Structured Reasoning for LLMs: A Unified Framework for Efficiency and Explainability
Authors: Yubo Dong
Hehe Fan
Linchao Zhu
Yi Yang
Venue: ICLR 2026 Poster (2026)
Keywords: Large Language Models
Reasoning
Chain of thought
Reinforcement Learning
Neurosymbolic AI
Interpretability
Primary area: reinforcement learning

Abstract: Recent Large Language Models (LLMs) have made remarkable progress, but they still struggle with complex reasoning tasks such as logical deduction and planning. This is partly because they rely primarily on token-level probability relationships, which limits their ability to reason effectively. 
In this paper, inspired by cognitive science and neurosymbolic AI, we introduce **Structured Reasoning**, which aimes at enhancing the reasoning capabilities of LLMs from the step level. 
To this end, we first collect high‑frequency, domain‑agnostic reasoning step tags and  construct a structured reasoning dataset with those tags. 
Then, we treat a reasoning process as a *directed acyclic graph*, where the vertices represent steps and the edges indicate the direction of reasoning. 
In this context, an efficient reasoning process corresponds to, or can be characterized by, a sparse reasoning graph.  
To construct reasoning graphs, we introduce *structured tags* for reliable step extraction from LLM outputs. For single-graph optimization, we propose the *MaxFlow reward*, which rewards graphs with balanced node contributions and fewer redundant steps. The quality of a sparse reasoning graph can be reflected by the total flow from all steps to the final answer. For multi-graph comparison, we propose the *LCS reward*, which selects reliable reasoning paths by identifying optimal common subsequences (consecutive steps) shared across multiple generated responses (sequences). 
Experiments with DeepSeek-R1-Distill-Qwen-1.5B and 7B models show that our method  consistently outperforms GRPO and other carefully tuned baselines across various context lengths (0.5k–8k).
Structured Reasoning shows particular strength in efficiency (better performance with fewer steps) and stability (consistently generating high-quality outputs across a temperature range of 0.1 to 1.0).  
Methods and examples is currently available on our website: https://cnsdqd-dyb.github.io/structured-reasoning.

Published as a conference paper at ICLR 2026
STRUCTURED REASONING FOR LLMs: A UNIFIED FRAMEWORK FOR EFFICIENCY AND EXPLAINABILITY
Yubo Dong, Hehe Fan, Linchao Zhu, Yi Yang College of Computer Science and Technology Zhejiang University Hangzhou, China
ABSTRACT
Recent Large Language Models (LLMs) have made remarkable progress, but they still struggle with complex reasoning tasks such as logical deduction and planning. This is partly because they rely primarily on token-level probability relationships, which limits their ability to reason effectively. In this paper, inspired by cognitive science and neurosymbolic AI, we introduce Structured Reasoning, which aimes at enhancing the reasoning capabilities of LLMs from the step level. To this end, we first collect high-frequency, domain-agnostic reasoning step tags and construct a structured reasoning dataset with those tags. Then, we treat reasoning process as a directed acyclic graph, where the vertices represent steps and the edges indicate the direction of reasoning. this context, an efficient reasoning process corresponds to, or can be characterized by, a sparse reasoning graph. To construct reasoning graphs, we introduce structured tags for reliable step extraction from LLM outputs. For single-graph optimization, graphs with balanced node contributions and fewer redundant steps. The quality sparse reasoning graph can be reflected by the total flow from all steps to the final answer. For multi-grajy aulti-graph comparison, we propose the LCS reward, which selects reliable reasoning paths by identifying optimal common subsequences (consecutive steps) shared across multiple generated responses (sequences). Experiments with DeepSeek-R1 --Distilll--eenee 1.5B and 7B models show that our method consistently outperforms GRPO and other carefully tuned baselines across various context lengths (0.5k-8k). Structured Reasoning shows particular strength in efficiency (better performance with fewer steps) and stability (consistently generating high- quality outputs across a temperature range of 0.1 to 1.0). Methods and examples is currently available on our website: (Structured StractureddRRassoiingg
propose the MaxFlow reward, which rewards
INTRODUCTION
Large Language Models (LLMs) such as DeepSeek-R1 (DeepSeek-Al et al. 2025aa. OpenAl- ol (OpenAl) 2024), and QwQ (QwQ, 2025) have rapidly advanced the state of natural language processing, knowledge access, and automated decision support. Despite their impressive language capabilities and broad applicability, the existing reasoning patterns suffer from several limitations: (i) redundant and verbose content, (ii) unstable performance, and (iii) poor interpretability of internal reasoning logic. These challenges hinder LLMs' safety, controllability and trustworthiness in practical applications.
We posit that advancing trustworthy reasoning in LLMs requires a transition to explicitly struc- tured, auditable processes. Structured reasoning, inspired by cognitive science and dual-process theories (Bronkhorst et al.] 2022] Forstmann et al. [0166] Evans, 2018 Miller & Cohen 2001). breaks down problem solving into clear steps with specific purposes (like restating the problem and checking the answer). Making these steps explicit and central to the process helps in several ways: (i) keeps the reasoning focused and on-track, (ii) allows us evaluate each step properly, (iii) makes it easier to understand how different layers of the model handle these steps.
This paper proposes novel approach to enhance LLMs with structured reasoning capabilities, inspired by cognitive science theories and recent advances in neurosymbolic artificial intelligence.
"Corresponding author. This work was supported by the National Natural Science Foundation of China (No. 92570101

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Published as a conference paper at ICLR 2026
Bfficiencyy
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Figure I: Structured reasoning improves efficiency, stability, and interpretability. Left: an example of our structured reasoning process. Right: across general tasks, combining structured data tuning with structure-awar optimization outperforms GRPO and other baselines in (i) efficiency (fewer, denser steps), (ii) stability (robust across temperatures), and (iii) interpretability (clear step dependencies).
Specifically, we introduce mechanisms that explicitly encode structured knowledge representations and reasoning processes in LLMs. Then, we treat reasoning processes as directed graphs, where the vertices represent steps and the edges indicate the direction of reasoning, leveraging both the flexibility of neural networks and the interpretability and precision of symbolic reasoning.
Our framework first transforms unstructured data into structured format by incorporating explicit reasoning step tags that clearly indicate each step of the reasoning process. These structured annotations enable adaptive fine-tuning that helps models develop systematic reasoning patterns. Additionally, we implement a layer-wise dependency tracing procedure using step-to-step attention matrices, enabling detailed analysis of reasoning relationships within the LLM's computation process.
To further enhance reasoning efficiency, we extend Group Relative Policy Optimization (GRPO) Shao et af.] (2024b) with two structure-aware algorithms: (1) MAX-Flow: Constructs sparse reasoning graphs by analyzing step-to-step attention matrices and measures the quality of the graph based on each step's ' contribution to the final answer, (2) Longest Common Subsequence (LCS): Improves reasoning quality by identifying optimal common subsequences across multiple generated responses and leveraging these consistent steps as reliable reasoning paths. Our contributions are as follows:
We propose a novel Structured Reasoning approach that achieves more concise reasoning and stable performance, demonstrating significant improvements in efficiency (better per- formance at shorter lengths), stability (consistent quality across temperatures 1-10), and interpretability across various scenarios DeepSeek-R 1-------DDssi-----
models.
We develop method automatically extract common reasoning patterns and convert unstructured reasoning into structured formats, creating a dataset that helps transform free-form reasoning steps into well-organized structured reasoning chains.
We propose attention- pieention-based wise analysis framework that constructs step-to-step attention maps across model layers, providing enhanced interpretability reasoning steps and revealing that middle layers play crucial role in integrating broader reasoning context.
We enhance GRPO with two complementary algorithms: 1) MAX-Flow, which constructs sparse reasoming graphs by analyzing step-to-step attention matrices and measures each step's contribution to the final answer, and 2) LCS, which improves reasoning quality by identifying optimal common subsequences across multiple generated responses and leveraging these consistent steps as reliable reasoning paths.
2 RELATED WORK
Reinforcement Learning Helps Efficiency Improvement Recent approaches use RL to improve
reasoning efficiency, from basic length penalties (Team et al. 2025
[i et al. 2025 Arora & Zanette
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O Data Collection
C Step Dependency Computation
+ Structured Awared Optimization
Original Query
Structured Input
Max-Flow Algorithm
4. Convert the point 5(0.3)$ ...?
Question>... VVerify
QQuestion <Verity>
[1] Graph Constrution
(2) Step Importance
Unstructured LIM Reasoning
Input LLM
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1 remember that to find ....
Attention Matrix Extraction
So, the coordinates are: (box((3 Vrac[pi](2)))
A
Label Extraction
(3) Robustness Evaluacion Zohii &
set sourcelt) and target(A) compute
Attention Matrix A &e head
1. Inference
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remove compute
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4. Conclusion
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calculate importance
=F== F.,
Filtering & Merging
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LCS Algorithm
Inference
Layer Local
Layer Global
Question
Interence
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Show middle layers intagrate brunter reasoning context.
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Illustration of our three-stage pipeline for enhancing LLMs with Structured Reasoning. (1) Data Collection: Extract structured reasoning labels from unstructured LLM responses, producing outputs with structured tags. (2) Step Dependency Computation: Compute step attention matrices to construct reasoning directed graph. (3) Structure-Awared Opitmization: Apply Max-Flow algorithm for providing a significantly more accurate understanding of reasoning step dependencies and LCS algorithm for improving reasoning quality by identifying optimal common subsequences across multiple generated responses and leveraging these consistent steps as reliable reasoning paths.
Figure 2:
2025) to more sophisticated methods. 1.1 (Aggarwal & Welleck 2025) embeds length constraints in training instructions, while O1-Pruner (Luo et al.] 2025a) balances brevity and accuracy against reference benchmarks. DAST (Shen et al. (025b) introduces adaptive reasoning through token- length budget, allocating resources based on problem complexity. THINKPRUNE (Hou et al. 2025) employs length-aware reward with tightening constraints, while Think When You Need (Ynng et al. 2025
uses comparative rewards to guide models toward concise yet effective solutions.
Efficient CoT According to Perplexity Several works optimize reasoning chains using perplexity- based methods (Jelinck et al., 2005). including stepwise refinement (Cui et al. 2025b), token pruning (Xia al. (2025), attack detection (Alon & Kamfonas 2023) and step elimination strate- gies (Liu et al.] 2024). Furthermore, (Zhang et (005)) proposes exploration based on entropy for multistep reasoning. Our research reveals that perplexity metries inadequately assess the impor- tance of reasoning steps, demonstrating that our MAX-Flow algorithm outperforms perplexity-basee approaches in evaluating the importance of reasoning steps.
Language Model Reasoning (for Math) Since OpenAI-O1 (Jaech et al.
2024 followed by 03 (Ope
nAI, 2025) and DeepSeck-RR R11 (DeepSeek-AI/ 2025), researchers have proposed increasingly sophisti-
cated RL. algorithms, including Dr. (Liu et al. 2025b), I.CPO (Aggarwal & Welleck 2025).
REINFORCE+ (Hul 2025), DAPO (Yu et al. 2025), ) DPO VP (Tu et al. 2025). VinePPO (Kazemne
jad at. 2024). CPPO (Lin et al.] (025). VAPO Yue et al. 2025), ) and GRO (Cai 2023). Empirical
investigations have explored data scaling (Shen et al. (025a), curriculum strategies (Wen et al. 2025
Roux et al. 2025), and reward engineering (Gao a 2024b; Cui et al. 2025a Ma et al. 2023).
Recent evaluations (Hochlehnert et al. 2025) show many reported improvements fail against properly optimized baselines. Our methods evaluate across multiple seeds to ensure reproducibility.
3 MOTIVATION: REASONING AS FLOW ON STRUCTURED GRAPHS
We propose to view the reasoning process as a single-source single-sink flow diffusion process from the question step the answer step, illustrated in Figure This perspective transforms
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the challenge of optimizing redundant reasoning steps and improving efficiency into problem of optimizing reasoning graph structure.
