mlsanityData to 14 Oct 2026

Interpreting Reasoning of Large Language Models via Partial Information Decomposition

arXiv 2610.00571 ↗First posted 30 Sep 2026cs.IT cs.AI cs.CYcited by 0

On the map: LLM reasoning → Test-time compute and efficient thinking also fits: Reasoning benchmarks and evaluation

Abstract (arXiv)

Large reasoning models (LRMs) have achieved substantial improvements in solving complex mathematical problems, but often produce lengthy, repetitive, or erroneous reasoning trajectories. In this work, we introduce a new interpretability framework, SLIDER, to evaluate the quality of the reasoning process. SLIDER leverages an emerging body of work from information theory called Partial Information Decomposition to disentangle the information about the final answer between two consecutive reasoning steps into non-negative components: unique information (in preceding steps or current step), redundant information, and synergistic information. Building on this decomposition, we propose the *Step-wise Repetitive Reasoning Index (Step-RRI)*, a theoretically grounded measure that assesses whether the answer-relevant information in the current step Si is predominantly redundant with the past steps S<i, relative to its unique and synergistic contributions. To evaluate the effectiveness of Step-RRI in detecting repetitiveness, we apply SLIDER to the redundancy class of the PRMBench dataset where Step-RRI improves step-level redundancy identification accuracy by over 10 points compared to embedding-similarity and information-gain baselines. Next, we define *Trajectory-RRI*, an aggregate measure of repetitiveness for an individual reasoning trajectory. To demonstrate its practical relevance, we show that average Trajectory-RRI strongly correlates with actual reasoning length across QwQ-32B, DeepSeek-R1-Distill-Qwen-32B, and GPT-4.1, motivating its use as a signal for improving reasoning efficiency. Finally, we introduce *Trajectory-RRI-guided data selection for fine-tuning*, demonstrating that selecting training data based on Trajectory-RRI can improve a fine-tuned model's reasoning efficiency while largely preserving its task performance.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning. Builds on 21 of its 41 references that are in the map. First posted on arXiv 30 Sep 2026.

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21 of 41 references.

Closest ancestors · 2

Same direction, newest first

  1. 2025Think or Not? Exploring Thinking Efficiency in Large Reasoning Models via an Information-Theoretic Lens23 May
  2. 2025Rethinking External Slow-Thinking: From Snowball Errors to Probability of Correct Reasoning26 Jan

Other references · 19

  1. 2021LoRA: Low-Rank Adaptation of Large Language Modelscited by 14,380
  2. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,459
  3. 2021Training Verifiers to Solve Math Word Problemscited by 10,109
  4. 2019Sentence-BERT: Sentence Embeddings using Siamese BERT-Networkscited by 9,170
  5. 2024Semantic Entropy Probes: Robust and Cheap Hallucination Detection in LLMscited by 259
  6. 2025PRMBench: A Fine-grained and Challenging Benchmark for Process-Level Reward Modelscited by 99
  7. 2024Understanding Chain-of-Thought in LLMs through Information Theorycited by 37
  8. 2021A Rigorous Information-Theoretic Definition of Redundancy and Relevancy in Feature Selection Based on (Partial) Information Decompositioncited by 26
  9. 2023Multimodal Learning Without Labeled Multimodal Data: Guarantees and Applicationscited by 21
  10. 2023Gaussian Partial Information Decomposition: Bias Correction and Application to High-dimensional Datacited by 17
  11. 2024DiffusionPID: Interpreting Diffusion via Partial Information Decompositioncited by 16
  12. 2020Fairness Under Feature Exemptions: Counterfactual and Observational Measurescited by 15
7 more
  1. 2024Quantifying Knowledge Distillation Using Partial Information Decompositioncited by 13
  2. 2023More Synergy, Less Redundancy: Exploiting Joint Mutual Information for Self-Supervised Learningcited by 11
  3. 2023Demystifying Local and Global Fairness Trade-offs in Federated Learning Using Partial Information Decompositioncited by 10
  4. 2024Towards Formalizing Spuriousness of Biased Datasets Using Partial Information Decompositioncited by 6
  5. 2026A Comprehensive Information-Decomposition Analysis of Large Vision-Language Modelscited by 4
  6. 2024A Unified View of Group Fairness Tradeoffs Using Partial Information Decompositioncited by 3
  7. 2025Learning Invariant Graph Representations Through Redundant Informationcited by 1

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  1. 2026How Much Thinking is Enough? Quantifying and Understanding Redundancy in LLM Reasoning
  2. 2025Efficient Inference for Large Reasoning Models: A Survey
  3. 2024The Role of Deductive and Inductive Reasoning in Large Language Models
  4. 2026Reasoning Structure of Large Language Models
  5. 2025Reasoning Relay: Evaluating Stability and Interchangeability of Large Language Models in Mathematical Reasoning
  6. 2023Large Language Models are Versatile Decomposers: Decompose Evidence and Questions for Table-based Reasoning
  7. 2026Divergent-Convergent Reasoning: Scaling Test-Time Compute through Structured Solution Synthesis
  8. 2025Advancing Reasoning in Large Language Models: Promising Methods and Approaches