# What is Your Data Worth to GPT? LLM-Scale Data Valuation with Influence Functions

arXiv: https://arxiv.org/abs/2405.13954 · HTML: https://mlsanity.com/paper/2405.13954/

## Key facts

- Cited by 94 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 64 references that are in the map.
- First posted on arXiv 22 May 2024.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [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)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [Captum: A unified and generic model interpretability library for PyTorch](https://mlsanity.com/paper/2009.07896/) (2020)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation](https://mlsanity.com/paper/2008.03703/) (2020)
- [Dolma: an Open Corpus of Three Trillion Tokens for Language Model Pretraining Research](https://mlsanity.com/paper/2402.00159/) (2024)
- [Studying Large Language Model Generalization with Influence Functions](https://mlsanity.com/paper/2308.03296/) (2023)
- [TRAK: Attributing Model Behavior at Scale](https://mlsanity.com/paper/2303.14186/) (2023)
- [Towards Efficient Data Valuation Based on the Shapley Value](https://mlsanity.com/paper/1902.10275/) (2019)
- [TernGrad: Ternary Gradients to Reduce Communication in Distributed Deep Learning](https://mlsanity.com/paper/1705.07878/) (2017)
- [Influence Functions in Deep Learning Are Fragile](https://mlsanity.com/paper/2006.14651/) (2020)
- [Beta Shapley: a Unified and Noise-reduced Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2110.14049/) (2021)
- [Explaining Black Box Predictions and Unveiling Data Artifacts through Influence Functions](https://mlsanity.com/paper/2005.06676/) (2020)
- [If Influence Functions are the Answer, Then What is the Question?](https://mlsanity.com/paper/2209.05364/) (2022)
- [A Kronecker-factored approximate Fisher matrix for convolution layers](https://mlsanity.com/paper/1602.01407/) (2016)
- [Scaling Up Influence Functions](https://mlsanity.com/paper/2112.03052/) (2021)
- [Data Banzhaf: A Robust Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2205.15466/) (2022)
- [DataInf: Efficiently Estimating Data Influence in LoRA-tuned LLMs and Diffusion Models](https://mlsanity.com/paper/2310.00902/) (2023)

## Built on by (most cited first, 30 of 94)

- [Data Shapley in One Training Run](https://mlsanity.com/paper/2406.11011/) (2024)
- [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)
- [Procedural Knowledge in Pretraining Drives Reasoning in Large Language Models](https://mlsanity.com/paper/2411.12580/) (2024)
- [Capturing the Temporal Dependence of Training Data Influence](https://mlsanity.com/paper/2412.09538/) (2024)
- [Harnessing Diversity for Important Data Selection in Pretraining Large Language Models](https://mlsanity.com/paper/2409.16986/) (2024)
- [AttriBoT: A Bag of Tricks for Efficiently Approximating Leave-One-Out Context Attribution](https://mlsanity.com/paper/2411.15102/) (2024)
- [Improving Influence-based Instruction Tuning Data Selection for Balanced Learning of Diverse Capabilities](https://mlsanity.com/paper/2501.12147/) (2025)
- [CUPID: Curating Data your Robot Loves with Influence Functions](https://mlsanity.com/paper/2506.19121/) (2025)
- [Do Influence Functions Work on Large Language Models?](https://mlsanity.com/paper/2409.19998/) (2024)
- [Attribute-to-Delete: Machine Unlearning via Datamodel Matching](https://mlsanity.com/paper/2410.23232/) (2024)
- [Position: The Most Expensive Part of an LLM should be its Training Data](https://mlsanity.com/paper/2504.12427/) (2025)
- [How Much Can We Forget about Data Contamination?](https://mlsanity.com/paper/2410.03249/) (2024)
- [Montessori-Instruct: Generate Influential Training Data Tailored for Student Learning](https://mlsanity.com/paper/2410.14208/) (2024)
- [LEAD: Iterative Data Selection for Efficient LLM Instruction Tuning](https://mlsanity.com/paper/2505.07437/) (2025)
- [LayerIF: Estimating Layer Quality for Large Language Models using Influence Functions](https://mlsanity.com/paper/2505.23811/) (2025)
- [Scalable Data Ablation Approximations for Language Models through Modular Training and Merging](https://mlsanity.com/paper/2410.15661/) (2024)
- [Interpretation Meets Safety: A Survey on Interpretation Methods and Tools for Improving LLM Safety](https://mlsanity.com/paper/2506.05451/) (2025)
- [Better Training Data Attribution via Better Inverse Hessian-Vector Products](https://mlsanity.com/paper/2507.14740/) (2025)
- [TAROT: Targeted Data Selection via Optimal Transport](https://mlsanity.com/paper/2412.00420/) (2024)
- [Dissecting Representation Misalignment in Contrastive Learning via Influence Function](https://mlsanity.com/paper/2411.11667/) (2024)
- [Enhancing Training Data Attribution with Representational Optimization](https://mlsanity.com/paper/2505.18513/) (2025)
- [GraSS: Scalable Data Attribution with Gradient Sparsification and Sparse Projection](https://mlsanity.com/paper/2505.18976/) (2025)
- [The Signal is in the Steps: Local Scoring for Reasoning Data Selection](https://mlsanity.com/paper/2510.03988/) (2025)
- [Beyond Similarity: A Gradient-based Graph Method for Instruction Tuning Data Selection](https://mlsanity.com/paper/2502.11062/) (2025)
- [ALinFiK: Learning to Approximate Linearized Future Influence Kernel for Scalable Third-Party LLM Data Valuation](https://mlsanity.com/paper/2503.01052/) (2025)
- [IF-GUIDE: Influence Function-Guided Detoxification of LLMs](https://mlsanity.com/paper/2506.01790/) (2025)
- [Fast Data Attribution for Text-to-Image Models](https://mlsanity.com/paper/2511.10721/) (2025)
- [TiKMiX: Take Data Influence into Dynamic Mixture for Language Model Pre-training](https://mlsanity.com/paper/2508.17677/) (2025)
- [A Versatile Influence Function for Data Attribution with Non-Decomposable Loss](https://mlsanity.com/paper/2412.01335/) (2024)

## Abstract (arXiv)

Large language models (LLMs) are trained on a vast amount of human-written data, but data providers often remain uncredited. In response to this issue, data valuation (or data attribution), which quantifies the contribution or value of each data to the model output, has been discussed as a potential solution. Nevertheless, applying existing data valuation methods to recent LLMs and their vast training datasets has been largely limited by prohibitive compute and memory costs. In this work, we focus on influence functions, a popular gradient-based data valuation method, and significantly improve its scalability with an efficient gradient projection strategy called LoGra that leverages the gradient structure in backpropagation. We then provide a theoretical motivation of gradient projection approaches to influence functions to promote trust in the data valuation process. Lastly, we lower the barrier to implementing data valuation systems by introducing LogIX, a software package that can transform existing training code into data valuation code with minimal effort. In our data valuation experiments, LoGra achieves competitive accuracy against more expensive baselines while showing up to 6,500x improvement in throughput and 5x reduction in GPU memory usage when applied to Llama3-8B-Instruct and the 1B-token dataset.