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.

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