mlsanityData to 14 Oct 2026

Pre-training under infinite compute

arXiv 2509.14786 ↗First posted 18 Sep 2025cs.LGcited by 29

Not on the map. Why?

Abstract (arXiv)

Since compute grows much faster than web text available for language model pre-training, we ask how one should approach pre-training under fixed data and no compute constraints. We first show that existing data-constrained approaches of increasing epoch count and parameter count eventually overfit, and we significantly improve upon such recipes by properly tuning regularization, finding that the optimal weight decay is 30× larger than standard practice. Since our regularized recipe monotonically decreases loss following a simple power law in parameter count, we estimate its best possible performance via the asymptote of its scaling law rather than the performance at a fixed compute budget. We then identify that ensembling independently trained models achieves a significantly lower loss asymptote than the regularized recipe. Our best intervention combining epoching, regularization, parameter scaling, and ensemble scaling achieves an asymptote at 200M tokens using 5.17× less data than our baseline, and our data scaling laws predict that this improvement persists at higher token budgets. We find that our data efficiency gains can be realized at much smaller parameter counts as we can distill an ensemble into a student model that is 8× smaller and retains 83% of the ensembling benefit. Finally, our interventions designed for validation loss generalize to downstream benchmarks, achieving a 9% improvement for pre-training evals and a 17.5× data efficiency improvement over continued pre-training on math mid-training data. Our results show that simple algorithmic improvements can enable significantly more data-efficient pre-training in a compute-rich future.

Key facts. Cited by 29 papers in the map (data through 14 Oct 2026). Builds on 75 of its 100 references that are in the map. First posted on arXiv 18 Sep 2025.

Builds on

75 of 100 references.

References · 75

  1. 2020Language Models are Few-Shot Learnerscited by 32,419
  2. 2015Distilling the Knowledge in a Neural Networkcited by 10,324
  3. 2021Training Verifiers to Solve Math Word Problemscited by 10,109
  4. 2020Scaling Laws for Neural Language Modelscited by 6,586
  5. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,371
  6. 2018Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challengecited by 4,886
  7. 2019DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lightercited by 4,307
  8. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,926
  9. 2017Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layercited by 3,509
  10. 2019PIQA: Reasoning about Physical Commonsense in Natural Languagecited by 2,883
  11. 2024Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameterscited by 1,986
  12. 2015Deep Reinforcement Learning with Double Q-learningcited by 1,745
38 more
  1. 2022Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference timecited by 1,396
  2. 2016On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minimacited by 1,352
  3. 2024Large Language Monkeys: Scaling Inference Compute with Repeated Samplingcited by 991
  4. 2023On-Policy Distillation of Language Models: Learning from Self-Generated Mistakescited by 939
  5. 2018Reconciling modern machine learning practice and the bias-variance trade-offcited by 927
  6. 2016Sequence-Level Knowledge Distillationcited by 801
  7. 2017Crowdsourcing Multiple Choice Science Questionscited by 765
  8. 2019Deep Double Descent: Where Bigger Models and More Data Hurtcited by 672
  9. 2019MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalismscited by 662
  10. 2018Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNscited by 588
  11. 2017Deep Learning Scaling is Predictable, Empiricallycited by 582
  12. 2022Beyond neural scaling laws: beating power law scaling via data pruningcited by 528
  13. 2020Scaling Laws for Autoregressive Generative Modelingcited by 522
  14. 2019Surprises in High-Dimensional Ridgeless Least Squares Interpolationcited by 513
  15. 2019Be Your Own Teacher: Improve the Performance of Convolutional Neural Networks via Self Distillationcited by 497
  16. 2017Snapshot Ensembles: Train 1, get M for freecited by 350
  17. 2022Tensor Programs V: Tuning Large Neural Networks via Zero-Shot Hyperparameter Transfercited by 288
  18. 2018An Empirical Model of Large-Batch Trainingcited by 281
  19. 2023Physics of Language Models: Part 3.1, Knowledge Storage and Extractioncited by 270
  20. 2019Model Fusion via Optimal Transportcited by 219
  21. 2019A Constructive Prediction of the Generalization Error Across Scalescited by 210
  22. 2017Regularizing and Optimizing LSTM Language Modelscited by 205
  23. 2022Will we run out of data? Limits of LLM scaling based on human-generated datacited by 195
  24. 2014Recurrent Neural Network Regularizationcited by 189
  25. 2020Self-Distillation Amplifies Regularization in Hilbert Spacecited by 173
  26. 2020Spectral Bias and Task-Model Alignment Explain Generalization in Kernel Regression and Infinitely Wide Neural Networkscited by 166
  27. 2015A Theoretically Grounded Application of Dropout in Recurrent Neural Networkscited by 161
  28. 2024Rephrasing the Web: A Recipe for Compute and Data-Efficient Language Modelingcited by 161
  29. 2024Nemotron-CC: Transforming Common Crawl into a Refined Long-Horizon Pretraining Datasetcited by 160
  30. 2023Beyond Chinchilla-Optimal: Accounting for Inference in Language Model Scaling Lawscited by 159
  31. 2017Breaking the Softmax Bottleneck: A High-Rank RNN Language Modelcited by 152
  32. 2024Is Model Collapse Inevitable? Breaking the Curse of Recursion by Accumulating Real and Synthetic Datacited by 151
  33. 2024Observational Scaling Laws and the Predictability of Language Model Performancecited by 130
  34. 2020Optimal Regularization Can Mitigate Double Descentcited by 109
  35. 2025Fantastic Pretraining Optimizers and Where to Find Themcited by 100
  36. 2016Improving Neural Language Models with a Continuous Cachecited by 82
  37. 2020On the Generalization Benefit of Noise in Stochastic Gradient Descentcited by 82
  38. 2017Data Noising as Smoothing in Neural Network Language Modelscited by 78

