The CoT Encyclopedia: Analyzing, Predicting, and Controlling how a Reasoning Model will Think
Authors: Seongyun Lee
Seungone Kim
Minju Seo
Yongrae Jo
Dongyoung Go
Hyeonbin Hwang
Jinho Park
Xiang Yue
Sean Welleck
Graham Neubig
Moontae Lee
Minjoon Seo
Venue: ICLR 2026 Poster (2026)
Keywords: Reasoning in Language Models
Chain-of-Thought Interpretability
Model Behavior Control
Primary area: applications to computer vision, audio, language, and other modalities
TL;DR: We propose the CoT Encyclopedia, a bottom-up framework for analyzing, predicting, and controlling reasoning strategies in language models, revealing the impact of training data format and enabling performance gains via optimal strategy steering.

Abstract: Long chain-of-thought (CoT) is an essential ingredient in effective usage of modern large language models, but our understanding of the reasoning strategies underlying these capabilities remains limited. While some prior works have attempted to categorize CoTs using predefined strategy types, such approaches are constrained by human intuition and fail to capture the full diversity of model behaviors. In this work, we introduce the CoT Encyclopedia, a bottom-up framework for analyzing and steering model reasoning. Our method automatically extracts diverse reasoning criteria from model-generated CoTs, embeds them into a semantic space, clusters them into representative categories, and derives contrastive rubrics to interpret reasoning behavior. Human evaluations show that this framework produces more interpretable and comprehensive analyses than existing methods. Moreover, we show that this understanding translates into measurable improvements on both problem-solving and safety benchmarks. We can predict which strategy a model is likely to use and guide it toward more effective alternatives. Finally, we show that training data format (e.g., free-form vs. multiple-choice) impacts reasoning far more than data domain, highlighting the importance of format-aware model design. In short, the CoT Encyclopedia turns reasoning from a black box into a controllable asset, enabling LLMs that think more clearly, perform more reliably, and act more safely.

Published as a conference paper at ICLR 2026
THE COT ENCYCLOPEDIA: ANALYZING, PREDICTING, AND CONTROLLING HOW A REASONING MODEL WILL THINK
Seongyun Leetä*
Seungone Kim
Minju Sco
Yongrae Jo
Dongyoung Go
Hyeonbin Hwang!
Jinho Park
Xiang Yue?
Sean 2elleck2
Graham Neubig²
Moontae 3.e
Minjoon Seo!
KAIST AI
Carnegie Mellon University?
LG Al Research
Coreell University*
University of Illinois Chicago"
(seongyun, minjoon) wwaist.ac..tc........ee.......
seungone@cmu.ede
ABSTRACT
Long chain-of-thought (CoT) is an essential ingredient in effective usage of modern large language models, but our understanding of the reasoning strategies underly- ing these capabilities remains limited. While some prior works have attempted to categorize CoTs using predefined strategy types, such approaches are constrained by human intuition and fail to capture the full diversity of model behaviors. In this work, we introduce the CoT ENCYCLOPEDIA, a bottom-up framework for analyzing and steering model reasoning. Our method automatically extracts diverse reasoning criteria from model-generated CoT's, emheds them into a semantic space, clusters them into representative categories, and derives contrastive rubrics inter- pret reasoning behavior. Human evaluations show that this framework produces more interpretable and comprehensive analyses than existing methods. Moreover, we show that this understanding translates into measurable improvements on both problem-solvee and safety benchmarks. We can predict which strategy a model is likely to use and guide it toward more effective alternatives. Finally. we show that training data format (e.g., free-form vs. multiple-choice) impacts reasoning far more than data domain, highlighting the importance of format-aware model design. In short, the CoT ENCYCLOPEDI turns reasoning from a black box into a controllable asset, enabling LLMs that think more clearly, perform more reliably, and act more safely.
INTRODUCTION
Chain-of-thoughe (CoT) prompting (Wei et al. 2022) is an effective inference-time method for elicit- ing reasoning in large language models (LLMs) by generating intermediate reasoning steps before producing a final answer. While CoT reasoning has led to impressive performance gains -sspecillly
when extended to long chains involving multiple reasoning strategies (Guo et al.) (2025] Jaech et al.)
2024 Muennighoff et al. 2025 Yeo et al. 2025)- -our)-our our understanding of the specific strategies that models tend to employ remains limited. Key questions remain underexplored: What varieties of reasoning strategies do models use? How do these strategies differ across models and tasks? Can they be systematically controlled to improve performance? Recent work on CoT monitoring (Korbak al. 2025) underscores the importance of addressing these questions, showing that the transparency of intermediate reasoning steps is not only valuable for performance analysis but also critical opportunity for ensuring safety.
'Equal contribution. Scongyun conducted this work during an internship LG AT Research.

