mlsanityData to 14 Oct 2026

The Geometry of Self-Verification in a Task-Specific Reasoning Model

arXiv 2504.14379 ↗First posted 19 Apr 2025cs.AI cs.LGcited by 13

On the map: LLM reasoning → Test-time compute and efficient thinking

Abstract (arXiv)

How do reasoning models verify their own answers? We study this question by training a model using DeepSeek R1's recipe on the CountDown task. We leverage the fact that preference tuning leads to mode collapse, yielding a model that always produces highly structured chain-of-thought sequences. With this setup, we do top-down and bottom-up analyses to reverse-engineer how the model verifies its outputs. Top-down, we find Gated Linear Unit (GLU) weights encoding verification-related tokens, such as ``success'' or ``incorrect''. Bottom-up, we find that ``previous-token heads'' are mainly responsible for self-verification in our setup. Our analyses meet in the middle: drawing inspiration from inter-layer communication channels, we use the identified GLU weights to localize as few as three attention heads that can disable self-verification, pointing to a necessary component of a potentially larger verification circuit. Finally, we verify that similar verification components exist in our base model and a general reasoning DeepSeek-R1 model.

Key facts. Cited by 13 papers in the map (data through 14 Oct 2026). Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning. Builds on 34 of its 45 references that are in the map. First posted on arXiv 19 Apr 2025.

Builds on

34 of 45 references.

Closest ancestors · 4

Same direction, newest first

  1. 2025To Backtrack or Not to Backtrack: When Sequential Search Limits Model Reasoning9 Apr
  2. 2025Reasoning Models Know When They're Right: Probing Hidden States for Self-Verification7 Apr
  3. 2024Stream of Search (SoS): Learning to Search in Language1 Apr
  4. 2023Tree of Thoughts: Deliberate Problem Solving with Large Language Models17 May

Other references · 30

  1. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,459
  2. 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learningcited by 6,330
  3. 2013Efficient Estimation of Word Representations in Vector Spacecited by 4,375
  4. 2016Gaussian Error Linear Units (GELUs)cited by 3,502
  5. 2020GLU Variants Improve Transformercited by 1,804
  6. 2023Representation Engineering: A Top-Down Approach to AI Transparencycited by 1,336
  7. 2023Inference-Time Intervention: Eliciting Truthful Answers from a Language Modelcited by 1,302
  8. 2023Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Promptingcited by 1,122
  9. 2023Steering Llama 2 via Contrastive Activation Additioncited by 1,085
  10. 2024Refusal in Language Models Is Mediated by a Single Directioncited by 1,032
  11. 2025Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?cited by 982
  12. 2022In-context Learning and Induction Headscited by 964
18 more
  1. 2022Discovering Latent Knowledge in Language Models Without Supervisioncited by 767
  2. 2023The Linear Representation Hypothesis and the Geometry of Large Language Modelscited by 716
  3. 2023Measuring Faithfulness in Chain-of-Thought Reasoningcited by 703
  4. 2023Understanding the Effects of RLHF on LLM Generalisation and Diversitycited by 396
  5. 2025Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRscited by 377
  6. 2023Emergent Linear Representations in World Models of Self-Supervised Sequence Modelscited by 319
  7. 2024LLMs Know More Than They Show: On the Intrinsic Representation of LLM Hallucinationscited by 244
  8. 2024Transcoders Find Interpretable LLM Feature Circuitscited by 200
  9. 2023Does Writing with Language Models Reduce Content Diversity?cited by 192
  10. 2024A Mechanistic Understanding of Alignment Algorithms: A Case Study on DPO and Toxicitycited by 185
  11. 2025Chain-of-Thought Reasoning In The Wild Is Not Always Faithfulcited by 170
  12. 2023Linear Representations of Sentiment in Large Language Modelscited by 163
  13. 2024Fine-Tuning Enhances Existing Mechanisms: A Case Study on Entity Trackingcited by 149
  14. 2024Do I Know This Entity? Knowledge Awareness and Hallucinations in Language Modelscited by 115
  15. 2024One fish, two fish, but not the whole sea: Alignment reduces language models' conceptual diversitycited by 58
  16. 2024Designing a Dashboard for Transparency and Control of Conversational AIcited by 46
  17. 2024Talking Heads: Understanding Inter-layer Communication in Transformer Language Modelscited by 41
  18. 2025Shared Global and Local Geometry of Language Model Embeddingscited by 36

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 4; 2026: 9.

13 papers.

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  1. 2026LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signalscited by 24
  2. 2025Verifying Chain-of-Thought Reasoning via Its Computational Graphcited by 20
  3. 2025Can We Predict Alignment Before Models Finish Thinking? Towards Monitoring Misaligned Reasoning Modelscited by 17
  4. 2026Valence-Arousal Subspace in LLMs: Circular Emotion Geometry and Multi-Behavioral Controlcited by 16
  5. 2025How Well Can Reasoning Models Identify and Recover from Unhelpful Thoughts?cited by 11
  6. 2025Internal states before wait modulate reasoning patternscited by 6
  7. 2026Decomposing Query-Key Feature Interactions Using Contrastive Covariancescited by 3
  8. 2026Recursive Self-Improvement via On-Policy Distillation for Reasoningcited by 3
  9. 2026Convergent World Representations and Divergent Taskscited by 2
  10. 2026Tensor Product Representation Probes Reveal Shared Structure Across Linear Directionscited by 1
  11. 2026Fluid Reasoning Representationscited by 0
  12. 2026Decoding the Critique Mechanism in Large Reasoning Modelscited by 0
1 more
  1. 2026Taking the PULSE of Medical Reasoning: Step-Level Retrieval Timing for Knowledge-Grounded Inferencecited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Can LLMs Predict Their Own Failures? Self-Awareness via Internal Circuits
  2. 2025Incentivizing LLMs to Self-Verify Their Answers
  3. 2025Are DeepSeek R1 And Other Reasoning Models More Faithful?
  4. 2026Self-Verification Dilemma: Experience-Driven Suppression of Overused Checking in LLM Reasoning
  5. 2025Self-Reasoning Language Models: Unfold Hidden Reasoning Chains with Few Reasoning Catalyst
  6. 2024Self-Discover: Large Language Models Self-Compose Reasoning Structures
  7. 2026Can We Break LLMs Out of Self-Loops? Fine-Grained Reasoning Control with Activation Steering
  8. 2023A Closer Look at the Self-Verification Abilities of Large Language Models in Logical Reasoning