50 most cited of 75 All 75 (JSON)

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 26.

29 papers.

Sort:

By area:

  1. 2026Deriving Neural Scaling Laws from the statistics of natural languagecited by 23
  2. 2025Beyond Multi-Token Prediction: Pretraining LLMs with Future Summariescited by 15
  3. 2026Shaping capabilities with token-level data filteringcited by 13
  4. 2026Prescriptive Scaling Laws for Data Constrained Trainingcited by 12
  5. 2026Scaling Behavior Cloning Improves Causal Reasoning: An Open Model for Real-Time Video Game Playingcited by 11
  6. 2026A Bitter Lesson for Data Filteringcited by 8
  7. 2026Data-efficient pre-training by scaling synthetic megadocscited by 7
  8. 2026The Effect of Mini-Batch Noise on the Implicit Bias of Adamcited by 4
  9. 2026Weight Decay Improves Language Model Plasticitycited by 4
  10. 2026Nexus: Same Pretraining Loss, Better Downstream Generalization via Common Minimacited by 4
  11. 2026Demystifying Training-Time Augmentation for Data-Constrained Language Model Pretrainingcited by 4
  12. 2026Explorative Modeling: Unlocking a Third Pretraining Axis and End-to-End Generationcited by 4
17 more
  1. 2025Coherence Mechanisms for Provable Self-Improvementcited by 3
  2. 2025The Law of Multi-Model Collaboration: Scaling Limits of Model Ensembling for Large Language Modelscited by 3
  3. 2026JTok: On Token Embedding as another Axis of Scaling Law via Joint Token Self-modulationcited by 3
  4. 2026Scaling Recurrence-aware Foundation Models for Clinical Records via Next-Visit Predictioncited by 3
  5. 2026Data-Constrained Language Model Pretraining: Improved Regularization and Scaling Lawscited by 3
  6. 2026How Model Growth, Recursion, and Boundary Operators Influence Scaling Exponentscited by 2
  7. 2026Synthetic Mixed Training: Scaling Parametric Knowledge Acquisition Beyond RAGcited by 1
  8. 2026Small LLMs: Pruning vs. Training from Scratchcited by 1
  9. 2026Self-Play Pretraining with Zero Datacited by 1
  10. 2026Continually self-improving AIcited by 0
  11. 2026Tokens-per-Parameter Coverage Is Critical for Robust LLM Scaling Law Extrapolationcited by 0
  12. 2026Mix, Don't Tune: Bilingual Pre-Training Outperforms Hyperparameter Search in Data-Constrained Settingscited by 0
  13. 2026Validity Threats for Foundation Model Researchcited by 0
  14. 2026Uncertainty-aware damage identification in short-span bridges via physics-informed variational autoencodercited by 0
  15. 2026What Is a Repeated Token Worth? The Scaling Geometry of Multi-Epoch Pretrainingcited by 0
  16. 2026Scaling Repeated-Data Pretraining: Batch Size, Regularization, and GPU-Time Tradeoffscited by 0
  17. 2026Generative Representation Learning for Scalable Latent Tokenizationcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Predictable Scale: Part I, Step Law -- Optimal Hyperparameter Scaling Law in Large Language Model Pretraining
  2. 2024Scaling Laws for Precision
  3. 2023To Repeat or Not To Repeat: Insights from Scaling LLM under Token-Crisis
  4. 2024Rethinking Conventional Wisdom in Machine Learning: From Generalization to Scaling
  5. 2026Understanding the Weight Averaging Mechanism in LLM Training for Post-Training Quantization
  6. 2026Efficient Pre-Training with Token Superposition
  7. 2026Scaling Down the Scaling Laws: Parameter Efficiency and Compute-Optimal Training in Resource-Constrained Large Language Models
  8. 2026Negligible in Size, Significant in Effect: On Scale Vectors in Large Language Models