Single Reasoning Graph Perspective. For reasoning steps that are redundant, repetitive, mean- ingless, both the answer step and intermediate conclusion steps tend to ignore them, resulting in weaker connections for these step nodes to the final answer (sink). Conversely, consider ideal case of a strictly step-by-step dependent CoT reasoning process: each new intermediate inference step strongly depends the previous step. In such cases, removing any single reasoning step would interrupt the flow, making each step's contribution approximately equal. A high-quality reasoning process should thus exhibit balanced step contributions, where no single step dominates the flow, indicating a robust, non rondrddndddnt reasoning chain.
When comparing multiple reasoning graphs that reach the correct answers, we can optimize by identifying common attention edges. Under an ideal assumption, one reasoning graph's 's path is subset of another's, it appears more concise reasoning logic. Furthermore, if two graphs have identical reasoning paths, generally consider the process with shorter corresponding reasoning steps to be more efficient. This motivates our LCS-based reward that encourages alignment with correct completions with length suppression.
Multi-Graph Comparison Perspective.
METHOD
4.1
STRUCTURED REASONING DATA COLLECTION
Due to the free-form nature of reasoning passages, small LLMs struggle to reliably parse them into discrete reasoning steps. To address this, design pipeline construct structured reasoning data with explicit step labels.
Given a question set Qo and teacher model T' (DeepSeek-RI) for each q Qo obtain raw reasoning waw and answer a, then elicit a linear label chain 1 = (4 + ... - (m) via a self- summarization prompt A.8 We keep frequent labels, merge synonyms, and remove domain--peciiic ones to form the core set. Let P be the set of the labels.
To synthesize aligned structured traces over the questions Q, sample labels π E P for each q and prompt I' to generate a labeled reasoning r, producing the raw structured set Draw = {q, r, a)}. We apply a filtering function Fqq. π, r, a) to verify answer correctness and reasoning difficulty. The final corpus is:
Dammet ((g ,, æ,,; E Draw F(g,,,r,a) =3
This produces tiny but high-quality dataset suitable for structured tuning. We tuned models to produce structured reasoning under a designed prompt template that enforces explicit reasoning Seatrion-RRaoning----
labels. For each combined with our structured reasoning prompt I, which guides the model to use specific reasoning labels at the start of each sentence. The model learns to generate the structured reasoning and the answera. The structured model, Ostruct. is trained as follows:
triplet (g,r,a) in the dataset 2 Dstructs the question is
Oxtruct =
II
P(r,a q,
(Darro)Darues)
where / denotes our structured prompt and Dstruct is the set of selected high-quality samples.
4.2 LAYER-WISH STEP-DEPENDEN TRACING
Step-to-Step Attention Matrix. Given a layer attention tensor A E R x Loeg (H heads, sequence length Lgeg)), compute the normalized step attention matrix A Raxn for reasoning steps. For steps i, with token ranges [s gend) and [s gend) respectively:
H HT.
AG
Σ
max
An.a. BET,
(3)
h TET.
where To
[sstart 2 .nd]] denotes the token range of step k.
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The Longest Common Subsequence Reward The LCS reward requires at least one correct Published as a conference paper at ICLR 2026
We denote the token range of step k by Tk: [s sta The time complexity of this procedure is Q x H x n² x Twy). where Tagg is the average number of tokens per step. In practice, the inner max is computed with vectorized reductions, and per-layer intermediate buffers are released immediately, keeping memory footprint low.
4.3 REINFORCEMEN LEARNING FOR IMPROVED STRUCTURED REASONING
We assume that better reasoning process should have fewer unnecessary connections between steps.
1. Max-Flow Reward We assess step importance via max-flow/min-cut based reward (Ford Fulkerson 1956). Let the induced reasoning graph have V = n nodes and E retained edges after thresholding (edge density p E/n² < 1). We employ sparse max-flow implementation Frush-Relabel style with standard heuristics).
(a) Graph Construction. Construct directed graph G (V, Nodes V = {1, ..., n) representing steps (node 1: Question, node n: Answer); Edges (i,j) E with capacity Aú when Aij >
(threshold т = 0.05). Thresholding prunes weak edges, yielding sparser, quasilinear backbones that accelerate flow computation while preserving salient reasoning channels.
Compute max-flow F in G using Ford- Fulkerson algorithm. For each node k E V {s, 1J. A&v = F-k. k. where F- is the max-flow in subgraph G (node removed). The value AF,, quantifies how crucial step k is for reaching the conclusion.
(b) Step Importance. For source 1 and target
(c) Robustness Evaluation. Let Kop be the top-25% most important steps. The reasoning quality metric Q E [0, 1] is computed as:
Σ AFs
Q Q=
Σ AF
The resoning reward Tmaxflow if correct, else 1. Higher Q indicates more balanced reasoning.
Time Complexity. The theoretical worst-case complexity for max-flow is O(V2E) using Dinic's algorithm. For dense attention graphs where F = (n²),, this yields O(n"). However, our two-stage optimization (optimized Dinic + residual network reuse) achieves 7.41 speedup, with empirical complexity between On log n) and O(n2.5). The overall time complexity is:
O(BHn'Tag) On...).
with detailed analysis in Appendix F
completion reference. Given sampled reasoning completions R {r1..... ........ Fn for question, let (r,)( denote the correctness reward for reasoning completion r;. For each pair (rr,ry), we extract their reasoning steps and compute the longest common subsequence (LCS) of reasoning labels, denoted LCS((;, r3)-
Let Lies be the total length of the matched steps in the LCS and L, be the total length of steps in ri-
To prevent length hacking (i.e., artificially increasing the token count of each reasoning step to inflate scores), for each matched step & in the LCS with lengths fi and fi introduce length
suppression factor, defined as ratioą = 26:
6,* if li > lGK and ratio =
6, otherwise.
Subsequently, the length of the weighted LCS is defined as Lies ExELeS(rAr)) ratio Lr We define the pairwise LCS score as:
Lics L
if both r; and ry are correct, if both and are incorrect, if r; is correct, rý is incorrect, if r; is incorrect, ry is correct.
Lia
(6)
Litz
Here, a higher LCS ratio is rewarded when compared with correct completions (encouraging consen- on high-quality reasoning), while lower LCS ratio is rewarded when compared with incorrect
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Published as a conference paper at ICLR 2026
completions (encouraging diversity from incorrect reasoning). The length suppression factor ratio penalizes unnecessarily long steps and encourages concise reasoning.
Finally, the overall LCS reasoning reward for c; is averaged over all other completions:
1
(C)
Scoreies (y).
jzi
Time Complexity. For sequences of lengths L1 and L2. the code fills a DP table and backtracks, costing (LL, L2) time; the weight pass over LCS matches is ( L2}) and does not change the overall bound. Space usage is ((T,, I22) for the DP table (plus negligible ((min(Ta [1,, L2) set of indices), thus T22) overall.
4.4 VALIDATING ATTENTION- REAIIONNN CORRESPONDENCE:
To validate that our step-to-step attention matrices truly capture reasoning dependencies, we conduct experiments on the Entailment Trees dataset (Dalvi et al. 2022), which provides gold-standard reasoning dependency annotations (premise + intermediate + conclusion) for ARC (AI2 Reasoning Challenge) science exam questions. We convert examples into structured format and extract ground- truth dependencies as binary adjacency matrices. We compare the Structured group (feeding structured reasoning into DeepSeck-Ri-Distiie -walll--wee-BBBB and measuring alignment between step- wise attention and gold dependencies) against a Shuffled group (randomly shuffling step order while keeping question/answer positions fixed, thus destroying reasoning structure). For each example, compute the alignment score as the proportion of gold dependencies where attention weight exceeds the average attention, and calculate the win rate the percentage of examples where the Structured group outperforms the Shuffled group.
As shown in Table I we evaluate on two reasoning scenarios from ARC questions: Task 1 (no dis- tractor) contains only necessary reasoning steps, while Task 2 (with distractor) includes irrelevant information to test robustness. Across both tasks, the Structured group achieves significantly higher alignment with human annotations (71.27% vs 28 48% for Task 1; 72.27% vs 24.87% % for Task 2)
and overwhelming win rates (97.155 and 95.29%) demonstrating that attention matrices do capture meaningful reasoning dependencies rather than spurious correlations.
Table Attention denntdonny alignment on Entailment Trees dataset. The experimental group uses structured reasoning with preserved order, while the control group uses randomly shuffled steps.
Task no distractor
Avg Alignment
Win Rate
Task 2 with distractor
Avg Alignment
Win Rate
Shuffled Group
28.48%
5.50%
Shuffled Group
24.87%
4.71%
Structured Group
71.27% %
97.15%
Structured Group
72.27%
95.29%
5
EXPERIMENTS
In this section, evaluate the effectiveness of the proposed structured reasoning by comparining with GRPO and other models based on the same finetuned model.
5.1 COMPARED EFFICIENCY, STABILITY AND EXPLAINABILITY.
For structured reasoning tuning data, we use the S1 dataset MMennighoff et al. 2025), which contains 1, 1,000 high-quality problems, covering science, technology, engineering and mathematics (STEM) and related domains. select 500 high quality structured reasoning samples. In the second stage, Pwweee---rree--eeeee
(Luo al.) 2025b), mathematics dataset containing 40K question question-answer answer pairs drawn from AIME, AMC. Omni-Math (Gao et al. 2024a), and STILL (Song et al. 2025a).
we structured reasoning reinforcement learning on the
Efficiency Task.
We evaluate the effectiveness of our proposed methods by reporting Pass @ accuracy (mean + standard deviation) across nine benchmarks: the math (AIME 2024, AIME 2025, AMC, MATH500 (Hendrycks al. 2021b), Minerva, Olympiad-Bench (He et al. 2024

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Published as a conference paper at ICLR 2026
rexding-comprrhension (DROP), law (LSAT-AR Zhong et al. 2023) and massive multitask (MLU- ALL-VALID (Hendrycks et al. 2021a).) using standardized evaluation protocols. For AIME24, AIME25 and AMC23, we pertorm evaluations in 10 seeds each, while other evaluated in 3 seeds each. For the training of our method, the maximum response length is limited to 4k tokens, while we report 0.5k, 1k, 2k, 4k and 8k maximum token length evaluation result for efficiency display. The max-length constraint is enforced as hard decoding cap during generation, which terminates when reaching the specified token limit an -ee-on-euuuecee token, whichever comes first. Additionally, we compare other 1.5B models against our MaxFlow structured reasoning version across Math problems (ApeendixAA.b [A.6). We also performed detailed component ablation studies (Appendix B and comparisons between LCS and MaxFlow (Appendix C)
Table 2: Benchmark Results (Pass@1 Accuracy) under different maximum response lengths. All
results are reported as mean. Avg. score calculates the average across all nine benchmarks. DS is short for DeepSeek-R1. Comparison with baseline models and methods for fine-tuning 1.5B models. The shaded models are trained by otherworks. All other results are either evaluated on existing models or on models we trained using different approaches. Methods all fine-tune DeepSeek-R. on the same DeepScaleR dataset.
Model
AIME'24
AIME'25
AMC
MATH500
Minerva
Olympiad
DROP
LSAT-AR
MMLU-ALL
Avg.
IK Maximum Response Length
FasCuRR.
0.00
2.22
15.83
25:73
9.19
7.56
20.80
22.75
40.54
16.07
DeepScaleR
0.00
35.00
13:11
17.75
DS- DS-Distll-Qween-..88
1.11
1.11
15.83
27
12.01
8.10
23:25
24.49
44.05
17:46
GRPO
0.00
0.00
25.00
45,20
13.73
12.94
34.50
22.17
40.67
21.58
Ours(LCC)
1.67
1,11
22.50
53.40
20.04
18.04
32.20
23.15
44.50
24.28
Ourst MaxFlM)
2.22
1,11
23.33
44.67
14.95
14.42
34.65
22.32
42.04
22.19
Respoone Length
FasiCuRL
1.67
3.33
27.50
54.90
17.10
19.41
28.71
22.75
45.35
24.52
DeepScaleR
7.78
5,56
36.67
65.20
24.63
27.36
28.70
22.90
45,13
29.33
DS- Di-Dittll-Qwen--.5B
3.33
1.11
36.67
52.33
20.96
19.95
25.29
21.45
46.72
25.31
GRPO
6.67
6.67
45.83
68.07
24.39
30.52
38.99
24.04
45,44
32,33
Ours(LCS)
Ourst MaasFM)
6.67
6.67
46.00
69.13
26.39
31.86
39.41
22.30
46.72
32.78
4K Maximum Response Length
FasiCRL
14.44
15.56
50.00
76.60
29.29
36.84
33.76
23.04
48.51
36.45
DeepSealeR
22.22
24.44
63.33
77.13
32.11
40.04
30.33
24.06
48.55
40,25
DS-Distill-Qee Bisnill-Qwen--.5B
71.73
47.51
33.79
GRPO
17.78
16.67
58. 38.33
77.13
29:90
40.40
42.00
24.49
46.81
39.
