# Queryable LoRA: Instruction-Regularized Routing Over Shared Low-Rank Update Atoms

arXiv: https://arxiv.org/abs/2605.08423 · HTML: https://mlsanity.com/paper/2605.08423/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 32 references that are in the map.
- First posted on arXiv 8 May 2026.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [RACE: Large-scale ReAding Comprehension Dataset From Examinations](https://mlsanity.com/paper/1704.04683/) (2017)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classification](https://mlsanity.com/paper/1602.02068/) (2016)
- [SOAP: Improving and Stabilizing Shampoo using Adam](https://mlsanity.com/paper/2409.11321/) (2024)
- [On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learning](https://mlsanity.com/paper/1704.00805/) (2017)
- [Attention Residuals](https://mlsanity.com/paper/2603.15031/) (2026)
- [Text-to-LoRA: Instant Transformer Adaption](https://mlsanity.com/paper/2506.06105/) (2025)
- [MoELoRA: Contrastive Learning Guided Mixture of Experts on Parameter-Efficient Fine-Tuning for Large Language Models](https://mlsanity.com/paper/2402.12851/) (2024)
- [VB-LoRA: Extreme Parameter Efficient Fine-Tuning with Vector Banks](https://mlsanity.com/paper/2405.15179/) (2024)
- [Doc-to-LoRA: Learning to Instantly Internalize Contexts](https://mlsanity.com/paper/2602.15902/) (2026)
- [Multimodal Instruction Tuning with Conditional Mixture of LoRA](https://mlsanity.com/paper/2402.15896/) (2024)
- [ShareLoRA: Parameter Efficient and Robust Large Language Model Fine-tuning via Shared Low-Rank Adaptation](https://mlsanity.com/paper/2406.10785/) (2024)
- [Low-Rank Interconnected Adaptation across Layers](https://mlsanity.com/paper/2407.09946/) (2024)
- [RepLoRA: Reparameterizing Low-Rank Adaptation via the Perspective of Mixture of Experts](https://mlsanity.com/paper/2502.03044/) (2025)
- [On the Mathematical Relationship Between Layer Normalization and Dynamic Activation Functions](https://mlsanity.com/paper/2503.21708/) (2025)
- [DoRAN: Stabilizing Weight-Decomposed Low-Rank Adaptation via Noise Injection and Auxiliary Networks](https://mlsanity.com/paper/2510.04331/) (2025)
- [Hypernetwork-Driven Low-Rank Adaptation Across Attention Heads](https://mlsanity.com/paper/2510.04295/) (2025)

## Abstract (arXiv)

We present a data-adaptive method for parameter-efficient fine-tuning of large neural networks. Standard low-rank adaptation methods improve efficiency by restricting each layer update to a fixed low-rank form, but this static parameterization can be too rigid when the appropriate correction depends on the input and on the evolving depth-wise computation of the network. Our approach replaces a purely layer-local adapter with a shared queryable memory of low-rank update atoms. For each block of layers, the model forms a query from the current low-rank state and a running summary of previous blocks, uses this query to retrieve a content-dependent combination of shared update components via attention, and applies the resulting routed operator within the low-rank bottleneck. In this way, the method retains the efficiency and scalability of low-rank adaptation while allowing the effective update to vary across inputs and to share reusable structure across layers. The resulting architecture provides a principled middle ground between static LoRA-style updates and fully generated parameter updates: it remains compact and parameter-efficient while supporting dynamic, context-sensitive adaptation. Further, we incorporate instruction-regularization by augmenting routing logits with a language-induced prior over update atoms, thereby biasing the selection of low-rank transformations toward semantically relevant directions without generating unconstrained parameter updates. Experiments on noisy non-linear regression tasks and LLM fine-tuning suggest that this queryable update-memory formulation can improve final test performance and training stability compared to standard low-rank adaptation, while using a comparable number of trainable parameters.