Beyond Neural Scaling Laws: Beating Power Law Scaling Via Data Pruning
Open accessAbstract
Widely observed neural scaling laws, in which error falls off as a power of the training set size, model size, or both, have driven substantial performance improvements in deep learning. However, these improvements through scaling alone require considerable costs in compute and energy. Here we focus on the scaling of error with dataset size and show how in theory we can break beyond power law scaling and potentially even reduce it to exponential scaling instead if we have access to a high-quality data pruning metric that ranks the order in which training examples should be discarded to achieve any pruned dataset size. We then test this improved scaling prediction with pruned dataset size empirically, and indeed observe better than power law scaling in practice on ResNets trained on CIFAR-10, SVHN, and ImageNet. Next, given the importance of finding high-quality pruning metrics, we perform the first large-scale benchmarking study of ten different data pruning metrics on ImageNet. We find most existing high performing metrics scale poorly to ImageNet, while the best are computationally intensive and require labels for every image. We therefore developed a new simple, cheap and scalable self-supervised pruning metric that demonstrates comparable performance to the best supervised metrics. Overall, our work suggests that the discovery of good data-pruning metrics may provide a viable path forward to substantially improved neural scaling laws, thereby reducing the resource costs of modern deep learning.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Sorscher et al. [2022] argued that the power-law dependence on data is not inevitable: with a good example-difficulty ranking, aggressive data pruning can in principle yield faster-than-power-law decay of error.
“Sorscher et al. [2022] argued that the power-law dependence on data is not inevitable: with a good exampledifficulty ranking, aggressive data pruning can in principle yield faster-than-power-law decay of error”
From Training Compute-Optimal Transformer Models: A Review of Scaling Laws, Allocation, and Practice (2026) · cites this paper as Sorscher et al., 2022
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
No references could be resolved yet.
Research works printed but not linked: 48
- [1][1] Joel Hestness, Sharan Narang, Newsha Ardalani, Gregory Diamos, Heewoo Jun, Hassan Kianinejad, Md Patwary, Mostofa Ali, Yang Yang, and Yanqi Zhou. Deep learning scaling is predictable, empirically. arXiv preprint arXiv:1712.00409 , 2017. - · arXiv
- [2][2] Jared Kaplan, Sam McCandlish, Tom Henighan, Tom B Brown, Benjamin Chess, Rewon Child, Scott Gray, Alec Radford, Jeffrey Wu, and Dario Amodei. Scaling laws for neural language models. arXiv preprint arXiv:2001.08361 , 2020. - · arXiv
- [3][3] Tom Henighan, Jared Kaplan, Mor Katz, Mark Chen, Christopher Hesse, Jacob Jackson, Heewoo Jun, Tom B Brown, Prafulla Dhariwal, Scott Gray, et al. Scaling laws for autoregressive generative modeling. arXiv preprint arXiv:2010.14701 , 2020. - · arXiv
- [4][4] Jonathan S. Rosenfeld, Amir Rosenfeld, Yonatan Belinkov, and Nir Shavit. A constructive prediction of the generalization error across scales. International Conference on Learning Representations , 2020. -
- [5][5] Mitchell A Gordon, Kevin Duh, and Jared Kaplan. Data and parameter scaling laws for neural machine translation. In Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing , pages 5915-5922, Online and Punta Cana, Dominican Republic, November 2021. Association for Computational Linguistics. -
- [6][6] Danny Hernandez, Jared Kaplan, Tom Henighan, and Sam McCandlish. Scaling laws for transfer. arXiv preprint arXiv:2102.01293 , 2021. - · arXiv
