneity of self-gated activations. This motivates a nonlinearity-aware principle for parameter-efficient fine-tuning: low-rank updates should allocate capacity to gate channels whose nonlinear states remain responsive and should shape the temporal evolution of selection. We propose NA-LoRA, a training-only method with two lightweight mechanisms: a derivative-based temporal-importance mask for gate-related LoRA updates and an activation-specific step-scaling rule when a meaningful coarse effective-homogeneity partition is available. NA-LoRA adds no auxiliary loss and incurs no inference-time overhead. Experiments on language-model fine-tuning and vision-language transfer benchmarks show that NA-LoRA consistently improves over vanilla LoRA and is competitive with or better than strong PEFT variants.