Interpreting Reasoning of Large Language Models via Partial Information Decomposition

Barproda Halder; Qiuyi Zhang; Sanghamitra Dutta

cs.ITSep 30, 2026

Interpreting Reasoning of Large Language Models via Partial Information Decomposition

Authors: Barproda Halder, Qiuyi Zhang, Sanghamitra Dutta

Organizations: University of Maryland, College Park · Elorian AI

Abstract

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 $S_i$ 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.

Figures & tables

Figure 1: Example illustrating the role of Slider in identifying repetitiveness. The sliding window compares each reasoning step with the preceding steps. A step that adds answer-relevant information, such as computing the remaining apples, has a low expected Step-RRI; a step that repeats the same calculation has a high expected Step-RRI.

Figure 2: Slider in a simple arithmetic problem: Demonstrates high synergistic information between Step 1 (3x) and Step 2 (2y) because they jointly provide complete information about (3x+2y).

Figure 3: PID of

\mathrm{I}({A;X,Y})

Figure 4: Our proposed framework Slider . Given a question and its reasoning trajectory, the sample generator creates multiple variants by changing only the numerical values while preserving the underlying problem structure. Each generated reasoning trajectory is then segmented into individual reasoning steps using the <step i> tags, from which we construct the preceding reasoning $S_{<i}$ and the current step $S_{i}$ in text form. Then, we obtain embeddings of the current step $S_{i}$ , preceding steps $S_{<i}$ , and final answer $A$ using an encoder-only language model and discretize the resulting embeddings via $k$ -means clustering. Finally, we estimate the joint distribution from the discrete representations, compute the PID measures, and Step-RRI.

Figure 5: Interpretable trends of PID measures under errors for synthetic arithmetic problems. (a,b) Increasing error probability $p$ reduces synergy and the unique information of erroneous steps, while increasing the unique contribution of correct steps. (c) Perturbing $S_{3}$ similarly decreases $\mathrm{Uni}(S_{3})$ as $p$ increases. (d) Reference example for the reasoning steps.

Figure 6: PID estimation across reasoning trajectories. Redundant information becomes dominant compared to uniqueness in $S_{i}$ and synergistic information when the current step $S_{i}$ revisits answer-relevant information already established in the preceding steps $S_{<i}$ , resulting in positive Step-RRI.

Figure 7: Step-level redundancy detection. Step-RRI achieves higher accuracy than baselines on PRMBench.

	DeepSeek-R1		QwQ-32B		GPT-4.1
Dataset	$\rho$	$p$ -val	$\rho$	$p$ -val	$\rho$	$p$ -val
GSM8K	0.95	0.00	0.91	0.00	0.73	0.00
AIME2025	0.89	0.01	0.75	0.01	0.82	0.03

Table 1: Spearman correlation between average Trajectory-RRI and reasoning length.

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

#Clusters	Redundancy	Unique ( $S_{<i}$ )	Unique ( $S_{i}$ )	Synergy
$S_{<4}$ and $S_{4}$
10	0.3621	0.0846	0.7101	0.1181
15	0.4502	0.1319	0.6737	0.2166
20	0.5025	0.2378	0.6656	0.3353
$S_{<5}$ and $S_{5}$
10	0.6284	0.1178	0.3822	0.1515

Appendix

Table 2: Sensitivity of PID components for

S_{<i}

and

S_{i}

to the number of clusters.

Figure 10: Interpretable trends of PID measures under errors for word problem: (a,b) Under errors, uniqueness Uni( $S_{i}$ ) corresponding to a correct step increases with $p$ , reflecting that correct steps contribute increasingly distinct information relative to their erroneous counterparts. Conversely, Uni( $S_{i}$ ) associated with the erroneous step decreases as error probability $p$ increases. (c) Reference example for the reasoning steps in concise form.

Figure 11: Step-RRI for DeepSeek-R1-Distill-Qwen-32B reasoning trajectories. Step-wise PID components and the corresponding Step-RRI values for three representative GSM8K reasoning trajectories. Negative Step-RRI indicates that the current step contributes primarily new or complementary answer-relevant information, whereas positive Step-RRI indicates increased repetitiveness with respect to the preceding reasoning.

Avg. Trajectory-RRI	Accuracy (%)
3.50	88.55
3.34	89.31
3.19	89.46
3.02	89.31
2.84	88.78
2.42	89.16

Appendix

Table 3: Test accuracy on GSM8K across different average Trajectory-RRI levels.

Explore similar work

Giving Credit Where It's Due: Redundancy-Aware Learning for Efficient Reasoning
Sep 22, 2026Yuqing Zhou, Hong Wang, Manqing Mao +8Reasoning Traces Mathematical Reasoning Benchmarks
George Mason University · Amazon, Inc
How Much Thinking is Enough? Quantifying and Understanding Redundancy in LLM Reasoning
Apr 21, 2026Zhiyuan Zhai, Xinkai You, Wenjing Yan +1LLM Reasoning Strategies Redundancy
Fudan University · The Chinese University of Hong Kong
Selective Latent Thinking: Adaptive Compression of LLM Reasoning Chains
May 25, 2026Hui Xie, Jie Liu, Ziyue Qiao +1Latent Thoughts Chain-of-Thought Reasoning
Eindhoven University of Technology, Netherlands · School of Computing and Information Technology, Great Bay University, China

Sep 22, 2026, cs.CLJ/K move · Enter open · S save

Giving Credit Where It's Due: Redundancy-Aware Learning for Efficient Reasoning

Yuqing Zhou, Hong Wang, Manqing Mao, Zhuoer Wang+7

George Mason University · Amazon, Inc

Reasoning Traces Mathematical Reasoning Benchmarks Step-Level Credit Semantic Relationships

Open paper AskPDF arXiv

Large reasoning models can produce correct yet unnecessarily long reasoning traces. Existing methods improve reasoning efficiency with trajectory-level objectives or local token- and step-level signals, but rarely model inter-step semantic dependencies. This limits their ability to distinguish redundant steps from those that support later deductions, making it harder to shorten reasoning without sacrificing accuracy. We introduce RECAP (REdundancy-aware Credit Assignment via Propagation), which addresses this limitation by assigning credit where it is due based on both a step's downstream role in the reasoning structure and its contribution to solving the problem correctly. We define structural responsibility to capture the step's downstream role by measuring how strongly later reasoning depends on it, using credit propagated backward from the final-answer node through an outcome-independent, LLM-annotated semantic dependency graph. However, a step can have high structural responsibility yet steer the reasoning away from the correct solution. RECAP therefore introduces step efficacy to measure answer-directed progress through changes in gold-answer log-likelihood as each step is added. Together, these signals reshape rollout-level GRPO advantages into step-specific updates. RECAP requires neither a separately trained process reward model nor preconstructed concise trajectories. Across two 7B models and four mathematical reasoning benchmarks, RECAP improves the accuracy-efficiency trade-off. On Qwen2.5-Math-7B, it improves pass@1 by 2.0-3.7 percentage points while reducing reasoning tokens by 8%-31% relative to GRPO across all four benchmarks. Analysis suggests these savings reflect fewer reasoning operations and less dead-end reasoning, rather than more compact expression.

Abstract

Explore similar work

Giving Credit Where It's Due: Redundancy-Aware Learning for Efficient Reasoning

How Much Thinking is Enough? Quantifying and Understanding Redundancy in LLM Reasoning

Selective Latent Thinking: Adaptive Compression of LLM Reasoning Chains