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arXiv:2201.02177cs.LG

Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets

Alethea Power, Yuri Burda, Harri Edwards, Igor Babuschkin, Vedant Misra

Abstract

In this paper we propose to study generalization of neural networks on small algorithmically generated datasets. In this setting, questions about data efficiency, memorization, generalization, and speed of learning can be studied in great detail. In some situations we show that neural networks learn through a process of "grokking" a pattern in the data, improving generalization performance from random chance level to perfect generalization, and that this improvement in generalization can happen well past the point of overfitting. We also study generalization as a function of dataset size and find that smaller datasets require increasing amounts of optimization for generalization. We argue that these datasets provide a fertile ground for studying a poorly understood aspect of deep learning: generalization of overparametrized neural networks beyond memorization of the finite training dataset.

arXiv comments
Correspondence to alethea@openai.com. Code available at: https://github.com/openai/grok
Journal reference
DOI
Subjects
cs.LGMachine Learning

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Linked by 15 identifiable commenters in 16 comments across 12 threads, from Feb 2022 to Jun 2026. Found in 3 HN submissions from Jul 2022 to May 2023. Open submission discussions.

Comments linking this paper, per year.

Discussed in comments12 threads

  1. They’re made out of weights 2 comments

    • It's not often I see something that's fractally wrong but here we are. There is a dictionary, it's called the tokenizer. There are grammar rules, they are just very weak because the structure of human language is generally quite weak. When presented with languages which have…

      noosphrView on HNParent context

    • >There are grammar rules, they are just very weak because the structure of human language is generally quite weak. When presented with languages which have strong consistent grammars the weights are very easily interpretable as a grammar: https://arxiv.org/abs/2201.02177 That…

      famouswafflesView on HNParent context

  2. Who discovered grokking and why is the name hard to find? 2 comments

    • https://arxiv.org/abs/2201.02177 This paper is not hard to find; it's the first result when you search for "grokking" with https://scholar.google.com

      yorwbaView on HNParent context

    • Yes I did find that paper, I did not find which one of the 5 authors it was, or someone not listed as an author. The word 'vacation' is not in the paper. https://arxiv.org/pdf/2201.02177.

      asmodeusluciferView on HNParent context

  3. Groq surpasses 1,200 tokens/sec with Llama 3 8B 1 comment
  4. How do machines ‘grok’ data? 1 comment

    • NNs (indeed, all statistical fitting algs) have no relevant properties here: properties derive just from the structure of the dataset. Here (https://arxiv.org/abs/2201.02177) NNs are trained on a 'complete world' problem, ie., modulo arithmetic where the whole outcome space is…

      mjburgessView on HNParent context

  5. Do Machine Learning Models Memorize or Generalize? 1 comment

    • I don't think that is true? As far as I know the grokking phenomenon was first observed (and the name coined) in this paper, not in any blog post: https://arxiv.org/abs/2201.02177

      woopwoopView on HNParent context

  6. PaLM 2 Technical Report [pdf] 1 comment

    • > once a company creates a proto AGI where the path to a functional AGI is entirely predictable with more compute, I find it hard to believe this will happen. I expect AGI training to be more like a phase transition (or a bit like grokking https://arxiv.org/pdf/2201.02177.pdf)

      sebzim4500View on HNParent context

  7. DyLoRA: Parameter Efficient Tuning of Pre-Trained Models 1 comment

    • I can see that. But are we sure that a rank-based difference that doesn't manifest early in the training process won't manifest as you get further along? See also 'grokking' [0] [0]: https://arxiv.org/abs/2201.02177

      whimsicalismView on HNParent context

  8. And yet It Understands 1 comment

    • To some limited extent, they are already good at maths: https://ar5iv.labs.arxiv.org/html/2201.02177 This paper makes me believe it's less about the lack of ability to understand maths, but the power to learn more of it.

      rhn_mk1View on HNParent context

  9. Jailbreaking ChatGPT with Dan (Do Anything Now) 1 comment

    • > ChatGPT doesn’t “comprehend” anything. You’re anthropomorphizing it. It wouldn't be a ChatGPT HN thread without someone claiming that LLMs are stupid predictors incapable of "real" understanding. Of course ChatGPT comprehends things. It does so under any useful definition of…

      quotemstrView on HNParent context

  10. Understanding the limits of large language models 1 comment

    • > It will never learn math this way, no matter how much training you give it. Not so. Actually, (for example) the phenomenon of "grokking" is when with enough training a NN eventually experiences a phase-change from memorising data to learning the general rules underlying it…

      versteegenView on HNParent context

  11. Socratic Models – Composing Zero-Shot Multimodal Reasoning with Language 1 comment

    • This is not the consensus among ML researchers. Transformers are showing strong generalisation[1] and their performance continues to surprise us as they scale[2]. The Socratic paper is not about “higher intelligence”, it’s about demonstrating useful behaviour purely by…

      moconnorView on HNParent context

  12. I asked GPT-NeoX-20B a hundred arithmetic questions 3 comments

    • Take a look at this paper: Deep Symbolic Regression for Recurrent Sequences https://arxiv.org/abs/2201.04600 If you look at embedding visualization it is very clear that the model learns order of numbers. (Interactive demo…

      IsinlorView on HNParent context

    • https://arxiv.org/pdf/2201.02177.pdf This paper shows fairly conclusively that the network 'groks' modular addition.

      plutonormView on HNParent context

    • Sure: Deep Symbolic Regression for Recurrent Sequences https://arxiv.org/abs/2201.04600 (Interactive demo: http://recur-env.eba-rm3fchmn.us-east-2.elasticbeanstalk.com... ) Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets https://arxiv.org/abs/2201.02177…

      IsinlorView on HNParent context

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