LCr)(LSS)
20.67
18.33
65.00
78.20
30.51
41.70
35.25
25.15
49.65
40.50
OarFoMa)Flow)
27.78
24.44
60.83
76.73
29.90
41.90
40.10
24.59
48.81
41.68
8K Maximum Response Length
FasiCuRI.
17.78
49.51
DeepScaleR
36.67
26.67
77.50
87 80
33.56
56.22
33.73
32.17
48.92
48. 14
DS- DS-Distill-ueen -Saill-Qwen--.S
23.33
18.33
66.25
80.33
31.00
44.49
30.52
26:26
50.60
41.23
GRPO
23.33
21.11
69.17
83.20
31.37
48.89
42.23
24.20
45.98
43.28
Ours(LCCS
23.33
20.00
72.50
82.20
30.51
48.59
40.80
28.50
$1.25
44.19
Ours( Max((M)
36.67
27.78
34,22
49.60
Stability Task. To assess model stability, conduct experiments across LSAT-AR, MATH500, and Beechh
Olympiad- Bench datasets (3 seeds each) under varying sampling temperatures (0.1 to 1.0). Using a fixed 8k token maximum response length, measure accuracy variance quantify how robust methods are to different temperature settings, with lower variance indicating better stability.
Explainablity Task. We design experiment (Interference Injection and Selective Removal, ISR) (3.13) to assess our ability to analyze reasoning step importance. Since existing datasets rarely provide direct importance annotations for reasoning steps, and LLM-based scoring noisy, we inject obviously irrelevant reasoning steps into existing chains. While we cannot confirm the relative importance of original steps, we can be certain about the irrelevance of injected ones. We compare our max-flow algorithm (4.3), top-p/top-k backtracking (0. average step perplexity 10). and random selection based on their Error Filtering Efficiency (A. when removing 1-11 steps from mixed reasoning chains. The experiment uses 70 correctly structured reasoning examples from SIk, covering STEM and related domains, selected for their longer trace lengths and more uniform reasoning steps. We define four types of interference steps: (1) Redundant statements like "Let's summarize what we' ve done so far, our previous work is correct" that add no value to reasoning; (2) Distracted comments indicating distraction such "This reminds me of another problem": (3) Harmful - randomly injected reasoning steps from other problems; and (4) Confused copies of current reasoning steps randomly injected at incorrect positions in the reasoning chain.
impporur
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Table Comparison with baseline models and methods for fine-tuning 7B models. Methods in the bottom section all fine-tune DeepSeek- 1---i-till--eee Siilll--wen-7Hh 7B on the same DeepScaleR dataset.
Madel
AIME 24
AIME 25
AMC.
MATH500
Minerva
Olympiad
DROP
TSAT-AR
MMLD-ALL
Avg.
1K Maximum Response Length
Light-RI
3.33
3.33
25.00
38.35
17.65
11.95
43.27
23.04
54,50
24.49
DS-Distil-Qaca-12
5.56
4.44
16.67
35.00
19.00
11.01
43.44
21.74
59.20
24.01
GRPO
8.89
6.67
27.50
50.73
23.65
16.69
49.75
22.03
56.76
29.19
OusiLLC)
24.50
50.15
35.06
(uasoM))))oo)
11.11
10.13
30.00
57.67
27.21
20.94
50.33
25.80
58.96
32.32
2K Maximum Response Length
Light-RI
22.22
14.11
43.33
67.67
35.66
32.20
45.72
29.42
62.42
39.
D55DistillQQeen
15.56
13.33
38.33
65,33
32.60
28.89
45.46
31,09
63.44
37.11
GRPO
22.22
18.89
56.67
77.27
35.42
38.96
51.82
28.78
60.25
43.36
Qusi(LCS)
28.89
25.44
63.50
$0.40
38,90
42.75
52,90
31.10
62,20
47.34
Ours(MaxFlow)
22.22
77.53
37.63
38.87
51.65
31.13
61.02
45.28
4K Maximum Response
Length
Light-RI
48.25
34.35
50.95
DS- DSS-Disill-Qwen-77
35,56
38. 89
62.50
81,20
39:46
68
45.74
37.61
64.58
50.
GRPO
42.22
35.56
70.00
84,40
39.09
50.07
51.79
37.83
61.45
52.49
Ouri(LCS)
40.00
32.22
75.83
85.60
40.15
51.25
53,20
40.25
63.15
53.52
(MssFo)))
43,89
38,89
80.83
87,53
40.56
$2.99
52.86
44,49
61.70
55.97
Maximum Response Length
LighttRR RI
44,44
45.56
80.83
89.47
38
$9.56
46,00
50,00
64.50
$7.62
DS-Distill- Suilll--een-BBB
59.26
52.32
$8.05
GRPO
48.89
40.00
85.50
90.27
40.26
59.70
$1.78
46.74
61.79
58.33
OursLCCS)
46.67
38.89
82.50
88,
39.85
58.45
52.45
48.90
62.35
$7.66
(lasww))
53.78
41.00
91.25
92.67
41.54
61.78
53.03
52.74
62.77
61.17
Table Comparison of model performance variance and stability under temperature changes from 0.1 to 1.0. Results MATH500, OlympiadBench, and LSAT-AR benchmarks demonstrate model robustness across different temperature settings. Methods in the bottom section fine-tune both PeopSeck-RI-Ditilll Qwen-1.5B and 7B models using the same DeepScaleR dataset.
1,58 Models
7B Models
Performance
MATH550
OlympiadBench
LSAT-AR
MATH500
OlympadBcack
LSAF-AR
-wentil-Qwea-138
78.00= 94
42.50+2.74
36.8000.64
DS-Distill-Qwen-77
91.33:1.42
59
52.3242,69
FasCuRL
80.6621.09
45.2640.80 8.000000000000
26.3620.94
Light-RI
89.47=1.12
59 56.56.0.57
50.0013.37
GRPO
72.51=0.79
48.0750.5
28. 28.98=0.50
GRPO
90.27:0.92
59.70=0.70
46. 26.74+2.39
Ours(TCS)
83.74=0.48
50.154048
59
Ours(LCS)
90.85+001
49.3843.24
Ourst MaxFlow)
85.0820.33
54,2840.29
31.35:0.47
Ours/MaxFlow low)
92.67241488
61.78:0.50
$2.74=2.08
Models. Our experiments are conducted two base models: DeepSeek-R1-1e Riii-R---Diiill-weeeee 1.5B and DeepSeek-RI. Saii--RRR-ittil-weeeee
(DeepSeek-AT et al. 2025b). For both model sizes, we train for 500 steps and derive three variants through different reinforcement learning approaches. GRPO represents models trained using the GRPO algorithm to optimize the reasoning process. Max-Flow denotes models trained with our proposed maximum flow reward, which evaluates the balance of step contributions in the reasoning response (4.3) LCS refers to models trained using a reward based on reasoning process similarity to select optimal reasoning sequences (4.) The structured reasoning example can be found in A.12 The experiment comparison can be found in A.4.4
Baselines. We compare our proposed methods with several state-of- baselines: (1) DeepSeek-
R1 RI-Distill-Qwen-I-. 1B,, DeepSeek-R1-Disse -isttlilll----ee---7 Qwen-7B (DeepSeek-AL et al. 2025b) (2) FastCuRL-
1.5B Pre-ireveww (Song et al.) (2025)), which employs curriculum learning for reasoning; (3) DeepScaleR-
1.5B (Luo et 2025b), which incorporates entropy regularization in GRPO; (4) GRPO (Shao et al.)
2024a), which uses guided reinforcement learning for reasoning optimization; and (5) Light-R111 larger model variant. All these models, including ours, are initialized from DeepSeek- 1iobeekk-R---stttii 1-Distill- 1.5B/7B and subsequently fine-tuned via reinforcement learning to enhance reasoning capabilitics.
Training Details. We train all methods (GRPO, Max-Flow reward, LCS reward) on DeepSeek-RR Distill-Qwen-I and 7B backbones. Models are initialized with brief structured tuning pass on the 500 Structured Reasoning set (2 epochs, learning rate 1 x 10-3 cosine schedule without floor, weight decay 10-4 micro-batch 1 on a single A A100); this stage is uniform across methods. Structure- -rreaaeee---Pee-----eee
aware optimization then uses the inference runs under v vLLM (70% GPU memory, max sequence length 4096). Per-device batch size 6, gradient accumulation 4 (effective batch 24), gradient checkpointing enabled. Learning rate sweep: (1 x 10 6, 2 10 10-6 66; 2 x 10 works better for 1.5B, x 10 -6 for 7B. Cosine scheduler with 0.1x floor; weight decay 1 x 10-1, Each training sample yields 6 completions temperature 0.6 (same
in bfloat16 with FlashAttention2;
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Published as a conference paper at ICLR 2026
for evaluation). All reward settings include Format Score (weight 1.0). The Max-Flow reward carries weight 2.0; its graph is built by thresholding seep-teep attention at T = 0.05 then rumning a to match Format Score scale. GRPO uses 3 = 1 x 10-3 When a KI. constraint is enabled, we set 5 = 1 x 10-1 (average K= 2 x 10-9) and 3KL. 103, giving effective penalty SKI. Rs 0.1 upon violation. No dynamic sampling or samplc-inflating heuristics are used (fixed 6 candidates per prompt), Validation occurs at fixed intervals; we report the best checkpoint on held-out metrics. Structural reward computation adds only modest overhead versus the base forward and decoding costs (Appendix A.4.2
capacity-scaling max flow. The LCS structural reward is
Efficiency Performance. As shown in Tables 2 and A.6 we evaluate all models across six haatheemmatis-ffocssee benchmark datasets and three out-of-domain datasets (reading, legal, and massive multitask) to demonstrate the effectiveness of MaxFlow and LCS. From Table we observe that our proposed structure-aware optimization methods consistently outperform other baselines for 1.5B models. Notably, MaxFlow with 4k training length achieves significant average improvement over GRPO and surpasses DeepScaleR- 1.5---B-PP SB-rreie which was trained with maximum 24k length and evaluated with 32k length (Table A. Similarly for 7B models, Table shows that the LCS method performs excellently under 4k maximum length, while MaxFlow outperforms by a large margin across the entire length range. Besides, Figure 7 ssows LCS generate more correct responses in the 1024 token range and fewer that exceed 8 8192 tokens, indicating more efficient reasoning.
Table 5: Comparison of Error Filtering Efficiency (EFE) percentage when removing 3, 5, 7, and 9 steps from responses. Perplexity uses step-level lowest perplexity ordering for removal, while both top-k and MaxFlow are based on our proposed step attention matrix method.
DeepScck-R1 R-ii-iiilill-.55
DeepSeck- RI -Distill-BB
Method
3 steps
5 steps
steps
steps
3 steps
5 steps
7 steps
9 steps
Random
54.97
54.98
53.39
53,57
56.60
36.12
55.56
55.25
Perplexity
56.65
59.52
62.91
68.07
57.87
61.40
65.36
65.13
Ours(Top-ky
59.36
67.39
69.84
76.29
59.63
64.22
68.65
75.38
Ours(Max-Floomm
69.22
72.71
75.36
76.67
65.16
73.55
74.34
75.16
Structured Reasoning Models Produce More Stable Outputs. As shown in Table we observe contrasting behaviors between baseline and structured reasoming models across temperature variations. Bascline DeepSeck-Rl-Distie models exhibit sigmificant temperature sensitivity, with performance improving substantially as temperature increases from 0.1 to 0.9. For example, the 1.5B baseline shows accuracy gains from 77.47 to 82.33 on MATH500 when temperature rises. This suggests that baseline models rely heavily on sampling diversity to achieve better performance. In contrast, our MaxFlow method maintains consistent performance across all temperature settings, achieving the lowest variance: +0.53 on MATH500 and #0.29 on OlympiadBench for the 1.5B model. This temperature robustness indicates that structured reasoning frameworks produce inherently stable outputs without requiring specific sampling parameters, making them more reliable.
