mlsanityData to 14 Oct 2026

Explaining grokking through circuit efficiency

arXiv 2309.02390 ↗First posted 5 Sep 2023cs.LGcited by 111

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Abstract (arXiv)

One of the most surprising puzzles in neural network generalisation is grokking: a network with perfect training accuracy but poor generalisation will, upon further training, transition to perfect generalisation. We propose that grokking occurs when the task admits a generalising solution and a memorising solution, where the generalising solution is slower to learn but more efficient, producing larger logits with the same parameter norm. We hypothesise that memorising circuits become more inefficient with larger training datasets while generalising circuits do not, suggesting there is a critical dataset size at which memorisation and generalisation are equally efficient. We make and confirm four novel predictions about grokking, providing significant evidence in favour of our explanation. Most strikingly, we demonstrate two novel and surprising behaviours: ungrokking, in which a network regresses from perfect to low test accuracy, and semi-grokking, in which a network shows delayed generalisation to partial rather than perfect test accuracy.

Key facts. Cited by 111 papers in the map (data through 14 Oct 2026). Builds on 24 of its 45 references that are in the map. First posted on arXiv 5 Sep 2023.

Builds on

24 of 45 references.

References · 24

  1. 2017Attention Is All You Needcited by 60,361
  2. 2020Scaling Laws for Neural Language Modelscited by 6,586
  3. 2020Transformer Feed-Forward Layers Are Key-Value Memoriescited by 1,336
  4. 2022Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 smallcited by 1,165
  5. 2022Toy Models of Superpositioncited by 971
  6. 2022In-context Learning and Induction Headscited by 964
  7. 2023Progress measures for grokking via mechanistic interpretabilitycited by 839
  8. 2017The Implicit Bias of Gradient Descent on Separable Datacited by 655
  9. 2022Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasetscited by 629
  10. 2017Deep Learning Scaling is Predictable, Empiricallycited by 582
  11. 2022Emergent World Representations: Exploring a Sequence Model Trained on a Synthetic Taskcited by 431
  12. 2019Gradient Descent Maximizes the Margin of Homogeneous Neural Networkscited by 320
12 more
  1. 2022Towards Understanding Grokking: An Effective Theory of Representation Learningcited by 230
  2. 2022Hidden Progress in Deep Learning: SGD Learns Parities Near the Computational Limitcited by 187
  3. 2022Omnigrok: Grokking Beyond Algorithmic Datacited by 146
  4. 2023A Toy Model of Universality: Reverse Engineering How Networks Learn Group Operationscited by 144
  5. 2023The Quantization Model of Neural Scalingcited by 138
  6. 2017A Bayesian Perspective on Generalization and Stochastic Gradient Descentcited by 135
  7. 2018Three Mechanisms of Weight Decay Regularizationcited by 113
  8. 2022The Slingshot Mechanism: An Empirical Study of Adaptive Optimizers and the Grokking Phenomenoncited by 94
  9. 2023A Tale of Two Circuits: Grokking as Competition of Sparse and Dense Subnetworkscited by 83
  10. 2023Unifying Grokking and Double Descentcited by 50
  11. 2020The Implicit Bias for Adaptive Optimization Algorithms on Homogeneous Neural Networkscited by 46
  12. 2023Predicting Grokking Long Before it Happens: A look into the loss landscape of models which grokcited by 35

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 11; 2024: 21; 2025: 29; 2026: 50.

111 papers.

