mlsanityData to 7 Oct 2026

Neural Networks Learn Statistics of Increasing Complexity

arXiv 2402.04362 ↗First posted 6 Feb 2024cs.LGcited by 30

Not on the map. Why?

Abstract (arXiv)

The distributional simplicity bias (DSB) posits that neural networks learn low-order moments of the data distribution first, before moving on to higher-order correlations. In this work, we present compelling new evidence for the DSB by showing that networks automatically learn to perform well on maximum-entropy distributions whose low-order statistics match those of the training set early in training, then lose this ability later. We also extend the DSB to discrete domains by proving an equivalence between token n-gram frequencies and the moments of embedding vectors, and by finding empirical evidence for the bias in LLMs. Finally we use optimal transport methods to surgically edit the low-order statistics of one class to match those of another, and show that early-training networks treat the edited samples as if they were drawn from the target class. Code is available at https://github.com/EleutherAI/features-across-time.

Key facts. Cited by 30 papers in the map (data through 7 Oct 2026). Builds on 27 of its 45 references that are in the map. First posted on arXiv 6 Feb 2024.

Builds on

27 of 45 references.

References · 27

  1. 2020Scaling Laws for Neural Language Modelscited by 6,411
  2. 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,283
  3. 2016Gaussian Error Linear Units (GELUs)cited by 3,431
  4. 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,597
  5. 2020The Pile: An 800GB Dataset of Diverse Text for Language Modelingcited by 2,346
  6. 2019RandAugment: Practical automated data augmentation with a reduced search spacecited by 2,261
  7. 2023Pythia: A Suite for Analyzing Large Language Models Across Training and Scalingcited by 1,734
  8. 2018On the Spectral Bias of Neural Networkscited by 1,321
  9. 2021Swin Transformer V2: Scaling Up Capacity and Resolutioncited by 1,215
  10. 2020Designing Network Design Spacescited by 954
  11. 2022In-context Learning and Induction Headscited by 930
  12. 2018Reconciling modern machine learning practice and the bias-variance trade-offcited by 919
15 more
  1. 2023ConvNeXt V2: Co-designing and Scaling ConvNets with Masked Autoencoderscited by 703
  2. 2017Deep Neural Networks as Gaussian Processescited by 617
  3. 2019Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networkscited by 360
  4. 2018Deep learning generalizes because the parameter-function map is biased towards simple functionscited by 180
  5. 2019On the Inductive Bias of Neural Tangent Kernelscited by 177
  6. 2018Training behavior of deep neural network in frequency domaincited by 174
  7. 2020Spectral Bias and Task-Model Alignment Explain Generalization in Kernel Regression and Infinitely Wide Neural Networkscited by 166
  8. 2020Frequency Bias in Neural Networks for Input of Non-Uniform Densitycited by 140
  9. 2018Spreading vectors for similarity searchcited by 114
  10. 2023Battle of the Backbones: A Large-Scale Comparison of Pretrained Models across Computer Vision Taskscited by 72
  11. 2019Understanding Generalization through Visualizationscited by 54
  12. 2022Neural networks trained with SGD learn distributions of increasing complexitycited by 50
  13. 2021The Grammar-Learning Trajectories of Neural Language Modelscited by 36
  14. 2019On the adequacy of untuned warmup for adaptive optimizationcited by 35
  15. 2020Deep frequency principle towards understanding why deeper learning is fastercited by 30

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 6; 2025: 12; 2026: 12.

30 papers.

Sort:

By area:

  1. 2024Differentiation and Specialization of Attention Heads via the Refined Local Learning Coefficientcited by 39
  2. 2025Between Circuits and Chomsky: Pre-pretraining on Formal Languages Imparts Linguistic Biasescited by 36
  3. 2025The Non-Linear Representation Dilemma: Is Causal Abstraction Enough for Mechanistic Interpretability?cited by 34
  4. 2025PolyPythias: Stability and Outliers across Fifty Language Model Pre-Training Runscited by 33
  5. 2025Tracing the Representation Geometry of Language Models from Pretraining to Post-trainingcited by 33
  6. 2024A distributional simplicity bias in the learning dynamics of transformerscited by 23
  7. 2025Language Model Behavioral Phases are Consistent Across Architecture, Training Data, and Scalecited by 13
  8. 2024Sliding down the stairs: how correlated latent variables accelerate learning with neural networkscited by 12
  9. 2025Evolution of Concepts in Language Model Pre-Trainingcited by 8
  10. 2024Tending Towards Stability: Convergence Challenges in Small Language Modelscited by 7
  11. 2025A Mathematical Philosophy of Explanations in Mechanistic Interpretability -- The Strange Science Part I.icited by 6
  12. 2025What Happens During the Loss Plateau? Understanding Abrupt Learning in Transformerscited by 5
18 more
  1. 2026A theory of learning data statistics in diffusion models, from easy to hardcited by 5
  2. 2024Jet Expansions of Residual Computationcited by 4
  3. 2024Early learning of the optimal constant solution in neural networks and humanscited by 3
  4. 2025Convergence and Divergence of Language Models under Different Random Seedscited by 3
  5. 2026Position: Don't Just "Fix it in Post": A Science of AI Must Study Training Dynamicscited by 2
  6. 2025Gradient-Weight Alignment as a Train-Time Proxy for Generalization in Classification Taskscited by 1
  7. 2026The Geometric Anatomy of Capability Acquisition in Transformerscited by 1
  8. 2026Data Predictability Shapes Weibull Weight-Scale Growth in Transformer Trainingcited by 1
  9. 2025Examining Two Hop Reasoning Through Information Content Scalingcited by 0
  10. 2025Probing Geometry of Next Token Prediction Using Cumulant Expansion of the Softmax Entropycited by 0
  11. 2026Learning Beyond the Gaussian Data: Learning Dynamics of Neural Networks on an Expressive and Cumulant-Controllable Data Modelcited by 0
  12. 2026Deep Networks Favor Simple Datacited by 0
  13. 2026Distributional simplicity bias and effective convexity in Energy Based Modelscited by 0
  14. 2026A Fourier perspective on the learning dynamics of neural networks: from sample complexities to mechanistic insightscited by 0
  15. 2026Telescope: Improving Zero Shot Detection of LLM Generated Content By Measuring Token Repetition Probabilitycited by 0
  16. 2026Pretraining Curricula Enable Selective Fine-tuningcited by 0
  17. 2026Neural Collapse Is Forbidden: Information Floors in Language Modelscited by 0
  18. 2026Lasting Effects of Abstract Pretraining Beyond Perplexitycited by 0