mlsanityData to 7 Oct 2026

Iteration Head: A Mechanistic Study of Chain-of-Thought

arXiv 2406.02128 ↗First posted 4 Jun 2024cs.LG cs.AI cs.CLcited by 31

On the map: LLM reasoning → Prompting and chain-of-thought reasoning

Abstract (arXiv)

Chain-of-Thought (CoT) reasoning is known to improve Large Language Models both empirically and in terms of theoretical approximation power. However, our understanding of the inner workings and conditions of apparition of CoT capabilities remains limited. This paper helps fill this gap by demonstrating how CoT reasoning emerges in transformers in a controlled and interpretable setting. In particular, we observe the appearance of a specialized attention mechanism dedicated to iterative reasoning, which we coined "iteration heads". We track both the emergence and the precise working of these iteration heads down to the attention level, and measure the transferability of the CoT skills to which they give rise between tasks.

Key facts. Cited by 31 papers in the map (data through 7 Oct 2026). Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning. Builds on 32 of its 38 references that are in the map. First posted on arXiv 4 Jun 2024.

Builds on

32 of 38 references.

References · 32

  1. 2020Language Models are Few-Shot Learnerscited by 32,199
  2. 2020Retrieval-Augmented Generation for Knowledge-Intensive NLP Taskscited by 9,160
  3. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,203
  4. 2023Mamba: Linear-Time Sequence Modeling with Selective State Spacescited by 4,616
  5. 2022Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 smallcited by 1,130
  6. 2022In-context Learning and Induction Headscited by 930
  7. 2021An Explanation of In-context Learning as Implicit Bayesian Inferencecited by 915
  8. 2021Show Your Work: Scratchpads for Intermediate Computation with Language Modelscited by 871
  9. 2023RWKV: Reinventing RNNs for the Transformer Eracited by 814
  10. 2022What Can Transformers Learn In-Context? A Case Study of Simple Function Classescited by 700
  11. 2022What learning algorithm is in-context learning? Investigations with linear modelscited by 671
  12. 2023Dissecting Recall of Factual Associations in Auto-Regressive Language Modelscited by 512
20 more
  1. 2024Revisiting Feature Prediction for Learning Visual Representations from Videocited by 490
  2. 2021A Survey of Transformerscited by 399
  3. 2019Theoretical Limitations of Self-Attention in Neural Sequence Modelscited by 286
  4. 2020Understanding the Role of Individual Units in a Deep Neural Networkcited by 254
  5. 2023Think before you speak: Training Language Models With Pause Tokenscited by 254
  6. 2023How does GPT-2 compute greater-than?: Interpreting mathematical abilities in a pre-trained language modelcited by 199
  7. 2022Hidden Progress in Deep Learning: SGD Learns Parities Near the Computational Limitcited by 184
  8. 2022The merged-staircase property: a necessary and nearly sufficient condition for SGD learning of sparse functions on two-layer neural networkscited by 141
  9. 2019On the Turing Completeness of Modern Neural Network Architecturescited by 129
  10. 2023Sudden Drops in the Loss: Syntax Acquisition, Phase Transitions, and Simplicity Bias in MLMscited by 121
  11. 2023The mechanistic basis of data dependence and abrupt learning in an in-context classification taskcited by 115
  12. 2024The Evolution of Statistical Induction Heads: In-Context Learning Markov Chainscited by 115
  13. 2024How Transformers Learn Causal Structure with Gradient Descentcited by 114
  14. 2023A Theory for Emergence of Complex Skills in Language Modelscited by 111
  15. 2021An Interpretability Illusion for BERTcited by 94
  16. 2023How Many Pretraining Tasks Are Needed for In-Context Learning of Linear Regression?cited by 93
  17. 2017Failures of Gradient-Based Deep Learningcited by 79
  18. 2023How Do Transformers Learn In-Context Beyond Simple Functions? A Case Study on Learning with Representationscited by 72
  19. 2024Large Stepsize Gradient Descent for Logistic Loss: Non-Monotonicity of the Loss Improves Optimization Efficiencycited by 34
  20. 2023Outliers with Opposing Signals Have an Outsized Effect on Neural Network Optimizationcited by 13

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 5; 2025: 17; 2026: 9.

31 papers.

