# Deep Learning on a Data Diet: Finding Important Examples Early in Training

arXiv: https://arxiv.org/abs/2107.07075 · HTML: https://mlsanity.com/paper/2107.07075/

## Key facts

- Cited by 533 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 39 references that are in the map.
- First posted on arXiv 15 Jul 2021.

## Builds on (most cited first, 25 of 25)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [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)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [An Empirical Study of Example Forgetting during Deep Neural Network Learning](https://mlsanity.com/paper/1812.05159/) (2018)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (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)
- [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)
- [Identifying Mislabeled Data using the Area Under the Margin Ranking](https://mlsanity.com/paper/2001.10528/) (2020)
- [GLISTER: Generalization based Data Subset Selection for Efficient and Robust Learning](https://mlsanity.com/paper/2012.10630/) (2020)
- [The large learning rate phase of deep learning: the catapult mechanism](https://mlsanity.com/paper/2003.02218/) (2020)
- [Deep learning versus kernel learning: an empirical study of loss landscape geometry and the time evolution of the Neural Tangent Kernel](https://mlsanity.com/paper/2010.15110/) (2020)
- [Deep Learning Through the Lens of Example Difficulty](https://mlsanity.com/paper/2106.09647/) (2021)
- [Deep Active Learning for Named Entity Recognition](https://mlsanity.com/paper/1707.05928/) (2017)
- [Estimating Example Difficulty Using Variance of Gradients](https://mlsanity.com/paper/2008.11600/) (2020)
- [Turning Big data into tiny data: Constant-size coresets for k-means, PCA and projective clustering](https://mlsanity.com/paper/1807.04518/) (2018)
- [Harnessing the Power of Infinitely Wide Deep Nets on Small-data Tasks](https://mlsanity.com/paper/1910.01663/) (2019)
- [Coresets for Scalable Bayesian Logistic Regression](https://mlsanity.com/paper/1605.06423/) (2016)
- [Bayesian Coreset Construction via Greedy Iterative Geodesic Ascent](https://mlsanity.com/paper/1802.01737/) (2018)
- [On Coresets for Logistic Regression](https://mlsanity.com/paper/1805.08571/) (2018)
- [Emergent properties of the local geometry of neural loss landscapes](https://mlsanity.com/paper/1910.05929/) (2019)
- [Coresets for Robust Training of Neural Networks against Noisy Labels](https://mlsanity.com/paper/2011.07451/) (2020)

## Built on by (most cited first, 30 of 533)

- [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)
- [Beyond neural scaling laws: beating power law scaling via data pruning](https://mlsanity.com/paper/2206.14486/) (2022)
- [DoReMi: Optimizing Data Mixtures Speeds Up Language Model Pretraining](https://mlsanity.com/paper/2305.10429/) (2023)
- [Data Selection for Language Models via Importance Resampling](https://mlsanity.com/paper/2302.03169/) (2023)
- [From Quantity to Quality: Boosting LLM Performance with Self-Guided Data Selection for Instruction Tuning](https://mlsanity.com/paper/2308.12032/) (2023)
- [SemDeDup: Data-efficient learning at web-scale through semantic deduplication](https://mlsanity.com/paper/2303.09540/) (2023)
- [Aya Model: An Instruction Finetuned Open-Access Multilingual Language Model](https://mlsanity.com/paper/2402.07827/) (2024)
- [Prioritized Training on Points that are Learnable, Worth Learning, and Not Yet Learnt](https://mlsanity.com/paper/2206.07137/) (2022)
- [D4: Improving LLM Pretraining via Document De-Duplication and Diversification](https://mlsanity.com/paper/2308.12284/) (2023)
- [DeepCore: A Comprehensive Library for Coreset Selection in Deep Learning](https://mlsanity.com/paper/2204.08499/) (2022)
- [Dataset Pruning: Reducing Training Data by Examining Generalization Influence](https://mlsanity.com/paper/2205.09329/) (2022)
- [Skill-it! A Data-Driven Skills Framework for Understanding and Training Language Models](https://mlsanity.com/paper/2307.14430/) (2023)
- [Coverage-centric Coreset Selection for High Pruning Rates](https://mlsanity.com/paper/2210.15809/) (2022)
- [On the Diversity and Realism of Distilled Dataset: An Efficient Dataset Distillation Paradigm](https://mlsanity.com/paper/2312.03526/) (2023)
- [Dataset Condensation with Contrastive Signals](https://mlsanity.com/paper/2202.02916/) (2022)
- [DsDm: Model-Aware Dataset Selection with Datamodels](https://mlsanity.com/paper/2401.12926/) (2024)
- [Finding Support Examples for In-Context Learning](https://mlsanity.com/paper/2302.13539/) (2023)
- [Quality Not Quantity: On the Interaction between Dataset Design and Robustness of CLIP](https://mlsanity.com/paper/2208.05516/) (2022)
- [How to Train Data-Efficient LLMs](https://mlsanity.com/paper/2402.09668/) (2024)
- [InfoBatch: Lossless Training Speed Up by Unbiased Dynamic Data Pruning](https://mlsanity.com/paper/2303.04947/) (2023)
- [Perplexed by Perplexity: Perplexity-Based Data Pruning With Small Reference Models](https://mlsanity.com/paper/2405.20541/) (2024)
- [A Survey of Multimodal Large Language Model from A Data-centric Perspective](https://mlsanity.com/paper/2405.16640/) (2024)
- [D2 Pruning: Message Passing for Balancing Diversity and Difficulty in Data Pruning](https://mlsanity.com/paper/2310.07931/) (2023)
- [Data Pruning via Moving-one-Sample-out](https://mlsanity.com/paper/2310.14664/) (2023)
- [Large-scale Dataset Pruning with Dynamic Uncertainty](https://mlsanity.com/paper/2306.05175/) (2023)
- [MM-LIMA: Less Is More for Alignment in Multi-Modal Datasets](https://mlsanity.com/paper/2308.12067/) (2023)
- [PRISM: Self-Pruning Intrinsic Selection Method for Training-Free Multimodal Data Selection](https://mlsanity.com/paper/2502.12119/) (2025)
- [The Best Instruction-Tuning Data are Those That Fit](https://mlsanity.com/paper/2502.04194/) (2025)
- [Automatic Data Curation for Self-Supervised Learning: A Clustering-Based Approach](https://mlsanity.com/paper/2405.15613/) (2024)

## Abstract (arXiv)

Recent success in deep learning has partially been driven by training increasingly overparametrized networks on ever larger datasets. It is therefore natural to ask: how much of the data is superfluous, which examples are important for generalization, and how do we find them? In this work, we make the striking observation that, in standard vision datasets, simple scores averaged over several weight initializations can be used to identify important examples very early in training. We propose two such scores -- the Gradient Normed (GraNd) and the Error L2-Norm (EL2N) scores -- and demonstrate their efficacy on a range of architectures and datasets by pruning significant fractions of training data without sacrificing test accuracy. In fact, using EL2N scores calculated a few epochs into training, we can prune half of the CIFAR10 training set while slightly improving test accuracy. Furthermore, for a given dataset, EL2N scores from one architecture or hyperparameter configuration generalize to other configurations. Compared to recent work that prunes data by discarding examples that are rarely forgotten over the course of training, our scores use only local information early in training. We also use our scores to detect noisy examples and study training dynamics through the lens of important examples -- we investigate how the data distribution shapes the loss surface and identify subspaces of the model's data representation that are relatively stable over training.