Structured Analysis Helps Identify Redundant Reasoning Steps. Through IISR experiments, we found that as more reasoning steps were removed, our proposed methods based on step-matrix (See Section 4.3) (top-k, top-p, and max-flow) significantly outperformed random removal Fig- ure A1 The specific example can be found in Appendix [3.13] Additionally, in our comparison with perplexity-based algorithms 6 we found that removing steps with the lowest PPI. (PPI. Bot- tom) performed similarly (though slightly worse) to our methods when dealing with redundant but harmless information, as such information typically has low information content and low perplexity. Interestingly, for logically confused interference, removing steps with the highest PPL (PPL Top) performed slightly better, as steps appearing inappropriate positions caused significantly increased perplexity. This shows that PPL reflects information quantity and cannot distinguish reasoning from disruptive content. 5 step-matrix- -bssd methods outperformed PPL-based approaches.
5.2 WHAT ARE THE GAINS FROM STRUCTURED REASONING MODELS?
Benifit from Training-Fres Structured Rasoning. For large LLMs, leveraging their robust folluutionnfollowinng capabilities and inherent reasoning abilities, effectively guide them

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Published as a conference paper at ICLR 2026
towards structured reasoning without additional training. Table 6 summarizes the average token lengths and accuracies across several benchmarks, including MATH500, GPQA-Diamond, MMLU- ALL-VALID, AMC23, and AIME24. Notably, the structured reasoning model achieves similar or higher accuracy with much shorter answers, e.g., on MATH500, the average reasoning token length drops from 2945 (Base) to 1577 (Structured Guidance), while accuracy remains above 92% (See Appendix A. 14 for the fill in the middle prompting strategy).
Table 6: Token Length and Accuracy Analysis of DeepSeek-RR RI 671B Using Training- Frening--Freeeee Structured Guidance. Results shown across Mathematical and General Benchmarks under same settings.
Model
MATH500 Acc./Len.
GPQA Acc.LLnn
MMLU Acc./Len.
AMC23 ALc.Len.
Base
92.9% 93.0%%
70.3%/6637 71.18/4428-388499
88.8%/989 39.6%/512244.255
100%/1716 100%/2053+19.69
Structured Guidance
Cross-Scale Emergence of Broad Mid-to-Late Step-Span Attention. According to 70 samples from 1.5B and 7B models with our step attention matrix thresholded at 0.1, I, we found that layer 0 attends to an average 6.82 reasoning steps, while layer attends to only 1.41. This produces a early division of labor between (i) layers that aggregate multi-step context and (ii) layers that perform local refinement anchored to the immediately preceding step. Beginning around layer 14, all subsequent layers attend to >8 steps (peaking at 12.06), marking transition to a stable broad-span integration regime that more faithfully ranks step importance (Figure The same qualitative pattern appears in both 1.5B and 7B models: early oscillatory specialization + mid/late sustained global integration. The 7B model shows smoother (less jagged) broadening trajectory, whereas the 1.5B model preserves sharper alternating contrasts before converging. These consistent cross-scale dynamics imply (I) the broad-wy broad-span mid-late blocks encode globally consolidating reasoning signals, and (2) pruning distillation strategies could target redundant narrow-focur early layers or alternating pairs while preserving (or selectively enhancing) the globally integrative mid-late region.
repeating broad-versus-loch alternation through upproximately layers 0-13, suggesting
LLM 1.58 Layer-Wise Step Attention Distribution
LLM 7B Layer-Wise Step Attention Distribution
0 pl
Atterntonn Rocur Lavell thop p1
Figure Analysis of attention step range: 1.5B (Left) and 7B (Right). Darker means broader.
Analysis of Model Reasoning Patterns. We identify commain-invaiiann backbone: as s umpt i on + (decompose formalize) + verify + consequence + summarize ze, while variabil- ity concentrates in domain-shaped veri fy loops (e.g., contradiction cycles in Number Theory, associative loops in Clinical, evaluative grounding in Geometry). Algebra shows canonical setup, whereas Geometry's s early direct formalization yields the leanest loop density and Business Ethics exhibits high hypothesis suppression ratio with intensified evaluative chains. Loop density rises and the verify fy position shifts rightward in longer traces, signaling deferred iterative refinement. Full transition frequencies, loop densities, and positional distributions appear in Appendix A.5
chains Business Ethics, early wwwetiiioodddddeeeeeeeeeeeeeeeee
cormaliiee
CONCLUSION
In this paper, we reformulate structured reasoning graph optimization problem where reasoning flows from question + steps -> answer. Our approach introduces structured step annotations for reliable graph construction in small LLMs, MaxFlow reward for pruning redundant steps, LCS reward for reinforcing high-quality sub-paths. Experiments on DeepSeek- 1aak--R---iisss -Distill models demonstrate that MaxFlow provides significant performance gains with superior stability across context lengths.
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A APPENDIX
A.1 THE USE OF LARGE LANGUAGE MODELS (LLMS)
As Large Language Models (LLMs) have evolved into reliable research assistance tools, we maintain transparency about their usage in this work. In accordance with the submission guidelines, explicitly declare our LLM utilization in the following scenarios.
First, we employed LLMs for grammar and style enhancement, specifically for proofreading and improving the linguistic quality of the manuscript. All suggestions were manually reviewed and verified by the authors ensure accuracy and appropriateness.
Second, LLMs were utilized to assist in the layout and organization of paper figures, helping optimize the arrangement and presentation of visual elements. The actual content and design decisions remained entirely under the authors' control, with LLMs providing suggestions for effective visual organization and structural composition.
We emphasize that all LLM- -aM---errttedd content underwent thorough human verification and refinement. The core research ideas, methodology, experiments, and conclusions were independently developed by the authors. I.LMs served purely as assistive tools under careful human supervision to ensure the work's 's reliability and originality.
A.2 ETHICS STATEMENT
We affirm our full compliance with the ICLR Code of Ethics throughout this research. Our work primarily focuses on visualization techniques and does not involve human subjects, sensitive personal data, or potentially harmful applications. 'he visualizations and methodologies presented in this paper are designed to be general-purpoct tools that promote transparency and understanding in data analysis.
We acknowledge that any visualization tool could potentially misused for misrepresenting data. To address this concern, have implemented clear documentation of all visualization parameters, explicitly stated the limitations and appropriate use cases, and designed our tools with built-in safeguards against common forms of visual manipulation.
We declare no conflicts of interest, and our research was conducted independently without external commercial influence.
A.3 REPRODUCIBILITY STATEMENT
We are committed to ensuring the reproducibility of our research findings. Our com- plete set of interactive visualizations is currently available at anonymous website hww.://wws...oocccccccc//tttttte key findings discussed in the paper.
These visualizations demonstrate all the
While our source code and data are not yet publicly available due to the double-blin review process, are preparing comprehensive releases that will include the complete implementation code, processing scripts and documentation, sample datasets used in our experiments, along with configuration files and parameters.
Section 3 of our paper provides detailed technical specifications and methodology, with additional implementation details available in Appendix A.
A.4 TRAINING DETAILS AND RUNTIME ANALYSIS
We summarize the complexity of the two structural rewards: MAX-Flow and LCS, together with the scalability heuristics actually used.
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A.4.1 NOTATION
B batch size; H attention heads; n average reasoning steps; Tavg tokens per step; = n' awg avg total reasoning length; d, head dim; sparsification threshold; E' retained edges after thresholding; Cmax maximum edge capacity: m number of answer candidates; Luss average candidate length.
A.4.2 SCALING HEURISTICS
Layer selection: extract step attention only from small subset (e.g.. 23-27 layers), cutting propor- tional overhead. Adaptive threshold: choose T as a running quantile to stabilize E as context length grows, avoiding quadratic blow-up. Capacity bucketing (8-12 bit) bounds log Cmax and shortens scaling phases. Structural token filtering shrinks LCS input length before any quadratic DP.
Table 7: Observed MAX-Flow reward overhead (single evaluation).
Model
Max Len
Avg Steps
Peak Mem (MB)
Latency (ms)
1.5B
2048
6.23
69.10
258
7B
2048
6.18
177.59
395
7B
4096
11.05
373.89
1321
A.4.3 PRACTICAL SUMMARY
Overhead is dominated by sparse max-flow with E < n²; LCS becomes the main cost only when doing full pairwise alignment with large m; layer restriction, adaptive edge sparsity, and structural token filtering preserve tractability for long contexts (e.g.. 128K) without quadratic memory growth.
(a) Reward with mask
(b) Reward without mask
(c) Length mask
(d) Length wo mask
Figure 4: Impact of Truncated Completion Masking Training Stability
A.4.4 EXPERIMENTAL DETAILS
Table 8: Training Details. To ensure consistency in counting training steps, we standardized the batch size 128. This means that two steps with a batch size 64 are considered equivalent one step with batch size of 128.
Model Training Steps
Training Stages
Number of GPUs Used in Each Stage
Ours
RL(~ 23)
FastCuRL
RL(~ 860)
4
8, 8, 8,
DeepScaleR
RL(~ 1,750)
3
8, 16, 32
Truncation Robustness.
Our observations reveal that truncated long outputs induce notable gradient fluctuations and result in unstable training processes (Figure 4 To mitigate this issue, we mask the truncated completions to disregard their reward values and gradient updates. This approach effectively stabilizes optimization by omitting samples surpassing predefined length limit.
Tag Randomization for Robustness
Inspired by DeepSeck-RI! Rl's reasoning completions, we introduce randomization in the order of reasoning tags in the prompt during training. Specifically, for each question, retain the top tags
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and randomly sample 0-5 additional tags from the remaining set, shuffling their order in the prompt. This approach reduces overfitting to fixed reasoning patterns and encourages the model to generalize reasoning strategies.
A.5 DOMAIN- SPECIIC REASONING PATTERNS
Data & Extraction. We sample 1,000 MaxFlow reasoning traces across five domains: Algebra, Number Theory, Geometry, Clinical Knowledge, and Business Ethics. Each trace is segmented into induced step tags (e.g., assumpt. on, decompose, formal i ze, veri fy, case_ana 1 ys is, associal at on, consequence, summari ze). We construct a directed multigraph over step types; edges count adjacent transitions. Edges with global frequency 0.5% are pruned for clarity (full graph retained for reproducibility).
Metrics. (1) Average step count. (2) Top tri-gram pattern (local procedural schema). (3) Verify- centered loop density: proportion of transitions incident to verify that participate in back- reference to any earlier non-terminal step within a 6-step sliding window. (4) Hypothesis suppression ratio: 1 sonfaassmmtiinn-deccco tag (Fig. 8
(5) Positional distribution: normalized relative index of each
[rq[sasump_ion->
Cross-Domain Findings. A stable backbone
veri wowe-oooeeeeeeeeeeesseeeeee ssmmeennnee-smmma-eaammm ze) appears in domains, but modulation oc- curs in early structural translation and verification refinement: (1) Algebra: canonical pipeline before consolidation. (2) Number The- ory: elevated case anaalsiss contradiction and verify+> contradiction loops (proof refinement). (3) Geometry: suppressed decompose; early ossumption-tforee
grounding (equational coordinate forms). (4) Clinical: associative diagnostic path analysis; verification loops link symptom clusters to differential hypotheses. (5) Business Ethies: sparse innsuuttioontte -dcmoooooossse (limited hy- pothesis branching), intensified evaluative veri fyrify-ao conseeeeeeeeeee chains and veri fy-centric loops.
ass
Loop Dynamies. Loop density around verify increases with total step length (upper quartile traces show a right-shifted verify positional distribution), consistent with iterative late-stage refinement rather than premature validation. Number Theory and Business Ethics show the highest verify-loop densities (contradiction vs. evaluative implication), while Geometry exhibits the leanest loops due to early formal grounding reducing re-check cycles.