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  1. 2024Mechanistic Interpretability for AI Safety -- A Reviewcited by 422
  2. 2023Towards Best Practices of Activation Patching in Language Models: Metrics and Methodscited by 359
  3. 2025Emergent Misalignment: Narrow finetuning can produce broadly misaligned LLMscited by 172
  4. 2024A Practical Review of Mechanistic Interpretability for Transformer-Based Language Modelscited by 118
  5. 2023Grokking as the Transition from Lazy to Rich Training Dynamicscited by 108
  6. 2024Arithmetic Without Algorithms: Language Models Solve Math With a Bag of Heuristicscited by 97
  7. 2024A Primer on the Inner Workings of Transformer-based Language Modelscited by 85
  8. 2023Dichotomy of Early and Late Phase Implicit Biases Can Provably Induce Grokkingcited by 80
  9. 2024Grokked Transformers are Implicit Reasoners: A Mechanistic Journey to the Edge of Generalizationcited by 79
  10. 2025All Roads Lead to Likelihood: The Value of Reinforcement Learning in Fine-Tuningcited by 59
  11. 2024Deep Networks Always Grok and Here is Whycited by 51
  12. 2023Grokking as a First Order Phase Transition in Two Layer Networkscited by 48
38 more
  1. 2025Grokking at the Edge of Numerical Stabilitycited by 46
  2. 2024Why Do You Grok? A Theoretical Analysis of Grokking Modular Additioncited by 36
  3. 2023Benign Overfitting and Grokking in ReLU Networks for XOR Cluster Datacited by 33
  4. 2023Predicting Emergent Abilities with Infinite Resolution Evaluationcited by 28
  5. 2024Emergence in non-neural models: grokking modular arithmetic via average gradient outer productcited by 28
  6. 2024The Same But Different: Structural Similarities and Differences in Multilingual Language Modelingcited by 28
  7. 2023Grokking Group Multiplication with Cosetscited by 24
  8. 2024Critical Data Size of Language Models from a Grokking Perspectivecited by 24
  9. 2024Learning Syntax Without Planting Trees: Understanding Hierarchical Generalization in Transformerscited by 24
  10. 2024Unified View of Grokking, Double Descent and Emergent Abilities: A Perspective from Circuits Competitioncited by 23
  11. 2026Emergent Misalignment is Easy, Narrow Misalignment is Hardcited by 23
  12. 2025Questioning Representational Optimism in Deep Learning: The Fractured Entangled Representation Hypothesiscited by 22
  13. 2024σ-GPTs: A New Approach to Autoregressive Modelscited by 20
  14. 2024On Catastrophic Inheritance of Large Foundation Modelscited by 15
  15. 2025Provable Scaling Laws of Feature Emergence from Learning Dynamics of Grokkingcited by 15
  16. 2023Grokking as Compression: A Nonlinear Complexity Perspectivecited by 14
  17. 2024Towards Empirical Interpretation of Internal Circuits and Properties in Grokked Transformers on Modular Polynomialscited by 14
  18. 2025Let Me Grok for You: Accelerating Grokking via Embedding Transfer from a Weaker Modelcited by 13
  19. 2023Understanding Grokking Through A Robustness Viewpointcited by 12
  20. 2025Language models can learn implicit multi-hop reasoning, but only if they have lots of training datacited by 11
  21. 2026Low-Dimensional and Transversely Curved Optimization Dynamics in Grokkingcited by 11
  22. 2026Why Larger Models Learn More: Effects of Capacity, Interference, and Rare-Task Retentioncited by 10
  23. 2024Deep Learning Through A Telescoping Lens: A Simple Model Provides Empirical Insights On Grokking, Gradient Boosting & Beyondcited by 9
  24. 2026The Geometry of Multi-Task Grokking: Transverse Instability, Superposition, and Weight Decay Phase Structurecited by 9
  25. 2024Progress Measures for Grokking on Real-world Taskscited by 8
  26. 2025Is Grokking a Computational Glass Relaxation?cited by 8
  27. 2025Grokking and Generalization Collapse: Insights from textttHTSR theorycited by 8
  28. 2025Mechanistic Indicators of Understanding in Large Language Modelscited by 8
  29. 2025What Can Grokking Teach Us About Learning Under Nonstationarity?cited by 8
  30. 2026To Grok Grokking: Provable Grokking in Ridge Regressioncited by 8
  31. 2023Training Dynamics of Contextual N-Grams in Language Modelscited by 7
  32. 2025What Happens During the Loss Plateau? Understanding Abrupt Learning in Transformerscited by 7
  33. 2026The Norm-Separation Delay Law of Grokking: A First-Principles Theory of Delayed Generalizationcited by 7
  34. 2023Bridging Lottery Ticket and Grokking: Understanding Grokking from Inner Structure of Networkscited by 6
  35. 2024Composing Global Solutions to Reasoning Tasks via Algebraic Objects in Neural Netscited by 6
  36. 2025A Mathematical Philosophy of Explanations in Mechanistic Interpretability -- The Strange Science Part I.icited by 6
  37. 2025Mechanistic Insights into Grokking from the Embedding Layercited by 6
  38. 2024The Fair Language Model Paradoxcited by 4

50 most cited of 111 All 111 (JSON)