- [7][7] Xiaohua Zhai, Alexander Kolesnikov, Neil Houlsby, and Lucas Beyer. Scaling vision transformers. arXiv preprint arXiv:2106.04560 , 2021. - · arXiv
- [8][8] Jordan Hoffmann, Sebastian Borgeaud, Arthur Mensch, Elena Buchatskaya, Trevor Cai, Eliza Rutherford, Diego de Las Casas, Lisa Anne Hendricks, Johannes Welbl, Aidan Clark, et al. Training compute-optimal large language models. arXiv preprint arXiv:2203.15556 , 2022. - · arXiv
- [9][9] Mariya Toneva, Alessandro Sordoni, Remi Tachet des Combes, Adam Trischler, Yoshua Bengio, and Geoffrey J Gordon. An empirical study of example forgetting during deep neural network learning. In ICLR , 2019. -
- [10][10] Mansheej Paul, Surya Ganguli, and Gintare Karolina Dziugaite. Deep learning on a data diet: Finding important examples early in training. Adv. Neural Inf. Process. Syst. , 34, December 2021. -
- [11][11] Kashyap Chitta, José M Álvarez, Elmar Haussmann, and Clément Farabet. Training data subset search with ensemble active learning. IEEE Trans. Intell. Transp. Syst. , pages 1-12, 2021. -
- [12][12] Rishi Bommasani, Drew A Hudson, Ehsan Adeli, Russ Altman, Simran Arora, Sydney von Arx, Michael S Bernstein, Jeannette Bohg, Antoine Bosselut, Emma Brunskill, et al. On the opportunities and risks of foundation models. arXiv preprint arXiv:2108.07258 , 2021. - · arXiv
- [13][13] Vitaly Feldman and Chiyuan Zhang. What neural networks memorize and why: Discovering the long tail via influence estimation. Adv. Neural Inf. Process. Syst. , 33:2881-2891, 2020. -
- [14][14] Hrayr Harutyunyan, Alessandro Achille, Giovanni Paolini, Orchid Majumder, Avinash Ravichandran, Rahul Bhotika, and Stefano Soatto. Estimating informativeness of samples with smooth unique information. In International Conference on Learning Representations , 2021. -
- [16][16] Antoine Bordes, Seyda Ertekin, Jason Weston, Léon Botton, and Nello Cristianini. Fast kernel classifiers with online and active learning. J. Mach. Learn. Res. , 6(9), 2005. -
- [17][17] Zeyad Ali Sami Emam, Hong-Min Chu, Ping-Yeh Chiang, Wojciech Czaja, Richard Leapman, Micah Goldblum, and Tom Goldstein. Active learning at the ImageNet scale. arXiv preprint arXiv:2111.12880 , 2021. - · arXiv
- [18][18] Ozan Sener and Silvio Savarese. Active learning for convolutional neural networks: A core-set approach. arXiv preprint arXiv:1708.00489 , 2017. - · arXiv
- [19][19] Siddharth Karamcheti, Ranjay Krishna, Li Fei-Fei, and Christopher D Manning. Mind your outliers! Investigating the negative impact of outliers on active learning for visual question answering. arXiv preprint arXiv:2107.02331 , 2021. - · arXiv
- [20][20] Baharan Mirzasoleiman, Jeff Bilmes, and Jure Leskovec. Coresets for data-efficient training of machine learning models. In Hal Daumé Iii and Aarti Singh, editors, Proceedings of the 37th International Conference on Machine Learning , volume 119 of Proceedings of Machine Learning Research , pages 6950-6960. PMLR, 2020. -
- [21][21] V Birodkar, H Mobahi, and S Bengio. Semantic redundancies in Image-Classification datasets: The 10% you don't need. arXiv preprint arXiv:1901.11409 , 2019. - · arXiv
- [22][22] Kristof Meding, Luca M. Schulze Buschoff, Robert Geirhos, and Felix A. Wichmann. Trivial or impossible-dichotomous data difficulty masks model differences (on ImageNet and beyond). In International Conference on Learning Representations , 2022. -
- [23][23] Utkarsh Sharma and Jared Kaplan. Scaling laws from the data manifold dimension. Journal of Machine Learning Research , 23(9):1-34, 2022. -
- [24][24] Yasaman Bahri, Ethan Dyer, Jared Kaplan, Jaehoon Lee, and Utkarsh Sharma. Explaining neural scaling laws. CoRR , abs/2102.06701, 2021. - · arXiv
- [25][25] Jonathan S. Rosenfeld. Scaling Laws for Deep Learning . PhD thesis, Massachusetts Institute of Technology, USA, 2021. -
- [26][26] A Engel and C V den Broeck. Statistical Mechanics of Learning . Cambridge Univ. Press, 2001. -