Table Domain speciffc structural statistics (loop density suppression values illustrative; replace with empirical measurements).
Domain
Avg. Steps
Top Tri-gram
Verify Loop Density
Algebra
12.3
0.41
Number Theory
11.8
case
0.57
Geometry
10.5
0.38
Clinical
14.2
0.49
Business Ethics
13.6
0.53
Implications. The coexistence of a transferable backbone and domain-condee conain-conditioned verification loops suggests: (i) pruning strategies target high-density verify cycles (e.g., contradiction refinement) without harming structural progression; (ii) low hypothesis branching domains (Busi- ness Ethics) may benefit from explicit hypothesis expansion prompts; (iii) early formal grounding (Geometry) reduces downstream verification overhead avenue for curriculum design.
A.6 DETAILED MODEL COMPARISON AND REWARD ANALYSIS
Table II presents a comprehensive comparison three Small Structure Reasoning (SR) methods across various mathematical benchmarks. SR-FLOW demonstrates superior performance, achieving
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Table 10: Benchmark Results (Pass@) Accuracy). All results are reported as mean standard deviation. Avg. score calculates the average across all six benchmarks, while Large Avg. focuses on the more stable MATH500, Minerva, and Olympiad benchmarks. Top-3 models in each category are highlighted with increasing gray intensity.
Model
AIME'24 25ME'25
AMC'23
MATH500
Minerva
Olympiad
Avg.
Large Avg.
Based on: Qwen2.5-Math-L.55 (RL)
Math
11.343.6
5.742.7
44.0a49
51.745.5
11.3+2.2
26.0#0.6
25.0a3.3
29.74
Oat-Zero
16.0+3.2
6.7+3.4
52.5+29
73.5+1.7
26.3+0.8
37.2+1.
32.0+2.2
1..
Math
12.0+1.7
11.7+5.7
54.8+5.3
74.7+0.5
26.7+1.8
37.9+0.2
36.3+2.5
46.4+0.8
Based on: Neepseek-RL-Dsttll-OOeee
(RL)
RI-Distill
28. 3
22.3+5.2
71.5+3.9
84.940.3
30.5
52.4+0.4
48.4+2.6
55 25.9
LI-Exact
24.4+33.
22.3+b4.2
70.5+3.7
86.6#0.8
31.5+1.7
52.5+1.3
47.9=2.5
56.9+1.3
LI-Max
27.7::4.2
21.0+5.0
73.2+6.0
84.7+0.1
33.3+0.9
52.3+0.6
48.7=2.8
56.8+0.5
Open-RS1
28.926.0
21.3+442
75.0=3.3
85.1+0.8
30.4+0.2
53.2+199
49.0=2.7
56.2+1.0
Open-RS2 RS2
31.347.77
22.745.6
73.0+5.7
84.1+0.2
29.241.1
53.740.6
49.0+3.5
55.7+0.6
Op3
29.7:44.6
24.7#6.5
69.2255.5
84.2+1.1
28.642.3
$1.8+0.8
48.0=3.5
14.9+1.4
STIILI33
34.7+55.5
24.0#6.4
72.5+5.4
86.6211.9
30.0+0.6
53.9#1.5
50.3=3.6
16.8
ThTThught 32.045.9
24.0+4.1
79.5+5.1
86.640.6
31.7+006
$4.940.4
51,5+28
$7.7+0.5
FastCuRL 36.3+4.3
27.0=3.7
78.8+4.1
87.9+1.2
30.8+14
56.5#0.6
52.9#2.6
58. 18.1
DeepScaleR
37.026.6
30,3+4.3
76.244.6
87.8+1.0
31.0+1.5
55.5#1.1
53.0#3.2
18.1
Ours Based on: Reepseek-RT-DDeee Seesstll-Qwen--.tttt (RL.)
MAX-FLOW 36.748.9
27.0+8.2
77.826.6
85.3+1.6
34.242.9
54.9#1.9
52.6=5.0
58.1+2.1
the highest average accuracy (58.1%) while requiring fewer reasoning steps. SR-LCS offers the most token-efficient approach, using approximately 20% fewer tokens while maintaining competitive accuracy. Highlighted cells indicate top performances for each benchmark and method, showing that different reasoning approaches excel in different problem domains.
Table 11: Comparative analysis of GRPO training from to 500 global steps under four reward designs: accuracy (ACC), max-flow (FLOW), longest common subsequence (LCS), and their 1:1 joint combination (JOINT). We report Pass @ accuracy (%) across benchmarks plus average reasoning steps and tokens per sample. (JOINT rows omit standard deviations: single run variance not reported.) The table demonstrates the evolution of various metrics during GRPO training from O to 500 global steps under three reward functions: ACC, FLOW, LCS and JOINT, The metries are tracked throughout the training process to show how different reward mechanisms influence the performance of the model.
Method
Accuracy (%)
Steps
Tokens
AIME24
AIME25
AMC23
MATH500
Minerva
Olympiad
Large Avg.
Avg.
Avg.
GRPO
8.7
25.318.0
75.816.7
85.611.6
31.3128
53.3_1.9
56.7.12.1
9.57
1873
36.7-8.9
26.748.2
72.0-7.11
1..5+1.6
31.142.8
53.3-1.9
56.64-2.11
9.94
1796
30.0-8.5
21.347.6
74.0=7.0
1..7=1.6
32.42288
52.9=199
56.742..1
10.41
1808
24.0=7.8
22.547.7
74.0=7.0
83.7=1.7
33.022.9
52.2-1.9
56,342222
10.81
1859
8.73-8.7
24.217..
73.516.6
84.211.6
31.7128
55.61:2.1
1828
36.7-7.7
19.5
70.6
83.7
31.1428
1.99-199
55.24-2.1
10.85
1854
MAX-FLOW
32.7
25.318.0
75.816..7
1.66
31.3128
1.9
56.7122.1
9.57
1873
33.0-8.5
26.0+8.1
76.5+6.88
84.9-1.6
31.342288
53.6-1.9
56.64-2.11
9.63
1820
34.7-8.3
26.317.88
76.8
1.66
34.11229
53.5 1.9
$7.712.11
9.52
1779
3.77-8.9
27.0+8.2
77.8-6.6
85.3+1.6
34.24-29
548-11
58.14-2.1
9.24
1830
33.5-8.2
25.747.6
75.3=66.
85.0=1.6
33.242.9
53.7-19
57.342.1
8.78
1804
3..3-8.7
24.227.8
74.0=7.0
84.7-1.6
32.3228
$4.3=1.9
57.112.11
7.84
1798
LCS
32.7=8.7
25.3+8.0
75.8=667
85.6=1.6
31.3228
$3.3=1.9
56.7+2.11
9,57
1873
8.70=8.7
24.727.9
75.0=6..9
1.
32.0=288
14.1=199
57.012.11
9.61
1780
8.7
22.51.7.8
74.0
8.64
30.91288
$1.8
55.712.11
10.36
1668
30.3-8.5
23.34-7.8
74.0=7.0
8..3-1177
29.9422.8
51.6-199
54.9422.1
10.91
1614
3.77-8.7
23.727.9
75.0=6.9
84.9=16
31.8228
50.6=1.9
55.842.11
11.75
1509
31.0=8.5
23.3477.7
74.817.1
84.8
30.5#228
$2.7-199
$6.01:2.1
11.56
1504
FLOW&LCS
33.20:8.6
25.15:27.9
75.65=668
1..45:+1.66
31.80+2.8
53.55:1199
56.93=199
9.72
1978
33.75188.6
25.60-18.0
75.90-16.8
84.75.11.6
31.451288
54.10.19
$7.43=199
10.38
1821
33.65
24.6547.9
75.25-66.8
1.6
32.3542.8
52.90
57.17+199
9.53
1815
33.6548.6
25.40-8..0
76.15-66.7
14.15+1.6
32.204-2.8
53,44-99
57.27=19
1762
45:48.8
24.85=7.9
75.35=66.8
85 10:1:.6
32.65+2.88
52,40:199
$7.03=19
10.67
1718
30.80.18.4
23.90.17.8
74.65.6.9
84.90:11.6
31.25:12.8
$7.20=2.0
1638
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A.7 PART OF FIGURES AND TABLES
For better layout and presentation, we have placed some figures and tables in a unified location in the Appendix.
Disoribttion Conrect
Disribution
Rebotian Prsitiss Mio
(a) First Correct Answer Position Distribution
(b) Statistical distribution of reasoning path lengths
Figure 5: Analysis of Model Reasoning Patterns: Distribution First Correct Answers (Left) and Reasoning Path Lengths (Right).
Prociiion vv. Aug. Stepe Removed for Difffrent Sampling Methods
Precision vs. Avp. Stape Removed for Differant Sampling Methods
Pi:
Sanduw
Steps Romaved
Bemomed
(a) Redundant but harmless information
(b) Distracted harmless information
Precision vs. Avg. Steps Removed for Different Sampling Methods
Procision vs. Avg. Steps Removed for Different Sampling Methods
4.75
6.52
0.53
6.0
645
Gego
Stupe Removed
Aeppl
Slepe Ramaved
(c) Harmful irrelevant reasoning
(d) Logically confused information
Figure 6: IISR Results: Error Filtering Efficiency (Precision) of different algorithms when removing 1-11 steps under four types information interference.
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Taken Length Distribution with Smoothed Envelopes
125-00 Frow ope
LCS-150 brwakaze
US3 233-250 briskoze
LCS 50
KCS-1 to
Frequency
250
2014
NeW
0012
Token Length Buckets
Figure 7: Token length distribution of LCS models under different training stages. The smoothed envelopes show how reward training shifts the distribution towards optimal reasoning lengths (512- 1024 tokens) while maintaining performance.
250
140
140
120
250
252
102
300
202
150
200
50
Tug: eoaaleenn
Tag: alternativ
case analysis
specialize
140
60
120
300
10
10
RelMdiee
(80)
Rebadive Poodiion
Figure 8: Distribution of the relative positions of each tag within the reasoning process.
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Reasoning Path Transition Graph equivalent
START
assumptionial
Tormalize
decompase
Sunmariiz
verify
consequencce
analysis
241
END
alternative
Figure Illustration of Reasoning Path Transition Graph.
Table 12: Early Stopping Detection Parameters and Sample Statistics
Metric
Value
Number of valid samples
705
Top five frequent tags Token interval
verify, summarize, equivalent, formalize, consequence
128
Top five useful words
but, wait, however, check, alternatively
A.8 FULL PROMPTS
Free Tag Chain Extraction
Goal: Convert the raw reasoning into a linear sequence of abstract step labels (tags).
Rules: 1. Split the reasoning into semantic steps. 2. For each step invent ONE tag (a single
word; use lowercase letters or underscores only; no spaces, punctuation, or digits avoidable). consecutive steps would receive the same tag, merge them into one. 4. (No other text.)
two
Output ONLY one line: TAGS:
Input question: (QUESTION]
Input raw reasoning: (REASONING)
Output: TAGS:..
Mathematical Problem Solving Template
Please the following tags the beginning of each sentence in your reasoning: <rephrase>, <inference>, <analogy>, <equivalents, <association>, <reverse>, <summa- rize>, <verify>, <complete>, <decompose>, <counterexample>, <assumption>, <constraint>, <case_ <case_anatie _ass__anlssis,, <contradiction>, <abstraction>, <formalize>, <generalize>, <specialize>, <critique>, <alternatives, <consequence>, <intuitionz. [Question]
Please reason step by step, and put your final answer within boxed ).
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Table 13: Comparing Trigger Counts and Distances First Correct Answer Across Methods.
Irigger Type Settings
Avg. Trigger Count
Avg. Distance to First Correct Answer (tokens)
Top tags
'veriy". "ummmaize" etc.
2.02
78.01
Token chunks
128-token intervals
3.93
131.05
Keywords
"but", "wait", "however", etc.
