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Grokked Transformers are Implicit Reasoners: A Mechanistic Journey to the Edge of Generalization
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We study whether transformers can learn to implicitly reason over parametric knowledge, a skill that even the most capable language models struggle with. Focusing on two representative reasoning types, composition and comparison, we consistently find that transformers can learn implicit reasoning, but only through grokking, i.e., extended training far beyond overfitting. The levels of generalization also vary across reasoning types: when faced with out-of-distribution examples, transformers fail to systematically generalize for composition but succeed for comparison. We delve into the model's internals throughout training, conducting analytical experiments that reveal: 1) the mechanism behind grokking, such as the formation of the generalizing circuit and its relation to the relative efficiency of generalizing and memorizing circuits, and 2) the connection between systematicity and the configuration of the generalizing circuit. Our findings guide data and training setup to better induce implicit reasoning and suggest potential improvements to the transformer architecture, such as encouraging cross-layer knowledge sharing. Furthermore, we demonstrate that for a challenging reasoning task with a large search space, GPT-4-Turbo and Gemini-1.5-Pro based on non-parametric memory fail badly regardless of prompting styles or retrieval augmentation, while a fully grokked transformer can achieve near-perfect accuracy, showcasing the power of parametric memory for complex reasoning.
Forward citations
Cited by 7 Pith papers
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The Power of Power Law: Asymmetry Enables Compositional Reasoning
Power-law data sampling creates beneficial asymmetry in the loss landscape that lets models acquire high-frequency skill compositions first, enabling more efficient learning of rare long-tail skills than uniform distr...
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A transformer trained to imitate A* produces traces whose length reflects similarity to training data, not true problem complexity, so long chain-of-thought should not be read as more 'thinking'.
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Evaluating the Systematic Reasoning Abilities of Large Language Models through Graph Coloring
Standard LLMs make frequent errors on small graph coloring problems, while reasoning models o1-mini and DeepSeek-R1 make fewer but still nonzero errors, and no model reaches perfect accuracy.
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A Survey on Latent Reasoning
A survey that organizes latent reasoning methods into vertical recurrence, horizontal recurrence, and infinite-depth diffusion, arguing that silent reasoning can beat explicit chain-of-thought.
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Too Big to Think: Capacity, Memorization, and Generalization in Pre-Trained Transformers
Capacity-limited Transformers generalize on held-out single-digit arithmetic while larger models memorize facts; joint training suppresses extrapolation in all tested sizes.
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CryptoX : Compositional Reasoning Evaluation of Large Language Models
A benchmark that encodes prompts in secret codes and measures how much accuracy models lose, showing most LLMs, especially open-source ones, struggle on this two-step compositional task.
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