- [27][27] Madhu Advani, Subhaneil Lahiri, and Surya Ganguli. Statistical mechanics of complex neural systems and high dimensional data. J. Stat. Mech: Theory Exp. , 2013(03):P03014, 2013. -
- [28][28] Yasaman Bahri, Jonathan Kadmon, Jeffrey Pennington, Sam S Schoenholz, Jascha SohlDickstein, and Surya Ganguli. Statistical mechanics of deep learning. Annual Review of Condensed Matter Physics , March 2020. -
- [29][29] Lenka Zdeborová and Florent Krzakala. Statistical physics of inference: thresholds and algorithms. Adv. Phys. , 65(5):453-552, September 2016. -
- [31][31] H S Seung, H Sompolinsky, and N Tishby. Statistical mechanics of learning from examples. Phys. Rev. A , 45(8):6056, 1992. -
- [32][32] Yoav Freund, H Sebastian Seung, Eli Shamir, and Naftali Tishby. Information, prediction, and query by committee. Adv. Neural Inf. Process. Syst. , 5, 1992. -
- [33][33] Hai-Jun Zhou. Active online learning in the binary perceptron problem. Commun. Theor. Phys. , 71(2):243, February 2019. -
- [36][36] Mathilde Caron, Ishan Misra, Julien Mairal, Priya Goyal, Piotr Bojanowski, and Armand Joulin. Unsupervised learning of visual features by contrasting cluster assignments. In H. Larochelle, M. Ranzato, R. Hadsell, M.F. Balcan, and H. Lin, editors, Advances in Neural Information Processing Systems , volume 33, pages 9912-9924. Curran Associates, Inc., 2020. -
- [37][37] Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, et al. Learning transferable visual models from natural language supervision. In International Conference on Machine Learning , pages 8748-8763. PMLR, 2021. -
- [38][38] Dhruv Mahajan, Ross Girshick, Vignesh Ramanathan, Kaiming He, Manohar Paluri, Yixuan Li, Ashwin Bharambe, and Laurens Van Der Maaten. Exploring the limits of weakly supervised pretraining. In Proceedings of the European conference on computer vision (ECCV) , pages 181-196, 2018. -
- [39][39] Aditya Ramesh, Prafulla Dhariwal, Alex Nichol, Casey Chu, and Mark Chen. Hierarchical text-conditional image generation with clip latents. arXiv preprint arXiv:2204.06125 , 2022. - · arXiv
- [40][40] Aakanksha Chowdhery, Sharan Narang, Jacob Devlin, Maarten Bosma, Gaurav Mishra, Adam Roberts, Paul Barham, Hyung Won Chung, Charles Sutton, Sebastian Gehrmann, et al. Palm: Scaling language modeling with pathways. arXiv preprint arXiv:2204.02311 , 2022. - · arXiv
- [42][42] Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej Karpathy, Aditya Khosla, Michael Bernstein, et al. ImageNet large scale visual recognition challenge. International Journal of Computer Vision , 115(3):211-252, 2015. -
- [43][43] Kaiyu Yang, Klint Qinami, Li Fei-Fei, Jia Deng, and Olga Russakovsky. Towards fairer datasets: Filtering and balancing the distribution of the people subtree in the ImageNet hierarchy. In Proceedings of the 2020 Conference on Fairness, Accountability, and Transparency , pages 547-558, 2020. -
- [44][44] Yuki M Asano, Christian Rupprecht, Andrew Zisserman, and Andrea Vedaldi. PASS: An ImageNet replacement for self-supervised pretraining without humans. arXiv preprint arXiv:2109.13228 , 2021. - · arXiv
- [46][46] Justin M Johnson and Taghi M Khoshgoftaar. Survey on deep learning with class imbalance. Journal of Big Data , 6(1):1-54, 2019. -
- [47][47] Robert Geirhos, Kantharaju Narayanappa, Benjamin Mitzkus, Tizian Thieringer, Matthias Bethge, Felix A Wichmann, and Wieland Brendel. Partial success in closing the gap between human and machine vision. Advances in Neural Information Processing Systems , 34:2388523899, 2021. -
- [48][48] Felix A Wichmann, David HJ Janssen, Robert Geirhos, Guillermo Aguilar, Heiko H Schütt, Marianne Maertens, and Matthias Bethge. Methods and measurements to compare men against machines. Electronic Imaging, Human Vision and Electronic Imaging , 2017(14):36-45, 2017. -