2.69
139.97
Multiple Choice Problem Template
Please use the following tags at the beginning of each sentence in your reasoning: <rephrase>, <inference>, <analogy>, <equivalent>, <association>, <reverse>, <summa- rize>, <verify>, <complete>, <decompose>, <counterexample>, <assumption>, <constraint> <case_ane <case_analysis>, <contradiction>, <abstraction>, <formalize>, <generalize>, <specialize>, <critique>, <alternative>, <consequence>, <intuition>. [Question]
A) [A]
B) (B)
C) (C)
D) (D)
Please reason step by step, and answer the following multiple choice question. The last line of your response should be of the following format: 'Answer: $LETTER' (without quotes)
where LETTER is one ABCD.
A.9 IMPROVED COMPATIBILITY WITH TEST-TIME SCALING AND EARLY STOPPING.
For Test-time Scaling, existing work extends model outputs by injecting prompt tokens at thought- stopping points. Our method simplifies this by guiding outputs through the most likely next tag at stopping points. For early stopping, our tag-basce based approach outperforms traditional methods. In our experiment with 705 correct MATH500 reasoning completions (Table [2), we compared interval-based (128-token), keyword-based ("but", "wait", "however", etc.), and tag-based ("verify", "summarize", etc.) detection strategies. As Table shows, our structured approach reduces average Probe-In-Middo In-Middle interventions just 2.02 while maintaining closest proximity to correct answers (78.01 tokens).
A.
OTHER STEP IMPORTANCE EVALUATION ALGORITHI IMPLEMENTATION
Top-P and Top-K Selection. Based on the step matrix computed from different layers (See Sec- tion 4.3) we implement backtracking selection methods:
(A, = {st
(8)
where A E [Ruxn is the step attention matrix, and we select steps starting from the last step 8n-1 by either: Top-K- K: For each step s,, select up to preceding steps with highest attention scores. Top-P: Select preceding steps with cumulative normalized attention exceeding threshold
The algorithm traverses backward from the final step, adding important preceding steps to a visited set based attention weights, ensuring all critical reasoning dependencies captured. Average Perplexity. For each step, we compute token-level perplexity:
Perplexity(t.) = P(t:2æ, ti ti, 4-1))
where P(tsfæ, f1,... 1 is the probability of token t given the prompt a and all preceding tokens, derived from the softmax of logits:
exp(logits,)
Plk,,,,,,,.... E, exp(logits,)
(10)
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The average perplexity for step containing tokens {ti, 22, tm] is:
AvgPerplexity(s) = exp 1
log P(tila, (inll1))
(II)
Random Selection. A baseline approach where steps are selected randomly without leveraging attention patterns or perplexity metrics.
A.11
ERROR FILTERING EFFICIENCY (EFE) EVALUATION FORMULA
Performance Comparison of Different Step Filtering Methods
0.85
Optimal Region
0.75
Accuracy
0.70
0.65
Ideal Curve
Tep-P
0.55
Graph Centrality
Max Flow
Information Flow
0.50 0
Average Removed Steps Ratio
Figure 10: Comparison of Algorithms for Error Filtering Efficiency Averaged Across Four Tasks.
For the IISR experiment, where we randomly inject N interference steps into an M-step reasoning process, the Error Filtering Efficiency is calculated as:
Retaineedrreleeanttttppp |IrreevantStees/
EFE
(12)
where |IrrelevantSteps/ is the total number of interference steps injected (N), Reetiinellrelevanttteps is the number of interference steps that were incorrectly retained after filtering
EFE measures the algorithm's ability to identify and remove irrelevant steps, with a value of 1.0 indicating perfect filtering (all interference steps removed) and 0.0 indicating no filtering capability.
As shown in Figure 6 we first compared Top K. Top P, Ppl Top (where higher perplexity indicates higher step importance), Ppl Bottom (the opposite), and Random. We evaluated the Error Filtering Efficiency under four different interference injection methods. The results show that Ppl-based methods exhibit unstable performance across different tasks.
As illustrated in Figure A.II and Information-F -low. We found that the Max Flow method demonstrates a superior ability in evaluating reasoning steps, partieularly when removing small number of steps.
further compared the better performing methods: Top-P, Max-Flow,
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[TFL: divisoes
Fied all
Step inferenze (P91: 1.85] aced to Eind lis prine Eastocication of 186.
Seea 21 decompone (P91: 9.26] 108 i 2-000 2-46 2-7-773-4
Grep ansloer Dift- Decorpocition pairo RXAXIN
sumarize tnotectsation:
Aupky divioss (211)
Step tweify (POL: 62 16] Varify. exuments (2,
(8,3)
Step 7: case analsis DML: 11. tn3
List all cmbinnations: 1,2, 4, 16, 18, 40, 198
Stay 9: conceeenis [PP:: 328: 9e1
Ptral, confimotion: hos eseetls posticco disssors
Causal Reasoning Step Matrix
onsequence-
0.8
lysle
verty
verify-
summarize-
analogy-
rephrose
0.2
Inference
decomposs
rephrese-
reghaas
Inferatt
ASojeus
euiure
newnbo
Agina
vbetuoo
Alter pruning lhesping only critical stepa):
Stte 6:
reobrose
Fond all porseice onteger dovsence 198.
Steo 3: decomesse
188 on hwse 1BC 00
summerize
peine Enctuciaatinn
(211)
Stap
Verifr: expoeent (2,3) (5.3)
Step Bt. consegienee
Piral. confimation: 196 has ecactly 9 pocitive divisors
Figure 11: Using Max-flow Method for Filtering Steps during IISR Experiment.
A.12 STRUCTURE REASONING PROCESS DEMONSTRATION
Input Prompt:
Please use the following tags at the beginning of each sentence in your reason- ing: <rephrase>, <inference>, <analogy>, <equivalent>, <association>, <reverse>, <summarize>, <verify>, <complete>, <decompose>, <counterexample>, <assump- tion>, <constrainDs <case_ cease_analssis>, econtradictions, <abstraction>, <formalize>,
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<generalize>, <specialize>, <critique>, <alternative>, <consequence>, <intuition>
Convert the point (0,3) in rectangular coordinates polar coordinates. Enter your answer in the form (r, 0), where r > 0 and 0 < < 2n.
Please reason step by step, and put your final answer within
<summarize> The task is convert the rectangular coordinates (0,3) polar coordinates (r, 0) with r > 0 and 0 < < 2m.
cassumption> In rectangular (Cartesian) coordinates, point represented as (z, y). To convert to polar coordinates (r, !), we need to find:
r: distance from origin
0: angle with positive x-axis
<formalize> Conversion formulas:
x² + y²
arctan (y/x)
(when x a 0)
<decompose> Given point (0, 3):
3
<specialize> Calculate r:
02 - 3 3
<reverse> For 0: (3/0) is undefined. Observation:
and > + point lies on positive y-axis
<case analysis> Special case when 0:
1/2 if >
3r//2
if <
<verify> Check 0 range: x/2 E [0, 2T) is valid.
<complete> Final polar coordinates:
3, 2
Output:
The polar coordinates are (3, . 2
Input Prompt:
Please use the following tags at the beginning of each sentence in your reason- ing: <rephrase>, <inference>, <analogy>, <equivalent>, <association>, <reverse>, <summarize>, <verify>, <complete>, <decompose>, <counterexamplex, <assump- tion>, <constraint>, <case_and annalsssssssss <contradiction>, <abstraction>, <formalize>, <generalizes, <specialize>, <critique>, <alternative,, <consequence>, <intuition>
What is 553 in simplest radical form?
Please reason step by step, and put your final answer within D
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cassumption> To find the simplest radical form of v53, need to check 53 has any perfect square factors.
<decompose> First, let's factorize see its prime components. Since 53 a prime number, its only factors are and 53.
<verify> Since 53 is prime, there are smaller factors other than and itself. Therefore, v cannot be simplified further because there are no perfect squares greater than that divide 53.
<conclusion> Thus, the simplest radical form of 53 is v53 itself.
Output:
The simplest radical form is v53
A.13
EXAMPLE DEMONSTRATION OF INTERFERENCE INJECTION AND SELECTIVE REMOVAL (IISR)
Table 14: Steps retained by different filtering methods
Method
Retained Steps
Top-P (p=0.7)
[1, 3, 5, 10, 11]
Maximum Flow
[1, 3, 5, 7, 10, 11]
Graph Centrality
[3, 4, 6, 8, 9, 10, 11]
Information Flow
[1, 2, 3, 4, 5, 6, 7, 8, 10, 11]
Steps marked in red: [2, 4, 6, 9]
Interference types:
Irrelevant pauses (Step 2)
Off-topic reasoning (Steps 4)
Disordered repetition (Steps 6)
Redundant Reasoning (Step 9)
Input Prompt:
Please use the following tags at the beginning each sentence in your reason- ing: <rephrase>, <inference>, <analogy>, <equivalent>, <association>, <reverse>, <summarize>, <verify>, <complete>, <decompose>, <counterexample>, <assump- tion>, <constraint>, ccase_analysis> <contradiction>, <abstraction>, <formalize>, <generalizes, <specializes, <critique>, <alternative,, <consequence>, <intuition>
What is the smallest positive perfect cube that can be written as the sum of three?
Please reason step by step. and put your final answer within
<rephrase> The problem find the smallest positive perfect cube expressible as the sum of three consecutive integers.
<inference> [Interference Step] Pausing consider the implications of the next step.
<inference> First, recall that perfect cubes are numbers like 1, 8, 27. The sum of three consecutive integers can represented as 3n.
<inference> (Off-topic Interference] Gravity cancels out, so mass and distances are the key variables...
<analogy> Let the integers be (n - 1, 1, n + 1), then sum is 3n. The smallest cube divisible by 3 is 27.
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<inference> [Disordered Reasoning] Smaller cubes fail: 1st gives non-integer 2 gives
<verify> Check 27: + 9 10 = 27. Is there smaller cube? No. since and aren't divisible by 3.
<assumption> Alternative representation: (n, 1, + sums 3(n 1). Still requires divisibility by 3.
<reverse> [Redundant Reasoning] Alternatively, maybe the three consecutive integers could be... <consequence> Smaller cubes fail: 1 = gives non-integer n = 2 gives n = 3
<summarize> Therefore, the smallest positive perfect cube meeting the criteria is:
A.14 STRUCTURED REASONING THROUGH FILL IN THE MIDDLE API
The full message template is structured the same as the prompt in Appendix A.8
The API call is implemented as:
messages =
"rooe": "user", "content"; full_messagel
"role": "assistan:",
treasoning_content: Crephraae>\nnkay, I will organize my thoughts process in a hierarchical manner. hn</rephras>><ns", "content": "" "prefix": True
response await self.cliem chat cwwpletions create mode mmoell messages=messages
In particular, we initialize the reasoning process by injecting <rephrase> tag and metacognitive statement. This approach is effective in guiding DeepSeek-R 1 to perform structured reasoning in zero-shot setting, leading to more stable and organized reasoning patterns without additional training.
B DETAILED ABLATION STUDY
To better understand the contribution of the component, we conducted controlled experiments to systematically evaluate the individual and combined contributions of each proposed component.
B. EXPERIMENTAL DESIGN
We organized our ablation experiments into two categories. The first category evaluates isolated com- ponents measure their individual effectiveness: Structured Tags applies structured reasoning format with standard GRPO; LCS (free-form) applies LCS reward on free-form reasoning by extracting steps via An separation; MaxFlow (free-form) applies MaxFlow reward on free-form reasoning with the same step extraction method; Filtered Data GRPO trains standard GRPO only on filtered questions Q without any structural modifications; and Dr. GR.R implements the fangth-normaiiee GRPO variant proposed by Liu al. (025a) free-form reasoning.
The second category evaluates combined approaches to understand synergistic effects: Tags + GRPO combines structured reasoning with standard GRPO; Tags + LCS combines structured reasoning with LCS reward (our proposed method); Tags + MaxFlow combines structured reasoning with MaxFlow reward (our proposed method); and Tags Step-Level MaxFlow extends Tags MaxFlow
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Table 15: Complete ablation study showing performance improvements (percentage points) over DS- DS-Distill-Qwen-77 baseline across different maximum response lengths. Bold indicates best performance in each column.