Sort:

By area:

  1. 2025Thought Anchors: Which LLM Reasoning Steps Matter?cited by 126
  2. 2024Attention Heads of Large Language Models: A Surveycited by 65
  3. 2025Large Language Models for Planning: A Comprehensive and Systematic Surveycited by 38
  4. 2024How Far Can Transformers Reason? The Globality Barrier and Inductive Scratchpadcited by 35
  5. 2025Transformers Learn to Implement Multi-step Gradient Descent with Chain of Thoughtcited by 32
  6. 2025Attention Illuminates LLM Reasoning: The Preplan-and-Anchor Rhythm Enables Fine-Grained Policy Optimizationcited by 23
  7. 2025Towards Understanding Fine-Tuning Mechanisms of LLMs via Circuit Analysiscited by 20
  8. 2025Understanding and Mitigating Gender Bias in LLMs via Interpretable Neuron Editingcited by 14
  9. 2025Scalpel vs. Hammer: GRPO Amplifies Existing Capabilities, SFT Replaces Themcited by 14
  10. 2024LLMs Faithfully and Iteratively Compute Answers During CoT: A Systematic Analysis With Multi-step Arithmeticscited by 11
  11. 2025Compositional Generalization from Learned Skills via CoT Training: A Theoretical and Structural Analysis for Reasoningcited by 10
  12. 2025Interpretation Meets Safety: A Survey on Interpretation Methods and Tools for Improving LLM Safetycited by 10
19 more
  1. 2025Thinking Sparks!: Emergent Attention Heads in Reasoning Models During Post Trainingcited by 8
  2. 2025Transforming Calabi-Yau Constructions: Generating New Calabi-Yau Manifolds with Transformerscited by 5
  3. 2025From Concepts to Components: Concept-Agnostic Attention Module Discovery in Transformerscited by 4
  4. 2025Provable Benefits of In-Tool Learning for Large Language Modelscited by 4
  5. 2025On the Emergence of Induction Heads for In-Context Learningcited by 3
  6. 2026Indications of Belief-Guided Agency and Meta-Cognitive Monitoring in Large Language Modelscited by 3
  7. 2026How Does Reasoning Flow? Tracing Attention-Induced Information Flow for Targeted RL in LLMscited by 3
  8. 2024Interpretable Next-token Prediction via the Generalized Induction Headcited by 2
  9. 2025Function Induction and Task Generalization: An Interpretability Study with Off-by-One Additioncited by 2
  10. 2025Stream: Scaling up Mechanistic Interpretability to Long Context in LLMs via Sparse Attentioncited by 2
  11. 2026From Latent Signals to Reflection Behavior: Tracing Meta-Cognitive Activation Trajectory in R1-Style LLMscited by 2
  12. 2024A Mechanistic Study of Transformers Training Dynamicscited by 1
  13. 2026Mechanistic Interpretability of Chain-of-Thought Reasoning via Sequential Activation Patchingcited by 1
  14. 2025Localizing Task Recognition and Task Learning in In-Context Learning via Attention Head Analysiscited by 0
  15. 2026Automated Attention Pattern Discovery at Scale in Large Language Modelscited by 0
  16. 2026LLM Reasoning Is Latent, Not the Chain of Thoughtcited by 0
  17. 2026Assign and Add: A Mechanistic Study of Compositional Arithmeticcited by 0
  18. 2026Characterize Then Distill: Mechanistic Reasoning in Large Output Spacescited by 0
  19. 2026Generating Special Triangulations with Transformerscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025The Kinetics of Reasoning: How Chain-of-Thought Shapes Learning in Transformers?
  2. 2026The Potential of CoT for Reasoning: A Closer Look at Trace Dynamics
  3. 2023Igniting Language Intelligence: The Hitchhiker's Guide From Chain-of-Thought Reasoning to Language Agents
  4. 2025Analyzing the Power of Chain of Thought through Memorization Capabilities
  5. 2024How to think step-by-step: A mechanistic understanding of chain-of-thought reasoning
  6. 2025Explainable Chain-of-Thought Reasoning: An Empirical Analysis on State-Aware Reasoning Dynamics
  7. 2024Understanding Hidden Computations in Chain-of-Thought Reasoning
  8. 2024A Hopfieldian View-based Interpretation for Chain-of-Thought Reasoning