# Datamodels: Predicting Predictions from Training Data

arXiv: https://arxiv.org/abs/2202.00622 · HTML: https://mlsanity.com/paper/2202.00622/

## Key facts

- Cited by 189 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 98 references that are in the map.
- First posted on arXiv 1 Feb 2022.

## Builds on (most cited first, 30 of 53)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Extracting Training Data from Large Language Models](https://mlsanity.com/paper/2012.07805/) (2020)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (2017)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [BadNets: Identifying Vulnerabilities in the Machine Learning Model Supply Chain](https://mlsanity.com/paper/1708.06733/) (2017)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [Deduplicating Training Data Makes Language Models Better](https://mlsanity.com/paper/2107.06499/) (2021)
- [An Empirical Study of Example Forgetting during Deep Neural Network Learning](https://mlsanity.com/paper/1812.05159/) (2018)
- [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)
- [What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation](https://mlsanity.com/paper/2008.03703/) (2020)
- [Underspecification Presents Challenges for Credibility in Modern Machine Learning](https://mlsanity.com/paper/2011.03395/) (2020)
- [Does Learning Require Memorization? A Short Tale about a Long Tail](https://mlsanity.com/paper/1906.05271/) (2019)
- [Selection via Proxy: Efficient Data Selection for Deep Learning](https://mlsanity.com/paper/1906.11829/) (2019)
- [Functional Map of the World](https://mlsanity.com/paper/1711.07846/) (2017)
- [Differential Privacy Has Disparate Impact on Model Accuracy](https://mlsanity.com/paper/1905.12101/) (2019)
- [An Investigation of Why Overparameterization Exacerbates Spurious Correlations](https://mlsanity.com/paper/2005.04345/) (2020)
- [Towards Efficient Data Valuation Based on the Shapley Value](https://mlsanity.com/paper/1902.10275/) (2019)
- [Influence Functions in Deep Learning Are Fragile](https://mlsanity.com/paper/2006.14651/) (2020)
- [Deep learning: a statistical viewpoint](https://mlsanity.com/paper/2103.09177/) (2021)
- [Revisiting Model Stitching to Compare Neural Representations](https://mlsanity.com/paper/2106.07682/) (2021)

## Built on by (most cited first, 30 of 189)

- [DataComp: In search of the next generation of multimodal datasets](https://mlsanity.com/paper/2304.14108/) (2023)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [SalUn: Empowering Machine Unlearning via Gradient-based Weight Saliency in Both Image Classification and Generation](https://mlsanity.com/paper/2310.12508/) (2023)
- [TRAK: Attributing Model Behavior at Scale](https://mlsanity.com/paper/2303.14186/) (2023)
- [The Privacy Onion Effect: Memorization is Relative](https://mlsanity.com/paper/2206.10469/) (2022)
- [Data Banzhaf: A Robust Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2205.15466/) (2022)
- [Similarity of Neural Network Models: A Survey of Functional and Representational Measures](https://mlsanity.com/paper/2305.06329/) (2023)
- [Skill-it! A Data-Driven Skills Framework for Understanding and Training Language Models](https://mlsanity.com/paper/2307.14430/) (2023)
- [Foundation Models and Fair Use](https://mlsanity.com/paper/2303.15715/) (2023)
- [DsDm: Model-Aware Dataset Selection with Datamodels](https://mlsanity.com/paper/2401.12926/) (2024)
- [MATES: Model-Aware Data Selection for Efficient Pretraining with Data Influence Models](https://mlsanity.com/paper/2406.06046/) (2024)
- [ContextCite: Attributing Model Generation to Context](https://mlsanity.com/paper/2409.00729/) (2024)
- [Distilling Model Failures as Directions in Latent Space](https://mlsanity.com/paper/2206.14754/) (2022)
- [Cramming: Training a Language Model on a Single GPU in One Day](https://mlsanity.com/paper/2212.14034/) (2022)
- [Data Shapley in One Training Run](https://mlsanity.com/paper/2406.11011/) (2024)
- [In-context Example Selection with Influences](https://mlsanity.com/paper/2302.11042/) (2023)
- [Data Curation Alone Can Stabilize In-context Learning](https://mlsanity.com/paper/2212.10378/) (2022)
- [Measuring the Effect of Training Data on Deep Learning Predictions via Randomized Experiments](https://mlsanity.com/paper/2206.10013/) (2022)
- [Intriguing Properties of Data Attribution on Diffusion Models](https://mlsanity.com/paper/2311.00500/) (2023)
- [Improving Pretraining Data Using Perplexity Correlations](https://mlsanity.com/paper/2409.05816/) (2024)
- [The Journey, Not the Destination: How Data Guides Diffusion Models](https://mlsanity.com/paper/2312.06205/) (2023)
- [Incremental Residual Concept Bottleneck Models](https://mlsanity.com/paper/2404.08978/) (2024)
- [Scalable Influence and Fact Tracing for Large Language Model Pretraining](https://mlsanity.com/paper/2410.17413/) (2024)
- [Canary in a Coalmine: Better Membership Inference with Ensembled Adversarial Queries](https://mlsanity.com/paper/2210.10750/) (2022)
- [Capturing the Temporal Dependence of Training Data Influence](https://mlsanity.com/paper/2412.09538/) (2024)
- [Training Data Attribution via Approximate Unrolled Differentiation](https://mlsanity.com/paper/2405.12186/) (2024)
- [A Data-Based Perspective on Transfer Learning](https://mlsanity.com/paper/2207.05739/) (2022)
- [Most Influential Subset Selection: Challenges, Promises, and Beyond](https://mlsanity.com/paper/2409.18153/) (2024)
- [ModelDiff: A Framework for Comparing Learning Algorithms](https://mlsanity.com/paper/2211.12491/) (2022)
- [MoDoMoDo: Multi-Domain Data Mixtures for Multimodal LLM Reinforcement Learning](https://mlsanity.com/paper/2505.24871/) (2025)

## Abstract (arXiv)

We present a conceptual framework, datamodeling, for analyzing the behavior of a model class in terms of the training data. For any fixed "target" example x, training set S, and learning algorithm, a datamodel is a parameterized function 2S → ℝ that for any subset of S' subset S -- using only information about which examples of S are contained in S' -- predicts the outcome of training a model on S' and evaluating on x. Despite the potential complexity of the underlying process being approximated (e.g., end-to-end training and evaluation of deep neural networks), we show that even simple linear datamodels can successfully predict model outputs. We then demonstrate that datamodels give rise to a variety of applications, such as: accurately predicting the effect of dataset counterfactuals; identifying brittle predictions; finding semantically similar examples; quantifying train-test leakage; and embedding data into a well-behaved and feature-rich representation space. Data for this paper (including pre-computed datamodels as well as raw predictions from four million trained deep neural networks) is available at https://github.com/MadryLab/datamodels-data .