- [49][49] Robert Geirhos, Carlos RM Temme, Jonas Rauber, Heiko H Schütt, Matthias Bethge, and Felix A Wichmann. Generalisation in humans and deep neural networks. In Advances in Neural Information Processing Systems , 2018. -
- [50][50] Robert Geirhos, Patricia Rubisch, Claudio Michaelis, Matthias Bethge, Felix A. Wichmann, and Wieland Brendel. ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness. In International Conference on Learning Representations , 2019. -
- [51][51] Haohan Wang, Songwei Ge, Zachary Lipton, and Eric P Xing. Learning robust global representations by penalizing local predictive power. Advances in Neural Information Processing Systems , 32, 2019. -
- [52][52] Robert Geirhos, Kristof Meding, and Felix A Wichmann. Beyond accuracy: quantifying trialby-trial behaviour of CNNs and humans by measuring error consistency. Advances in Neural Information Processing Systems , 33, 2020. -
- [53][53] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Delving deep into rectifiers: Surpassing human-level performance on ImageNet classification. In Proceedings of the IEEE International Conference on Computer Vision , pages 1026-1034, 2015. -
- [54][54] John P Miller, Rohan Taori, Aditi Raghunathan, Shiori Sagawa, Pang Wei Koh, Vaishaal Shankar, Percy Liang, Yair Carmon, and Ludwig Schmidt. Accuracy on the line: on the strong correlation between out-of-distribution and in-distribution generalization. In International Conference on Machine Learning , pages 7721-7735. PMLR, 2021.
Cited by
Sorted by citations
Reproducible Scaling Laws for Contrastive Language-Image Learning
Cherti, M., Beaumont, R., Wightman, R., Wortsman, M., Ilharco, G., Gordon, C., Schuhmann, C., Schmidt, L., & Jitsev, J. (2023) · 2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr52729.2023.00276 · Cited by 673 · see citing works
A review of LLMs and their applications in the architecture, engineering and construction industry
Kampelopoulos, D., Tsanousa, A., Vrochidis, S., & Kompatsiaris, I. (2025) · Artificial Intelligence Review · doi:10.1007/s10462-025-11241-7 · Cited by 69 · see citing works
General intelligence requires rethinking exploration
Jiang, M., Rocktäschel, T., & Grefenstette, E. (2022) · arXiv · doi:10.48550/arxiv.2211.07819 · Cited by 17
WISE: Rethinking the Knowledge Memory for Lifelong Model Editing of Large Language Models
Wang, P., Li, Z., Zhang, N., Xu, Z., Yao, Y., Jiang, Y., Xie, P., Huang, F., & Chen, H. (2024) · arXiv · doi:10.48550/arxiv.2405.14768 · Cited by 19 · see citing works
TT-SI: Self-Improving LLM Agents with Test-Time Training
Acikgoz, E. C., Qian, C., Ji, H., Hakkani-Tür, D., & Tur, G. (2026) · Findings of the Association for Computational Linguistics: ACL 2026 · doi:10.18653/v1/2026.findings-acl.462 · Cited by 1 · see citing works
Training Compute-Optimal Transformer Models: A Review of Scaling Laws, Allocation, and Practice
Memming, A. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.7142719
- Authors
- Sorscher, B., Geirhos, R., Shekhar, S., Ganguli, S., & Morcos, A.
- Venue
- Advances in Neural Information Processing Systems 35
- Published
- 2022
- Pages
- 19523-19536
- ISSN
- 1049-5258 (ISSN-L)
- OpenAlex
- W7133230676
- Cited by
- 142
- References
- 0
- Citations by year
- 2026: 36 · 2025: 25 · 2024: 35 · 2023: 41 · 2022: 5
- FWCI
- 9.61
- Type
- conference paper
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- neural information processing systems (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Advanced Neural Network Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning and Data Classification
- Physical Sciences › Computer Science › Artificial Intelligence › Stochastic Gradient Optimization Techniques
- Keywords
- neural scaling laws, power-law scaling, data pruning, model compression, training efficiency
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review