Method
1K
2K
4K
8K
Average
DS-Distill-Qwen-7B (Baseline)
0.00
0.00
0.00
0.00
0.00
Isolated Component Training
+ Structured Tags
+4.14
+4.64
+0.65
+0.36
+2.45
+ LCS (free-form)
+6.23
+4.00
+1.00
+0.89
+3.03
+ MaxFlow (free-form)
+3.39
+1.25
-0.64
-1.09
+0.73
+ Filtered Data GRPO
+0.28
+0.11
+0.06
-0.38
+0.02
+ Dr.GRPO
+4.22
+4.97
+1.31
+1.37
+2.97
Combined Component Training
Tags + GRPO
+5.18
+6.25
+2.35
+0,28
+3.52
Tags + LCS (Ours)
+10.79
+10.23
+3.38
-0,40
+6.00
Tags + MaxFlow (Ours)
+8.45
+8.17
+5.83
+3.12
+6.39
Tags + Step-Level MaxFlow (Ours)
+7.10
+8.13
+3.14
+1.68
+5.01
by applying step-level reward weighting, where each reasoning step receives importance weights normalized from MaxFlow scores (Appendix(D) D).
All experiments use identical base models (Qwen-7B), training data, and hyperparameters. We evaluate across four maximum response length settings (IK, 2K, 4K, 8K tokens) on 9 benchmark datasets, reporting average performance improvements over the baseline OS-Distill-Qwen- model.
B.2 COMPLETE ABLATION RESULTS
presents comprehensive results across all ablation experiments. Among isolated components, structured tags alone provide +2.45% average improvement. The LCS reward free-form reasoning achieves +3. 0.030%% average gain, showing modest effectiveness when applied to unstructured outputs. However, MaxFlow on free-form reasoning yields only +0.73% average improvement and shows negative performance at longer contexts (-0.64% at 4K, -1.09% at 8K), indicating that graph-based reward computation requires accurate step boundaries that free-form reasoning cannot reliably provide. The DR.GR baseline achieves +2.97% average improvement, providing a strong comparison point for addressing GRPO's length bias.
Table 15
The combined approaches demonstrate that components work better together. Tags GRPO achieves +3.52% average, improving upon isolated structured tags (+2.45%) by an additional +1.07%. Our Tags + LCS method achieves +6.00% average improvement, performing best at shorter contexts (+10.7995 79% at IK, + +10.33% at 2K). Our Tags + MaxFlow method achieves the highest overall performance at +6.39% average, with strongest gains longer contexts (+5.83% 4K, +3.12% 8K). The step-level weighting variant (Tags + Level MaxFlow) achieves +5,01 % average, suggesting that assigning rewards individual steps adds complexity without improving overall effectiveness.
B.3 INCREMENTAL CONTRIBUTION ANALYSIS
To quantify the synergistic effects between structured reasoning and rewards, Table decomposee the performance gains showing the incremental contribution of each reward method when added on top of the Structured Tags baseline.
The incremental analysis reveals that MaxFlow provides the largest additional gain (+3.95% average) when combined with structured reasoning, substantially outperforming its free-form variant which contributed only +0.73%. Similarly, LCS contributes +3.55% incremental gain on structured reason- ing compared to +3.03% free-form reasoning. This demonstrates that structured reasoning tags enable more effective reward shaping by providing accurate step boundaries for graph construction and sequence alignment.
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Table 16: Incremental performance gains when adding reward methods Structured Tags baseline
(+2. 4.5% average). Values show additional improvement beyond structured reasoning alone.
Added Component
1K
2K
4K
8K
Avg
Structured Tags (base)
+4.14
+4.64
+0.65
+0.36
+2.45
GRPO
+1.04
+1.61
+1.70
-0.08
+1.07
+ LCS
+6.65
+5.59
+2.73
-0.76
+3.55
+ MaxFlow
+4.31
+3.53
+5.18
+2.76
+3,95
+ Step- MaxFlow
+2.96
+3.49
+2.49
+1.32
+2.56
B.4 TRAINING-FRIE FREE STRUCTURED REASONING GUIDANCE
To evaluate whether structured reasoning guidance benefits small models without additional training, we conducted experiments across three model sizes (1.5B, 7B, 14B) at different context lengths.
Table 17: Performance Comparison with and without Training Free Guidance across Different Model Sizes. AI: AIME, AMC: AMC'23, LSAT: LSAT-AR, M500: MATH500, Min.: Minerva, Oly.: OlyBench, Avg: Average.
With Guidamce
Without Guidance
Tokens
A1'44
A1255
AMC
LSAT
M500
Min.
MMLL
Oly.
Arg
A1244
AI'25
AMC
LSAT
M100
Min.
MMLLU
Oly.
Arg
1.50 Afodels
IK
0.00
0.00
15.85
19.71
25.33
11.52
43.91
5.79
16.01
1.11
1.11
15.83
24.89
27.20
12.01
44.05
8.10
16.74
2K
3.33
3.56
31
21.59
$2.00
20.83
$7.05
18.62
25.08
3.35
1.11
36.67
21.45
52.35
20.96
46.72
19.95
25.32
4K
13.33
13.33
19.17
22.
71.73
26,
47.72
33.43
34.77
14.44
3,89
4T.50
25.07
71.73
29.41
47.51
33.5%
34.77
8K
23.33
22.22
68.33
26.35
$1.40
30.64
47.83
43.60
42.97
23.33
18.33
66.25
26.26
80.33
31,00
$2.60
44.49
42.57
Monters
IK
0.00
3.33
13.35
22.75
$4.93
16.67
59.95
10.86
20.23
5.56
4.64
16.67
21.74
35.00
19.00
59.20
11:01
21.58
2K
7.76
14.44
37.50
31.16
64.93
31.25
64.60)
28.79
35.06
15.55
13.33
38.33
31.09
65.33
32.60
63.44
25.39
36.30
4K
22.22
22.22
63.33
40.87
50.00
37.00
65.82
47.46
47.42
35.55
3M.59
62.50
37.61
81.20
39.46
64.55
45.08
50.89
8K
36.67
31.11
80.83
48.55
59.73
38.11
65.99
55.57
56.20
41.11
42.22
83.50
52.32
91.33
80.69
65.97
59 59.26
29.55
148 Modelt
4K
33.33
26.44
65 85
57.10
$4.40
42.3 28
82.78
48.99
$4.89
26.07
23.33
62.50
55.23
83.00
39.71
83.87
47.41
52.71
8K
$1.17
34.44
X2.67
72.63
92.10
43.35
83.02
61.85
65.36
50.00
36.67
82.50
72.17
91.60
43.38
$4.85
62.81
65.50
Table 17 reveals that vrining-frree structured reasoning guidance shows limited and inconsistent benefits. For the 1.5B model, structured guidance provides minimal average improvement: +0.40% 8K tokens. For the 7B model, observe negative impact. Only the 14B model shows consistent gains: +2.18% at 4K and -0.34% at 8K. Small models lack instruction-fol follooion--oooiingggg. capabilities to utilize structured formats during inference.
C COMPARATIVE ANALYSIS: LCS VS MAXFLOW
Both LCS and MaxFlow demonstrate strong performance when combined with structured reasoning, but exhibit distinct characteristics: LCS excels at shorter contexts (IK-2K) while MaxFlow performs better at longer contexts (4K-8K). Table shows their performance converges at 3K tokens.
Table 18: Performance comparison at 3K tokens (1.5B model) showing convergence point.
Benchmark
LCS
MaxFlow
A
AIME'24
11.33
11.67
+0.34
AIME'25
16.33
16.67
+0.34
AMC'23
61.50
61.25
-0.25
DROP
38.35
39.51
+1.16
LSAT-AR
25.65
26.30
+0.65
MATH500
71.10
73.20
+2.10
Minerva
26.15
27.02
+0.87
MMLU-ALL
44.62
44.84
+0.22
OlympiadBench
37.20
38.44
+1.24
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To understand why LCS favors shorter contexts while MaxFlow excels at longer ones, analyze response distribution patterns and reasoning metrics in Tables 19 and 20
Table 19: Response distribution across token ranges. Numbers shown as Correct/Error. LCS
concentrates correct answers in shorter ranges while MaxFlow shows balanced distribution.
Token Range
1.5B LCS 1.5B MaxFlow
7B LCS
7B MaxFlow
0-1K
232214
243/5
206/1
IK-2K
93/8
158/6
113/7
133/2
2K-3K
27/7
46/8
39/3
52/2
3K-4K
12/6
22/6
21/5
28/3
4K-5K
14/6
19/3
13/3
23/1
5K-6K
13/5
4/3
12/2
6K-7K
7/4
10/5
6/5
8/0
7K-8K
9/7
11/5
5/3
7/1
> (Truncated)
0/35
0/31
0/22
0/19
Total
409/91
428/72
444/56
469/31
Table 20: Reasoning metrics comparison. LCS produces shorter steps with higher path consistency, while MaxFlow maintains flexibility with longer steps.
Metric
1,5B LCS 1.5B MaxFlow
7B LCS
7B MaxFlow
Avg. Tokens per Step
120.1
235.6
123.1
219.5
Path Similarity (SequenceMatcher)
0.434
0.410
0.452
0.423
Path Similarity (Levenshtein)
0.323
0.290
0.336
0.297
Path Similarity (LCS Ratio)
0.410
0.390
0.427
0.403
LCS operates through cross-path comparison, rewarding paths with higher common subsequence proportions. This drives the model toward shorter, more consistent reasoning steps 120 tokens/step vs 220 for MaxFlow) and concentrates correct answers in the 0-2K range (243 vs 206 for 7B). Higher path consistency (0.452 0.423 SequenceMatcher) indicates more uniform reasoning patterns, explaining superior short-context performance.
MaxFlow computes flow individual reasoning graphs, rewarding streamlined reasoning without penalizing response length. This produces more balanced answer distribution across token ranges and fewer truncated responses (19 22 for 7B), resulting in better robustness at longer contexts.
D SEEE-LEVEL REWARD IMPLEMENTATION
For Tags Step-Level MaxFlow, explored modulating token-level advantages using step-level importance weights derived from MaxFlow scores:
lo:
1
Jsup-cRrr (0)
E
min(r wis Ad, clip(r.. -,, wiy A.) - 3DL
G
0
1=1
(13)
where Wi, is computed by normalizing step-level MaxFlow rewards to [0.5, 1.5]:
RMaaloo min, R max, R2 min, Hy
0.5
token belongs to step &
(14)
1.0
otherwise (tags, answer)
This approach achieves +5.01 % average improvement, lower than sequence-level MaxFlow (+6.39%) Fine-graing step-level credit assignment introduces complexity in determining appropriate weight scales, handling special tokens, and balancing contributions across reasoning stages. How to precisely control per-step rewards remains open research question.
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Table 21: MaxFlow Computation Time and Two-Stage Optimization Speedups. Tests conducted on dense directed graphs with varying node counts. Stage (Dinic) provides x.39x average speedup, while Stage 2 (residual reuse) adds x.38x incremental improvement.
Nodes
Tokens
Baseline (NetworkX, s)
Optimized (Dinie, s)
Final (+Residual,
Speedup (Stage 1)
Speedup (Stage
Total Speedup
x 256)
5
1,280
0.00046
0.00006
0.00004
7.96x
1.35
10.76x
10
2,560
0.00087
0.00028
0.00019
3.14x
1.44x
4.53
20
5,120
0.01766
0.00158
0,00112
11.16x
1.41
15.76x
30
7,680
0.03044
0.02284
0.01639
1.33x
1.39x
1.86x
40
10,240
0.07580
0,00817
0.00613
9.28x
1.33x
12.36
50
12,800
0. 12053
0.03061
0.02299
3.94x
1.33x
5.24x
100
25,600
0.60409
0.15618
0.11848
3,87x
1.32x
5.10x
200
51,200
3.74300
0.89507
0,62537
4.18x
1.43x
5,99
300
76,800
10.86789
2.09656
1,50382
5.18x
1.39x
7.23x
400
102,400
20.02902
4,40266
3.12438
4.55x
1,41x
6.41% x
500
128,000
32.97774
6.96468
4.96045
4.73x
1.40x
6.22
E
IMPLEMENTATION DETAILS
E.I STRUCTURED DATA COLLECTION
Our structured reasoning data collected through a four-stage pipeline. We first collect 2,000 correct free-form reasoning paths from DeepSeek-RI on the SIK dataset. A Free Tag Chain Extraction prompt converts these raw reasoning traces into abstract step labels, yielding 23 semantically distinct tags after removing duplicates and low-frequency labels. We then combine the SIK dataset with extracted tags using a Fill-in-the-Miche Middle API (Appendix 1. to generate structured reasoning outputs, answering each question 8 times with randomized tag orderings. Finally, filter based on tag coverage diversity and question difficulty, retaining 500 samples with richest tag usage and lowest correctness rates (but with least one correct solution) the final training set Q.
