mlsanityData to 14 Oct 2026

Rethinking Conventional Wisdom in Machine Learning: From Generalization to Scaling

arXiv 2409.15156 ↗First posted 23 Sep 2024cs.LG stat.MLcited by 23

On the map: LLM reasoning → Reasoning benchmarks and evaluation

Abstract (arXiv)

The remarkable success of large language pretraining and the discovery of scaling laws signify a paradigm shift in machine learning. Notably, the primary objective has evolved from minimizing generalization error to reducing approximation error, and the most effective strategy has transitioned from regularization (in a broad sense) to scaling up models. This raises a critical question: Do the established principles that proved successful in the generalization-centric era remain valid in this new era of scaling? This paper examines several influential regularization-based principles that may no longer hold true in the scaling-centric, large language model (LLM) era. These principles include explicit L2 regularization and implicit regularization through small batch sizes and large learning rates. Additionally, we identify a new phenomenon termed ``scaling law crossover,'' where two scaling curves intersect at a certain scale, implying that methods effective at smaller scales may not generalize to larger ones. Together, these observations highlight two fundamental questions within this new paradigm: bullet Guiding Principles for Scaling: If regularization is no longer the primary guiding principle for model design, what new principles are emerging to guide scaling? bullet Model Comparison at Scale: How to reliably and effectively compare models at the scale where only a single experiment is feasible?

Key facts. Cited by 23 papers in the map (data through 14 Oct 2026). Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning. Builds on 53 of its 98 references that are in the map. First posted on arXiv 23 Sep 2024.

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53 of 98 references.

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Same direction, newest first

  1. 2024DeepSeek LLM: Scaling Open-Source Language Models with Longtermism5 Jan

Other references · 52

  1. 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,399
  2. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  3. 2020An Image is Worth 16x16 Words: Transformers for Image Recognition at Scalecited by 30,186
  4. 2023GPT-4 Technical Reportcited by 18,396
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  7. 2020Scaling Laws for Neural Language Modelscited by 6,586
  8. 2023Mamba: Linear-Time Sequence Modeling with Selective State Spacescited by 4,718
  9. 2016Gaussian Error Linear Units (GELUs)cited by 3,502
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  11. 2017Decoupled Weight Decay Regularizationcited by 1,831
  12. 2020GLU Variants Improve Transformercited by 1,804
38 more
  1. 2020Sharpness-Aware Minimization for Efficiently Improving Generalizationcited by 1,417
  2. 2016On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minimacited by 1,352
  3. 2023GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpointscited by 1,346
  4. 2024The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scalecited by 1,160
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  7. 2019Fast Transformer Decoding: One Write-Head is All You Needcited by 717
  8. 2017Deep Learning Scaling is Predictable, Empiricallycited by 582
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  10. 2022Tensor Programs V: Tuning Large Neural Networks via Zero-Shot Hyperparameter Transfercited by 288
  11. 2018An Empirical Model of Large-Batch Trainingcited by 281
  12. 2020The large learning rate phase of deep learning: the catapult mechanismcited by 216
  13. 2020Understanding the Difficulty of Training Transformerscited by 210
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  17. 2018Towards Understanding the Role of Over-Parametrization in Generalization of Neural Networkscited by 142
  18. 2017A Bayesian Perspective on Generalization and Stochastic Gradient Descentcited by 135
  19. 2018Three Mechanisms of Weight Decay Regularizationcited by 113
  20. 2024A Dynamical Model of Neural Scaling Lawscited by 111
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  22. 2023Tensor Programs VI: Feature Learning in Infinite-Depth Neural Networkscited by 97
  23. 2017Implicit Regularization in Deep Learningcited by 90
  24. 2024Resolving Discrepancies in Compute-Optimal Scaling of Language Modelscited by 88
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  26. 2024Chinchilla Scaling: A replication attemptcited by 72
  27. 20244+3 Phases of Compute-Optimal Neural Scaling Lawscited by 68
  28. 2023Depthwise Hyperparameter Transfer in Residual Networks: Dynamics and Scaling Limitcited by 66
  29. 2024RecurrentGemma: Moving Past Transformers for Efficient Open Language Modelscited by 64
  30. 2024Scaling Laws in Linear Regression: Compute, Parameters, and Datacited by 57
  31. 2023A Theory on Adam Instability in Large-Scale Machine Learningcited by 56
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  35. 2020On the infinite width limit of neural networks with a standard parameterizationcited by 38
  36. 2024u-μP: The Unit-Scaled Maximal Update Parametrizationcited by 29
  37. 2023Beyond Implicit Bias: The Insignificance of SGD Noise in Online Learningcited by 10
  38. 2024An Empirical Study of μP Learning Rate Transfercited by 10

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 2; 2025: 13; 2026: 8.

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  1. 2025Small Batch Size Training for Language Models: When Vanilla SGD Works, and Why Gradient Accumulation Is Wastefulcited by 41
  2. 2025The Surprising Agreement Between Convex Optimization Theory and Learning-Rate Scheduling for Large Model Trainingcited by 33
  3. 2025Scaling Collapse Reveals Universal Dynamics in Compute-Optimally Trained Neural Networkscited by 22
  4. 2025Hyperparameter Transfer Enables Consistent Gains of Matrix-Preconditioned Optimizers Across Scalescited by 21
  5. 2025Proximal Supervised Fine-Tuningcited by 16
  6. 2024Adaptive Learn-then-Test: Statistically Valid and Efficient Hyperparameter Selectioncited by 15
  7. 2024Adaptive Sparse Allocation with Mutual Choice & Feature Choice Sparse Autoencoderscited by 9
  8. 2025Scaling with Collapse: Efficient and Predictable Training of LLM Familiescited by 9
  9. 2026Hybrid Policy Distillation for LLMscited by 9
  10. 2025Debunk the Myth of SFT Generalizationcited by 8
  11. 2025Robust Layerwise Scaling Rules by Proper Weight Decay Tuningcited by 8
  12. 2026On the Role of Batch Size in Stochastic Conditional Gradient Methodscited by 7
11 more
  1. 2025TensorGRaD: Tensor Gradient Robust Decomposition for Memory-Efficient Neural Operator Trainingcited by 6
  2. 2025How Memory in Optimization Algorithms Implicitly Modifies the Losscited by 6
  3. 2025Scaling Diffusion Transformers Efficiently via μPcited by 6
  4. 2025Towards Alignment-Centric Paradigm: A Survey of Instruction Tuning in Large Language Modelscited by 5
  5. 2026The Effect of Mini-Batch Noise on the Implicit Bias of Adamcited by 4
  6. 2026Optimistic Dual Averaging Unifies Modern Optimizerscited by 3
  7. 2025Context-Aware Doubly-Robust Semi-Supervised Learningcited by 2
  8. 2026Tight Complexity of Muon under Heavy-Tailed Noisecited by 2
  9. 2026Entropy-KL Divergence-based Token Masking: A Novel Approach for Selective Fine-tuning of Large Language Modelscited by 1
  10. 2026Double Preconditioning (DoPr): Optimization for Test-Time Performance, not Validation Losscited by 1
  11. 2026From Spectra to Joint Schedules in LLM Pre-training: 3+3(+2) Scaling-Law Regimescited by 0

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  7. 2025LLMs on the Line: Data Determines Loss-to-Loss Scaling Laws
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