# Data Valuation Without Training of a Model

arXiv: https://arxiv.org/abs/2301.00930 · HTML: https://mlsanity.com/paper/2301.00930/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 43 references that are in the map.
- First posted on arXiv 3 Jan 2023.

## Builds on (most cited first, 30 of 33)

- [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)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [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)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [DivideMix: Learning with Noisy Labels as Semi-supervised Learning](https://mlsanity.com/paper/2002.07394/) (2020)
- [An Empirical Study of Example Forgetting during Deep Neural Network Learning](https://mlsanity.com/paper/1812.05159/) (2018)
- [Learning to Reweight Examples for Robust Deep Learning](https://mlsanity.com/paper/1803.09050/) (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)
- [Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks](https://mlsanity.com/paper/1901.08584/) (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)
- [Dataset Cartography: Mapping and Diagnosing Datasets with Training Dynamics](https://mlsanity.com/paper/2009.10795/) (2020)
- [Identifying Mislabeled Data using the Area Under the Margin Ranking](https://mlsanity.com/paper/2001.10528/) (2020)
- [Geometry-aware Instance-reweighted Adversarial Training](https://mlsanity.com/paper/2010.01736/) (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)
- [Active Bias: Training More Accurate Neural Networks by Emphasizing High Variance Samples](https://mlsanity.com/paper/1704.07433/) (2017)
- [Deep Learning Through the Lens of Example Difficulty](https://mlsanity.com/paper/2106.09647/) (2021)
- [When Do Curricula Work?](https://mlsanity.com/paper/2012.03107/) (2020)
- [Estimating Example Difficulty Using Variance of Gradients](https://mlsanity.com/paper/2008.11600/) (2020)
- [Characterizing Structural Regularities of Labeled Data in Overparameterized Models](https://mlsanity.com/paper/2002.03206/) (2020)
- [FINE Samples for Learning with Noisy Labels](https://mlsanity.com/paper/2102.11628/) (2021)
- [Robust Inference via Generative Classifiers for Handling Noisy Labels](https://mlsanity.com/paper/1901.11300/) (2019)

## Built on by (most cited first, 30 of 35)

- [DataInf: Efficiently Estimating Data Influence in LoRA-tuned LLMs and Diffusion Models](https://mlsanity.com/paper/2310.00902/) (2023)
- [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)
- [Rethinking Data Shapley for Data Selection Tasks: Misleads and Merits](https://mlsanity.com/paper/2405.03875/) (2024)
- [A CLIP-Powered Framework for Robust and Generalizable Data Selection](https://mlsanity.com/paper/2410.11215/) (2024)
- [Dataset Difficulty and the Role of Inductive Bias](https://mlsanity.com/paper/2401.01867/) (2024)
- [BWS: Best Window Selection Based on Sample Scores for Data Pruning across Broad Ranges](https://mlsanity.com/paper/2406.03057/) (2024)
- [What do larger image classifiers memorise?](https://mlsanity.com/paper/2310.05337/) (2023)
- [Precedence-Constrained Winter Value for Effective Graph Data Valuation](https://mlsanity.com/paper/2402.01943/) (2024)
- [When Dynamic Data Selection Meets Data Augmentation](https://mlsanity.com/paper/2505.03809/) (2025)
- [GMValuator: Similarity-based Data Valuation for Generative Models](https://mlsanity.com/paper/2304.10701/) (2023)
- [Boosting Backdoor Attack with A Learnable Poisoning Sample Selection Strategy](https://mlsanity.com/paper/2307.07328/) (2023)
- [CHG Shapley: Efficient Data Valuation and Selection towards Trustworthy Machine Learning](https://mlsanity.com/paper/2406.11730/) (2024)
- [Where Did It Go Wrong? Attributing Undesirable LLM Behaviors via Representation Gradient Tracing](https://mlsanity.com/paper/2510.02334/) (2025)
- [Nonparametric Data Attribution for Diffusion Models](https://mlsanity.com/paper/2510.14269/) (2025)
- [Not All Data Matters: An End-to-End Adaptive Dataset Pruning Framework for Enhancing Model Performance and Efficiency](https://mlsanity.com/paper/2312.05599/) (2023)
- [RL-Selector: Reinforcement Learning-Guided Data Selection via Redundancy Assessment](https://mlsanity.com/paper/2506.21037/) (2025)
- [EcoVal: An Efficient Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2402.09288/) (2024)
- [Data-Centric AI in the Age of Large Language Models](https://mlsanity.com/paper/2406.14473/) (2024)
- [Fast Training Dataset Attribution via In-Context Learning](https://mlsanity.com/paper/2408.11852/) (2024)
- [UtilGen: Utility-Centric Generative Data Augmentation with Dual-Level Task Adaptation](https://mlsanity.com/paper/2510.24262/) (2025)
- [Data Agent: Learning to Select Data via End-to-End Dynamic Optimization](https://mlsanity.com/paper/2603.07433/) (2026)
- [Enhancing High-Energy Particle Physics Collision Analysis through Graph Data Attribution Techniques](https://mlsanity.com/paper/2407.14859/) (2024)
- [Private, Augmentation-Robust and Task-Agnostic Data Valuation Approach for Data Marketplace](https://mlsanity.com/paper/2411.00745/) (2024)
- [Unifying and Optimizing Data Values for Selection via Sequential Decision-Making](https://mlsanity.com/paper/2502.04554/) (2025)
- [Shapley-Guided Utility Learning for Effective Graph Inference Data Valuation](https://mlsanity.com/paper/2503.18195/) (2025)
- [Multimodal-Guided Dynamic Dataset Pruning for Robust and Efficient Data-Centric Learning](https://mlsanity.com/paper/2507.12750/) (2025)
- [VTruST: Controllable value function based subset selection for Data-Centric Trustworthy AI](https://mlsanity.com/paper/2403.05174/) (2024)
- [Reframing Data Value for Large Language Models Through the Lens of Plausibility](https://mlsanity.com/paper/2409.00284/) (2024)
- [Data Overvaluation Attack and Truthful Data Valuation in Federated Learning](https://mlsanity.com/paper/2502.00494/) (2025)

## Abstract (arXiv)

Many recent works on understanding deep learning try to quantify how much individual data instances influence the optimization and generalization of a model. Such attempts reveal characteristics and importance of individual instances, which may provide useful information in diagnosing and improving deep learning. However, most of the existing works on data valuation require actual training of a model, which often demands high-computational cost. In this paper, we provide a training-free data valuation score, called complexity-gap score, which is a data-centric score to quantify the influence of individual instances in generalization of two-layer overparameterized neural networks. The proposed score can quantify irregularity of the instances and measure how much each data instance contributes in the total movement of the network parameters during training. We theoretically analyze and empirically demonstrate the effectiveness of the complexity-gap score in finding `irregular or mislabeled' data instances, and also provide applications of the score in analyzing datasets and diagnosing training dynamics. Our code is publicly available at https://github.com/JJchy/CG_score