# Training Data Selection with Gradient Orthogonality for Efficient Domain Adaptation

arXiv: https://arxiv.org/abs/2602.06359 · HTML: https://mlsanity.com/paper/2602.06359/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 42 of its 54 references that are in the map.
- First posted on arXiv 6 Feb 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 30 of 42)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Large Language Models Encode Clinical Knowledge](https://mlsanity.com/paper/2212.13138/) (2022)
- [What Disease does this Patient Have? A Large-scale Open Domain Question Answering Dataset from Medical Exams](https://mlsanity.com/paper/2009.13081/) (2020)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Efficient Lifelong Learning with A-GEM](https://mlsanity.com/paper/1812.00420/) (2018)
- [Learning to Prompt for Continual Learning](https://mlsanity.com/paper/2112.08654/) (2021)
- [BloombergGPT: A Large Language Model for Finance](https://mlsanity.com/paper/2303.17564/) (2023)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Fine-Tuning can Distort Pretrained Features and Underperform Out-of-Distribution](https://mlsanity.com/paper/2202.10054/) (2022)
- [An Empirical Study of Catastrophic Forgetting in Large Language Models During Continual Fine-tuning](https://mlsanity.com/paper/2308.08747/) (2023)
- [FinQA: A Dataset of Numerical Reasoning over Financial Data](https://mlsanity.com/paper/2109.00122/) (2021)
- [CCNet: Extracting High Quality Monolingual Datasets from Web Crawl Data](https://mlsanity.com/paper/1911.00359/) (2019)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [Weak-to-Strong Generalization: Eliciting Strong Capabilities With Weak Supervision](https://mlsanity.com/paper/2312.09390/) (2023)
- [Gradient Projection Memory for Continual Learning](https://mlsanity.com/paper/2103.09762/) (2021)
- [Selection via Proxy: Efficient Data Selection for Deep Learning](https://mlsanity.com/paper/1906.11829/) (2019)
- [LegalBench: A Collaboratively Built Benchmark for Measuring Legal Reasoning in Large Language Models](https://mlsanity.com/paper/2308.11462/) (2023)
- [Data Selection for Language Models via Importance Resampling](https://mlsanity.com/paper/2302.03169/) (2023)
- [Continual Learning of Large Language Models: A Comprehensive Survey](https://mlsanity.com/paper/2404.16789/) (2024)
- [GLISTER: Generalization based Data Subset Selection for Efficient and Robust Learning](https://mlsanity.com/paper/2012.10630/) (2020)
- [PIXIU: A Large Language Model, Instruction Data and Evaluation Benchmark for Finance](https://mlsanity.com/paper/2306.05443/) (2023)

## Built on by (most cited first, 3 of 3)

- [SURGE: An Event-Centric Social Media Sentiment Time Series Benchmark with Interaction Structure](https://mlsanity.com/paper/2605.21198/) (2026)
- [Preference Data Selection for Mitigating the Alignment Tax in Large Language Models](https://mlsanity.com/paper/2608.24192/) (2026)
- [Outcome-Routed Distillation and Reinforcement Learning for Diffusion Language Models](https://mlsanity.com/paper/2610.19271/) (2026)

## Abstract (arXiv)

Fine-tuning large language models (LLMs) for specialized domains often necessitates a trade-off between acquiring domain expertise and retaining general reasoning capabilities, a phenomenon known as catastrophic forgetting. Existing remedies face a dichotomy: gradient surgery methods offer geometric safety but incur prohibitive computational costs via online projections, while efficient data selection approaches reduce overhead but remain blind to conflict-inducing gradient directions. In this paper, we propose Orthogonal Gradient Selection (OGS), a data-centric method that harmonizes domain performance, general capability retention, and training efficiency. OGS shifts the geometric insights of gradient projection from the optimizer to the data selection stage by treating data selection as a constrained decision-making process. By leveraging a lightweight Navigator model and reinforcement learning techniques, OGS dynamically identifies training samples whose gradients are orthogonal to a general-knowledge anchor. This approach ensures naturally safe updates for target models without modifying the optimizer or incurring runtime projection costs. Experiments across medical, legal, and financial domains demonstrate that OGS achieves excellent results, significantly improving domain performance and training efficiency while maintaining or even enhancing performance on general tasks such as GSM8K.