E.2 GRAPH CONSTRUCTION
To construct reasoning graphs from attention patterns, we aggregate token-level attention into step- wise attention matrices for each layer using the causal masking formula Equation (3) of the main paper. Based on experiments in Section 4.3 we select layers 23-27 which focus on global reasoning patterns and compute their mean obtain the final step-wise attention matrix A. We designate position (0,0) source (Question step) and position (-1,-1) sink (Answer step), with edge weights Wij = Aij. Edges below threshold 0.05 are pruned to zero while maintaining connectivity to improve computational efficiency.
F MAXFLOW COMPLEXITY OPTIMIZATION
F.1 OPTIMIZATION PIPELINE
Stage 1: Optimized Dinic Algorithm We implement an efficient Dinic algorithm with level graph construction via BFS and blocking flow computation via DFS. Unlike generic max-flow solvers, our implementation exploits the structure of causal DAGs by maintaining residual capacities.
Stage Residual Network Reuse After computing the original max-flow, we reuse cached residual capacities from the original computation, only updating edges incident the removed node
Algorithm D presents the optimized Dinic implementation, and Algorithm shows the complete critical node detection pipeline with residual network reuse.
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Published as a conference paper at ICLR 2026
Algorithm 1 Optimized Dinic Algorithm for Max-Flow Computation
Require: Graph G (V; E) with capacities E R+ source 8, sink /
Ensure: Maximum flow value fmax
Initialize residual graph G,- f- with r(u, v) c(u, v) for all (u, v) E
2: fmax +- 0
3: while (F, 8, finds augmenting path do
4: Construct level graph L via BFS from
5: level[s] <
6: for each vertex in BFS order do level[e] + levelfuj + where u is predecessor end for
7:
8:
9:
while DFS(s, oo; L) finds blocking flow do
10:
Find augmenting path P from f using DFS
11:
8 + (a.))) ruu, v) [Bottleneck capacity)
12:
for each edge (u, u) E do
r(u, v) + r(u v)
(Update residual capacity)
14: r(v, u) t r( u) + (Update reverse edge)
15: end for
16:
fmax + fmax + end while
18: end while
return fmax
Algorithm Critical Node Detection with Residual Network Reuse
Require: Graph G = EV, source s, sink t
Ensure: Set of critical nodes C and their contributions A.
1: fang <- DINIC(G,&, 8, (Stage I: Compute original max-flow]
2: C+ 0, A
(}
3: V' + V. {s [Candidate nodes]
4: for each node V" do
5: |Stage 2: Fast connectivity check)
6: if CBCSNSCCONECC s, then
7:
A. + forig [Node disconnects from t) (U))
8:
9: continue
10:
end if
11:
(Stage 2: Residual network reuse)
12:
Construct G' by removing v: E' + {(u, w) E E u v t}
13:
Initialize residual graph G", from cached residual capacities
14:
fnew + DINIC s, (Incremental max-flow]
A, + Sori fnew [Flow contribution)
16:
if A. > e then
10-9 numerical threshold) CU {v}
17:18
end if
end for
20: return C, A
F.2 EMPIRICAL VALIDATION AND COMPLEXITY ANALYSIS
We conducted scaling tests from = 5 to 500 nodes (corresponding to 128K token context with average 256 tokens per reasoning step). Table 21 demonstrates the effectiveness of both optimization stages, achieving 7.41 x total speedup over the NetworkX baseline.
Our implementation achieves empirical complexity between O(n log (R²=0.9976) and ( (R==0.9995). We therefore report the overall complexity O D(BHrr ( + O(n..5) where the first term (attention computation) dominates for practical reasoning chain lengths (n < 500).
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Reviews:
[{"review_id": "ObidBrHmxm", "reviewer": "Reviewer_PG2M", "summary": "This paper studies structured reasoning for LLMs by (1) explicitly labeling reasoning steps with semantic tags, (2) extracting step-wise dependencies from attention weights, and (3) introducing two reinforcement learning rewards: a Max-Flow reasoning reward that encourages balanced step utility and a longest-common-subsequence (LCS)-based consistency reward. The method aims to inject structure into chain-of-thought processes and improve reasoning efficiency. Experiments on math and reasoning benchmarks show improvements over supervised and GRPO baselines, alongside qualitative analyses of attention structure.", "questions": "1. Table 1 max-length execution. How is the “max length” constraint applied in Table 1? hard decoding cap? truncation after generation?\n2. Does attention truly correspond to reasoning structure?\n3. The Max-Flow reward implicitly assumes that “better reasoning” corresponds to more balanced (not overly concentrated) attention flow across intermediate steps. Can the authors clarify the motivation for this assumption?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper addresses an important problem: encouraging more structured and efficient reasoning in LLMs rather than unconstrained chain-of-thought generation.\n2. The proposed Max-Flow reward is a creative attempt to use internal model signals (attention structures) to shape reasoning behavior, moving beyond pure outcome-based rewards.\n3. Experiments are conducted on multiple reasoning benchmarks and across different model sizes, showing consistent improvements under constrained output budgets.", "weaknesses": "1. The approach heavily relies on attention maps reflecting causal reasoning order. This link is assumed rather than validated. No experiments demonstrate whether attention graphs truly correspond to semantic dependency structures, raising validity concerns.\n2. Key components (structured tags, Max-Flow reward, LCS reward) are not fully isolated. It remains unclear which part contributes most. A more refined ablation (e.g., Max-Flow only vs LCS only vs tags only) would strengthen the causal claims.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "DQlbzaCK4a", "reviewer": "Reviewer_sQTy", "summary": "This work targets the limitations of LLM on complex reasoning tasks such as logical deduction and planning, with a focus on efficiency and explaninability.\nIt aims to enhance the reasoning capabilities of LLM at the step-level by introducing the structured reasoning approach, viewing the reasoning process as a directed graph.\nThe proposed framework first extracts the unstructured data into a structured format by incorporating the explicit reasoning steps, which enable adaptive fine-tuning of LLM afterward.\nThe authors also propose a layer-wise dependency tracing procedure using step-to-step attention matrices for in-depth analysis.\nThe fine-tuning part, they also extend GRPO with two structure-aware algorithms- Max-Flow and Longest Common Subsequence.\n\nThe empirical experiments showcase the improved efficacy, efficiency as well as the stability.", "questions": "1. Can smaller LLMs also benefit from the training-free structured reasoning?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. This paper is well-motivated, and the proposed techniques are rational.\n2. The paper is well-written and easy to follow.\n3. The experiments are comprehensive, covering efficacy, efficiency, and stability.", "weaknesses": "1. As extensions of GRPO, the two proposed variants do not always demonstrate clear advantages over GRPO. For example, in some cases, MaxFlow outperforms GRPO while LCS achieves similar performance; in other cases, LCS performs better, whereas MaxFlow's results are comparable to GRPO.\nHowever, there is no discussion explaining these observations or directly comparing LCS and MaxFlow.\n\n2. The stability and efficiency study only considers the MaxFlow variant while the LCS variant is ignored.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "NN0UUhiM1T", "reviewer": "Reviewer_UN8i", "summary": "The authors propose an approach for reasoning using large language models (LLMs), introducing a framework called structured reasoning to improve efficiency through the pre-computation of the extracted common reasoning patterns. They apply this method to enhance the GRPO. The authors conduct experimental study to verify the proposed solution for insights.", "questions": "see the questions in the weaknesses section.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "This paper presents a Structured Reasoning approach that improves the efficiency, stability, and interpretability of reasoning, experimentally verified using models such as DeepSeek-R1-Distill-Qwen. The authors demonstrate that their method enhances performance even at shorter input lengths and maintains consistent quality across varied temperature settings. \n\nA key contribution from the work is the automatic extraction of common reasoning patterns, allowing unstructured reasoning to be restructured into coherent chains via a specially designed dataset. Furthermore, the introduction of an attention-based layer-wise analysis provides detailed step-to-step attention maps, underscoring the importance of middle layers in effectively integrating reasoning context. \n\nThe authors implement two algorithms, MAX-Flow and LCS. The former creates sparse reasoning graphs to evaluate the impact of each reasoning step, and the latter identifies optimal subsequences from multiple outputs to improve reasoning quality. \n\nOverall, the proposed methods offer promising advancements in structured reasoning frameworks.", "weaknesses": "The proposed three-stage pipeline for enhancing LLMs with Structured Reasoning presents an interesting and potentially valuable design that integrates multiple design choices and algorithmic components. However, this layered structure makes it challenging to clearly identify and understand the contribution and impact of each individual stage. The paper does not sufficiently analyze or disentangle these effects. Furthermore, the performance and behavior of each stage appear to depend on a number of implementation details that are not fully specified, which makes the overall approach somewhat difficult to evaluate and replicate. For example, the granularity of the labels to consider in the first step, and the edge weight definition in Step 3. \n\nHere are a few more detailed feedback:\n\nIn Equation 1, the notation F() in the condition is not explained in the text, unless I’ve overlooked something. It seems to be a filter, but it needs to be clearly defined.\n\nIt’s great to have the complexity estimate in Section 3.3. The authors should provide some insights into whether the scale of the complexity is reasonable or not\n\nIn Equation 5, the score design heavily relies on the correct completion, which is somewhat vague in the description. As a key concept or operation, the authors should elaborate on it.\n\nIn Table 1, the performance of LCS appears stronger than MaxFlow in most cases. If this aligns with expectations, the authors should explain the rationale.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "lIPz8bifNH", "reviewer": "Reviewer_7R1m", "summary": "The paper presents a new reasoning approach, aimed at structuring the reasoning traces of LLMs.  They convert unstructured reasoning traces by prompting a teacher LLM to output a linear sequence of abstract steps (labels). After some filtering, the teacher is prompted to generate reasoning for i) a given q and ii) a set of sampled labels from the label collection. \n\nThe resulting collection is the dataset used for training the model. The latter predicts answer / reasoning from question and a \"structured reasoning prompt\". A graph across reasoning steps is built, where they compute the \"step-to-step\" attention scores to measure the  strength of an edge, \n\nThey leverage the max flow of a given node / step to assess its performance (the bigger it is, the more important to reaching the final solution). The flow analogy is used to measure the \"robustness\" of the solution; a higher score if the spread of importance is high, i.e. no single or few crucial nodes, but rather many pathways to the solution. \n\nThe authors evaluate on math and reasoning benchmarks. The authors show gains overall, especially when capping the response length. The authors also show that performance of the overall system is more stable to temperature variations than the baselines. Finally, the authors also demonstrate that their approach for measuring the importance of a reasoning step is the better approach when filtering out reasoning steps w.r.t. performance", "questions": "1. Is a step reward given specifically to the step ? or do all step receive the same sequence level reward ?", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1. Overall an interesting approach for structuring reasoning traces. \n2. The authors' experiment protocol is quite rigorous, from the base set of results to the explainability tasks. \n3. Overall good performance on the benchmarks.", "weaknesses": "0. The paper is very dense, from the abstract to figure 2, and even section 3.1. The overall flow of the paper could be improved, where more explanations / motivations for the equations would be appreciated, and fewer results presented. For example, what is F in equation 1 ? \n\n1. The approach is quite cumbersome; from structuring / labelling reasoning traces to the 3 pronged loss function. \n\n2. The paper is missing several ablations to correctly access the importance of the proposed components. Likewise, simply training on the filtered data without any additional loss terms (i.e. standard GRPO) would be very informative. \n\n3. A comparison to Dr. GRPO [1] would be a nice addition to the paper, as they propose a simple, proper fix to the length issue in GRPO. \n\n\n[1] Understanding R1-Zero-Like Training: A Critical Perspective, Liu et al., COLM 2025.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)