mlsanityData to 7 Oct 2026

Beyond Scalars: Evaluating and Understanding LLM Reasoning via Geometric Progress and Stability

arXiv 2603.10384 ↗First posted 11 Mar 2026cs.AIcited by 4

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

Abstract (arXiv)

Evaluating LLM reliability via scalar probabilities often fails to capture the structural dynamics of reasoning. We introduce TRACED, a framework that assesses reasoning quality through theoretically grounded geometric kinematics. By decomposing reasoning traces into Progress (displacement) and Stability (curvature), we reveal a distinct topological divergence: correct reasoning manifests as high-progress, stable trajectories, whereas hallucinations are characterized by low-progress, unstable patterns (stalled displacement with high curvature fluctuations). Leveraging these signatures, our probabilistic framework achieves competitive performance and superior robustness across diverse benchmarks. Crucially, TRACED bridges geometry and cognition by mapping high curvature to ''Hesitation Loops'' and displacement to ''Certainty Accumulation'', offering a physical lens to decode the internal dynamics of machine thought.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning. Builds on 41 of its 67 references that are in the map. First posted on arXiv 11 Mar 2026.

Builds on

41 of 67 references.

Closest ancestors · 8

Same direction, newest first

  1. 2026GeoSteer: Faithful Chain-of-Thought Steering via Latent Manifold Gradients15 Jan
  2. 2025MONICA: Real-Time Monitoring and Calibration of Chain-of-Thought Sycophancy in Large Reasoning Models9 Nov
  3. 2025Tracing the Traces: Latent Temporal Signals for Efficient and Accurate Reasoning12 Oct
  4. 2025CoRE: Enhancing Metacognition with Label-free Self-evaluation in LRMs8 Jul
  5. 2025The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity7 Jun
  6. 2025SEAL: Steerable Reasoning Calibration of Large Language Models for Free7 Apr
  7. 2025Understanding Aha Moments: from External Observations to Internal Mechanisms3 Apr
  8. 2024Small Language Models Need Strong Verifiers to Self-Correct Reasoning26 Apr

Other references · 33

  1. 2024The Llama 3 Herd of Modelscited by 14,192
  2. 2021Training Verifiers to Solve Math Word Problemscited by 9,743
  3. 2025Qwen3 Technical Reportcited by 8,195
  4. 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learningcited by 6,146
  5. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,203
  6. 2024Qwen2 Technical Reportcited by 2,076
  7. 2023Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMscited by 946
  8. 2025Reasoning Models Don't Always Say What They Thinkcited by 388
  9. 2025Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRscited by 373
  10. 2025Layer by Layer: Uncovering Hidden Representations in Language Modelscited by 293
  11. 2022Prompting GPT-3 To Be Reliablecited by 258
  12. 2022Making Large Language Models Better Reasoners with Step-Aware Verifiercited by 231
21 more
  1. 2023TheoremQA: A Theorem-driven Question Answering datasetcited by 189
  2. 2025Phi-4-reasoning Technical Reportcited by 146
  3. 2025DeepSeek-R1 Thoughtology: Let's think about LLM Reasoningcited by 91
  4. 2023Attention Satisfies: A Constraint-Satisfaction Lens on Factual Errors of Language Modelscited by 67
  5. 2024Latent Space Chain-of-Embedding Enables Output-free LLM Self-Evaluationcited by 56
  6. 2025CoT-Kinetics: A Theoretical Modeling Assessing LRM Reasoning Processcited by 50
  7. 2023Look Before You Leap: An Exploratory Study of Uncertainty Measurement for Large Language Modelscited by 40
  8. 2025Detection and Mitigation of Hallucination in Large Reasoning Models: A Mechanistic Perspectivecited by 32
  9. 2020Uncertainty Estimation in Autoregressive Structured Predictioncited by 21
  10. 2025The Geometry of Reasoning: Flowing Logics in Representation Spacecited by 21
  11. 2025Verifying Chain-of-Thought Reasoning via Its Computational Graphcited by 20
  12. 2025Adaptive Multi-Subspace Representation Steering for Attribute Alignment in Large Language Modelscited by 16
  13. 2024A Hopfieldian View-based Interpretation for Chain-of-Thought Reasoningcited by 15
  14. 2025Understanding How Value Neurons Shape the Generation of Specified Values in LLMscited by 13
  15. 2025Understanding and Mitigating Cross-lingual Privacy Leakage via Language-specific and Universal Privacy Neuronscited by 13
  16. 2024OCEAN: Offline Chain-of-thought Evaluation and Alignment in Large Language Modelscited by 12
  17. 2025Investigating CoT Monitorability in Large Reasoning Modelscited by 8
  18. 2026AutoMonitor-Bench: Evaluating the Reliability of LLM-Based Misbehavior Monitorcited by 8
  19. 2025Curved Inference: Concern-Sensitive Geometry in Large Language Model Residual Streamscited by 6
  20. 2025Understanding and Mitigating Political Stance Cross-topic Generalization in Large Language Modelscited by 6
  21. 2025Beyond Accuracy: A Geometric Stability Analysis of Large Language Models in Chess Evaluationcited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 4.

4 papers.

  1. 2026Semantic Step Prediction: Multi-Step Latent Forecasting in LLM Reasoning Trajectories via Step Samplingcited by 1
  2. 2026Density Ridge Selective Prediction for LLM and VLM Hallucination Detection under Calibration Label Scarcitycited by 1
  3. 2026GeoFaith: A Spatio-Temporal Dual View of Faithful Chain-of-Thoughtcited by 0
  4. 2026GLIDE: Generalized Layer-wise Intrinsic Distributional Evaluation for Heterogeneous LLM Agentscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026Geometric Signatures of Reasoning: A Spectral Perspective on Task Hardness
  2. 2026LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signals
  3. 2026Reasoning Models Don't Just Think Longer, They Move Differently
  4. 2026Entropy trajectory shape predicts LLM reasoning reliability: A diagnostic study of uncertainty dynamics in chain-of-thought
  5. 2026Geometry of Divergence: Tracking Hidden-State Trajectories for Adaptive Multi-Turn Reasoning
  6. 2026How Hard Does It Think? Analyzing Step-Aware Reasoning Energy in LLM Chain-of-Thought Trajectories
  7. 2026The Geometry of Thought: How Scale Restructures Reasoning In Large Language Models
  8. 2024Beyond Lines and Circles: Unveiling the Geometric Reasoning Gap in Large Language Models