# Grokked Transformers are Implicit Reasoners: A Mechanistic Journey to the Edge of Generalization

arXiv: https://arxiv.org/abs/2405.15071 · HTML: https://mlsanity.com/paper/2405.15071/

## Key facts

- Cited by 79 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 61 of its 76 references that are in the map.
- First posted on arXiv 23 May 2024.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 30 of 61)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [REALM: Retrieval-Augmented Language Model Pre-Training](https://mlsanity.com/paper/2002.08909/) (2020)
- [Improving language models by retrieving from trillions of tokens](https://mlsanity.com/paper/2112.04426/) (2021)
- [Scaling Language Models: Methods, Analysis & Insights from Training Gopher](https://mlsanity.com/paper/2112.11446/) (2021)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Measuring and Narrowing the Compositionality Gap in Language Models](https://mlsanity.com/paper/2210.03350/) (2022)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Medusa: Simple LLM Inference Acceleration Framework with Multiple Decoding Heads](https://mlsanity.com/paper/2401.10774/) (2024)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [A Primer in BERTology: What we know about how BERT works](https://mlsanity.com/paper/2002.12327/) (2020)
- [The Implicit Bias of Gradient Descent on Separable Data](https://mlsanity.com/paper/1710.10345/) (2017)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [Eliciting Latent Predictions from Transformers with the Tuned Lens](https://mlsanity.com/paper/2303.08112/) (2023)
- [Towards Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2212.10403/) (2022)
- [Transformer Feed-Forward Layers Build Predictions by Promoting Concepts in the Vocabulary Space](https://mlsanity.com/paper/2203.14680/) (2022)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [Towards Best Practices of Activation Patching in Language Models: Metrics and Methods](https://mlsanity.com/paper/2309.16042/) (2023)
- [Quiet-STaR: Language Models Can Teach Themselves to Think Before Speaking](https://mlsanity.com/paper/2403.09629/) (2024)
- [MQuAKE: Assessing Knowledge Editing in Language Models via Multi-Hop Questions](https://mlsanity.com/paper/2305.14795/) (2023)
- [Towards Revealing the Mystery behind Chain of Thought: A Theoretical Perspective](https://mlsanity.com/paper/2305.15408/) (2023)
- [Transformers Learn Shortcuts to Automata](https://mlsanity.com/paper/2210.10749/) (2022)
- [Chain of Thought Empowers Transformers to Solve Inherently Serial Problems](https://mlsanity.com/paper/2402.12875/) (2024)
- [The Unlocking Spell on Base LLMs: Rethinking Alignment via In-Context Learning](https://mlsanity.com/paper/2312.01552/) (2023)

## Built on by (most cited first, 30 of 79)

- [A Practical Review of Mechanistic Interpretability for Transformer-Based Language Models](https://mlsanity.com/paper/2407.02646/) (2024)
- [Model Organisms for Emergent Misalignment](https://mlsanity.com/paper/2506.11613/) (2025)
- [Formal Mathematical Reasoning: A New Frontier in AI](https://mlsanity.com/paper/2412.16075/) (2024)
- [A Survey on Latent Reasoning](https://mlsanity.com/paper/2507.06203/) (2025)
- [Hopping Too Late: Exploring the Limitations of Large Language Models on Multi-Hop Queries](https://mlsanity.com/paper/2406.12775/) (2024)
- [Reasoning by Superposition: A Theoretical Perspective on Chain of Continuous Thought](https://mlsanity.com/paper/2505.12514/) (2025)
- [Knowledge Mechanisms in Large Language Models: A Survey and Perspective](https://mlsanity.com/paper/2407.15017/) (2024)
- [Disentangling Memory and Reasoning Ability in Large Language Models](https://mlsanity.com/paper/2411.13504/) (2024)
- [Implicit Reasoning in Large Language Models: A Comprehensive Survey](https://mlsanity.com/paper/2509.02350/) (2025)
- [Procedural Knowledge in Pretraining Drives Reasoning in Large Language Models](https://mlsanity.com/paper/2411.12580/) (2024)
- [Beyond Semantics: The Unreasonable Effectiveness of Reasonless Intermediate Tokens](https://mlsanity.com/paper/2505.13775/) (2025)
- [Out-of-distribution generalization via composition: a lens through induction heads in Transformers](https://mlsanity.com/paper/2408.09503/) (2024)
- [Do Large Language Models Perform Latent Multi-Hop Reasoning without Exploiting Shortcuts?](https://mlsanity.com/paper/2411.16679/) (2024)
- [RL Grokking Recipe: How Does RL Unlock and Transfer New Algorithms in LLMs?](https://mlsanity.com/paper/2509.21016/) (2025)
- [The Reasoning-Memorization Interplay in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2503.23084/) (2025)
- [Complexity Control Facilitates Reasoning-Based Compositional Generalization in Transformers](https://mlsanity.com/paper/2501.08537/) (2025)
- [How Do LLMs Perform Two-Hop Reasoning in Context?](https://mlsanity.com/paper/2502.13913/) (2025)
- [MIRAGE: Evaluating and Explaining Inductive Reasoning Process in Language Models](https://mlsanity.com/paper/2410.09542/) (2024)
- [Lessons from Studying Two-Hop Latent Reasoning](https://mlsanity.com/paper/2411.16353/) (2024)
- [Do LLMs Really Think Step-by-step In Implicit Reasoning?](https://mlsanity.com/paper/2411.15862/) (2024)
- [Understanding the Language Model to Solve the Symbolic Multi-Step Reasoning Problem from the Perspective of Buffer Mechanism](https://mlsanity.com/paper/2405.15302/) (2024)
- [Understanding the Interplay between Parametric and Contextual Knowledge for Large Language Models](https://mlsanity.com/paper/2410.08414/) (2024)
- [Provable Scaling Laws of Feature Emergence from Learning Dynamics of Grokking](https://mlsanity.com/paper/2509.21519/) (2025)
- [Extractive Structures Learned in Pretraining Enable Generalization on Finetuned Facts](https://mlsanity.com/paper/2412.04614/) (2024)
- [Is the Reversal Curse a Binding Problem? Uncovering Limitations of Transformers from a Basic Generalization Failure](https://mlsanity.com/paper/2504.01928/) (2025)
- [Let Me Grok for You: Accelerating Grokking via Embedding Transfer from a Weaker Model](https://mlsanity.com/paper/2504.13292/) (2025)
- [Grokking in the Wild: Data Augmentation for Real-World Multi-Hop Reasoning with Transformers](https://mlsanity.com/paper/2504.20752/) (2025)
- [Do Latent-CoT Models Think Step-by-Step? A Mechanistic Study on Sequential Reasoning Tasks](https://mlsanity.com/paper/2602.00449/) (2026)
- [Universal Reasoning Model](https://mlsanity.com/paper/2512.14693/) (2025)
- [Evaluating the Systematic Reasoning Abilities of Large Language Models through Graph Coloring](https://mlsanity.com/paper/2502.07087/) (2025)

## Abstract (arXiv)

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.