# LESS: Selecting Influential Data for Targeted Instruction Tuning

arXiv: https://arxiv.org/abs/2402.04333 · HTML: https://mlsanity.com/paper/2402.04333/

## Key facts

- Cited by 532 papers in the map (data through 14 Oct 2026).
- Builds on 65 of its 88 references that are in the map.
- First posted on arXiv 6 Feb 2024.

## Builds on (most cited first, 30 of 65)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [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)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Don't Stop Pretraining: Adapt Language Models to Domains and Tasks](https://mlsanity.com/paper/2004.10964/) (2020)
- [Multitask Prompted Training Enables Zero-Shot Task Generalization](https://mlsanity.com/paper/2110.08207/) (2021)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [WizardLM: Empowering large pre-trained language models to follow complex instructions](https://mlsanity.com/paper/2304.12244/) (2023)
- [Super-NaturalInstructions: Generalization via Declarative Instructions on 1600+ NLP Tasks](https://mlsanity.com/paper/2204.07705/) (2022)
- [Enhancing Chat Language Models by Scaling High-quality Instructional Conversations](https://mlsanity.com/paper/2305.14233/) (2023)
- [XTREME: A Massively Multilingual Multi-task Benchmark for Evaluating Cross-lingual Generalization](https://mlsanity.com/paper/2003.11080/) (2020)
- [The Flan Collection: Designing Data and Methods for Effective Instruction Tuning](https://mlsanity.com/paper/2301.13688/) (2023)
- [OpenAssistant Conversations -- Democratizing Large Language Model Alignment](https://mlsanity.com/paper/2304.07327/) (2023)
- [An Empirical Study of Example Forgetting during Deep Neural Network Learning](https://mlsanity.com/paper/1812.05159/) (2018)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [On Exact Computation with an Infinitely Wide Neural Net](https://mlsanity.com/paper/1904.11955/) (2019)
- [Deep Learning on a Data Diet: Finding Important Examples Early in Training](https://mlsanity.com/paper/2107.07075/) (2021)
- [Beyond neural scaling laws: beating power law scaling via data pruning](https://mlsanity.com/paper/2206.14486/) (2022)
- [What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation](https://mlsanity.com/paper/2008.03703/) (2020)

## Built on by (most cited first, 30 of 532)

- [SimPO: Simple Preference Optimization with a Reference-Free Reward](https://mlsanity.com/paper/2405.14734/) (2024)
- [Retrieval-Augmented Generation for AI-Generated Content: A Survey](https://mlsanity.com/paper/2402.19473/) (2024)
- [ReST-MCTS*: LLM Self-Training via Process Reward Guided Tree Search](https://mlsanity.com/paper/2406.03816/) (2024)
- [Reinforcement Learning for Reasoning in Large Language Models with One Training Example](https://mlsanity.com/paper/2504.20571/) (2025)
- [NVILA: Efficient Frontier Visual Language Models](https://mlsanity.com/paper/2412.04468/) (2024)
- [RegMix: Data Mixture as Regression for Language Model Pre-training](https://mlsanity.com/paper/2407.01492/) (2024)
- [Rho-1: Not All Tokens Are What You Need](https://mlsanity.com/paper/2404.07965/) (2024)
- [What is in Your Safe Data? Identifying Benign Data that Breaks Safety](https://mlsanity.com/paper/2404.01099/) (2024)
- [Act Only When It Pays: Efficient Reinforcement Learning for LLM Reasoning via Selective Rollouts](https://mlsanity.com/paper/2506.02177/) (2025)
- [MATES: Model-Aware Data Selection for Efficient Pretraining with Data Influence Models](https://mlsanity.com/paper/2406.06046/) (2024)
- [Learning Dynamics of LLM Finetuning](https://mlsanity.com/paper/2407.10490/) (2024)
- [DART-Math: Difficulty-Aware Rejection Tuning for Mathematical Problem-Solving](https://mlsanity.com/paper/2407.13690/) (2024)
- [What is Your Data Worth to GPT? LLM-Scale Data Valuation with Influence Functions](https://mlsanity.com/paper/2405.13954/) (2024)
- [Data Shapley in One Training Run](https://mlsanity.com/paper/2406.11011/) (2024)
- [A Survey of Multimodal Large Language Model from A Data-centric Perspective](https://mlsanity.com/paper/2405.16640/) (2024)
- [Nemotron-CLIMB: CLustering-based Iterative Data Mixture Bootstrapping for Language Model Pre-training](https://mlsanity.com/paper/2504.13161/) (2025)
- [Towards Lifelong Learning of Large Language Models: A Survey](https://mlsanity.com/paper/2406.06391/) (2024)
- [SEAL: Safety-enhanced Aligned LLM Fine-tuning via Bilevel Data Selection](https://mlsanity.com/paper/2410.07471/) (2024)
- [PRISM: Self-Pruning Intrinsic Selection Method for Training-Free Multimodal Data Selection](https://mlsanity.com/paper/2502.12119/) (2025)
- [Aligning Language Models to Explicitly Handle Ambiguity](https://mlsanity.com/paper/2404.11972/) (2024)
- [Clustering and Ranking: Diversity-preserved Instruction Selection through Expert-aligned Quality Estimation](https://mlsanity.com/paper/2402.18191/) (2024)
- [The Best Instruction-Tuning Data are Those That Fit](https://mlsanity.com/paper/2502.04194/) (2025)
- [Adaptive Data Optimization: Dynamic Sample Selection with Scaling Laws](https://mlsanity.com/paper/2410.11820/) (2024)
- [ReasonFlux-PRM: Trajectory-Aware PRMs for Long Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2506.18896/) (2025)
- [JiuZhang3.0: Efficiently Improving Mathematical Reasoning by Training Small Data Synthesis Models](https://mlsanity.com/paper/2405.14365/) (2024)
- [Prompt Curriculum Learning for Efficient LLM Post-Training](https://mlsanity.com/paper/2510.01135/) (2025)
- [GeoLLaVA-8K: Scaling Remote-Sensing Multimodal Large Language Models to 8K Resolution](https://mlsanity.com/paper/2505.21375/) (2025)
- [Scalable Influence and Fact Tracing for Large Language Model Pretraining](https://mlsanity.com/paper/2410.17413/) (2024)
- [What is the Role of Small Models in the LLM Era: A Survey](https://mlsanity.com/paper/2409.06857/) (2024)
- [Prismatic Synthesis: Gradient-based Data Diversification Boosts Generalization in LLM Reasoning](https://mlsanity.com/paper/2505.20161/) (2025)

## Abstract (arXiv)

Instruction tuning has unlocked powerful capabilities in large language models (LLMs), effectively using combined datasets to develop generalpurpose chatbots. However, real-world applications often require a specialized suite of skills (e.g., reasoning). The challenge lies in identifying the most relevant data from these extensive datasets to effectively develop specific capabilities, a setting we frame as targeted instruction tuning. We propose LESS, an optimizer-aware and practically efficient algorithm to effectively estimate data influences and perform Low-rank gradiEnt Similarity Search for instruction data selection. Crucially, LESS adapts existing influence formulations to work with the Adam optimizer and variable-length instruction data. LESS first constructs a highly reusable and transferable gradient datastore with low-dimensional gradient features and then selects examples based on their similarity to few-shot examples embodying a specific capability. Experiments show that training on a LESS-selected 5% of the data can often outperform training on the full dataset across diverse downstream tasks. Furthermore, the selected data is highly transferable: smaller models can be leveraged to select useful data for larger models and models from different families. Our qualitative analysis shows that our method goes beyond surface form cues to identify data that exemplifies the necessary reasoning skills for the intended downstream application.