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Published as a conference paper at ICLR 2026
Prior efforts to analyze long CoT reasoning have primarily followed top-down approach (Wen et al. 2025; Gandhi et al.; 2025 Guo et al. 2025). where researchers define a fixed set of strategy types such as backtracking or subgoal setting -addnng-nndda use language models to detect their presence in generated outputs. While interpretable, such approaches constrain analysis to known categories. Recent clustering-based methods (An et al. [0233] Xu et al., [024 Fang al. 2025) focus mainly on short/medium CoTs, leaving longer multi-strategy traces underexplored. For a direct comparison
between our bottom-up clustering framework and existing top-down approaches, see Figure T
In this paper, we introduce the COT ENCYCLOPEDIA, a framework to systematically analyze and control long CoT's that involve multiple, intertwined reasoning strategies. We do so through a bottom-up, clustering- strategies at scale. Rather than relying on predefined categories, our approach begins by prompting a LMs to produce free-form explanations of the reasoning strategies used in its own responses. These explanations are embedded and clustered to identify semantically similar reasoning patterns. For each resulting cluster, we generate contrastive rubrics (e.g., Inductive vs. Deductive, Directive vs. Non-Directive) through a second round of prompting, enabling precise characterization of reasoning dimensions. Finally, we classify new CoT responses by identifying which strategy from each rubric best aligns with the response. Human evaluation confirms the quality of our pipeline: annotators give high Likert ratings (4.2-4.4) across criteria, and in pairwise comparisons the CoT ENCYCLOPEDIA is preferred over the predefined analyzer with a 86% win+tie rate.
framework designed to capture, interpret, and steer diverse reasoning
Beyond interpretability, the COT ENCYCLOPEDIA offers three practical benefits. First, it can improve a reasoning model's s performance by guiding it to adopt more effective strategies. We predict likely reasoning strategies using COT ENCYCLOPEDIA, estimates their effectiveness, and guides the model to follow the most promising one. Across five benchmarks, we observe performance improvements of 12.2-16.11 1 % in diverse reasoning models. Second, we demonstrate how the CoT ENCYCLOPEDIA can reveal novel insights about model reasoning abilities, specifically performing controlled experiments on how training data format fundamentally shapes reasoning strategies, and enables behavior control through model merging. Our analysis shows that the domain of the training data (e.g., math vs. commonsense) has little effect on reasoning patterns. In contrast, the pormat-multiple-chooe (MC) versus free-form (FF)-has much larger effect. For instance, MC-trained models tend to produce structured, concise responses that resemble breadth- first reasoning, while FF-trained models favor longer, sequential chains with frequent verification, akin to depth- first reasoning. Finally, by linearly interpolating weights between MC- and transition in strategy, demonstrating controllability without fine-tuning. These findings highlight the COT ENCY CLOPEDIAA not only as a diagnostic tool, but also as a practical foundation for shaping reasoning behaviors to suit spek-sp needs.
models, we generate models that smoothly
2 RELATED WORK: ANALYZING REASONING STRATEGIES OF MODELS
Recent work has made significant progress in understanding LLM reasoning. Think patterns (Wen et al.) 2025) reveal recurring structures linked to accurate outcomes, while cognitive behavior
analysis (Gandhi al. 2025 draws connections to human psychology. Guo et al. (2225) examine
"aha moments" of sudden insight during multi-step reasoning, and Marjanović et al. 2025 introduce
structured <think> mechanism to enhance reasoning. Strategic example selection improves
in-context learning (Didolkar et al. 2024), and targeted data generation addresses specific reasoning
failures (Zeng al. 2025). Chen et al. (2024) propose a reasoning boundary framework to quantify and optimize the capacity of CoT reasoning in LLMs, focusing on systematic analysis and broad improvements. Complementary to this, our work emphasizes fine-graine ine-grained, data-driven decomposition that enables the identification and control of diverse, interpretable thinking patterns. In parallel, Zhou ct al. (2025) introduce a visualization tool for inspecting reasoning paths and diagnosing failures, providing valuable qualitative insights without direct mechanisms for behavioral control. Korbak et al. (2025) analyze the necessity and fragility of CoT monitoring, highlighting its potential as a safety mechanism but also its vulnerability to training choices and architectural shifts. Our work differs by moving from the question of whether CoTs can be monitored to providing methods for decomposing and controlling reasoning patterns.
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Conventional Approach
CoT Encyclopedia (Bottom-up)
Is self-verification strategy used in the response solving this math problem?
What strategles are used in this response and what strategies should LM use to get it correct?
Analysis data accumulated from other problems
Classifier
The self-verification strategy is used times this response, appears when the phrase "Wail"
The response employs self-verification
Exploring multiple approaches instead of repeatedly verifying calculations could improve accuracy by 4%
strategy based on [..] and also takes top- down approach [...]
Rigid Analysis
Flexible Analysis
Guidelines to improve LM
Limited to predefined criteria
Can automatically identify criteria tailored problem Recommends reasoning strategies based past success/ failure data from similar problems
Analysis doesn't provide practical guidelines for model improvement
Figure 1: Comparison between conventional reasoning analysis and the CoT Encyclopedia. Traditional methods use fixed criteria to identify strategies but offer limited guidance for improving reasoning. The COT ENCYCLOPEDIA takes bottom-up approach, uncovering diverse, task-specific
strategies and enabling flexible analysis and actionable insights to enhance model performance.
3. Criteria Compression via
1. Classification Criteria Identification
2. Classification Criteria Embedding
Hierarchical Clustering
criteria (s ee
Top-down
Analytool
Ansiytical
Perspcttive
Development: Multiple Single
Hds Deadeppert
Developmant
Reasoning Type:
Inductive Deductive
Rassoning Type
Type
Vertication Focus: hypothasi- -driven Data-drtven.
Verfication Focua
PC41
Varification Focus
Rubric
Analysis Report Generation
Use
Avalyced
Dettomwup: Chaary Bettornupp invedurndy
ressoming pattern appreach...
top-
Q Ressonhng patter
enalyai
X Optimal rassoning pattern centrol
Deaslopment
responae demonatrates multipla thinking ways
Type
Reasoning Type
Appreach Geveratintes sbility
te fint coneppaaaee entore
The given nerponae demonatrates strong deductive reasoning
Type
Werification Focus
Verification is driven by data rather than hypatheeas...
Genbri
Type C
Aolve problam.
UUs Pattirn
Figure 2: Overview of the CoT ENCYCLOPEDIA. The framework builds a reasoning taxonomy in five stages: (1) identifying criteria from CoTs, (2) embedding them, (3) clustering semantically similar ones, (4) generating contrastive rubrics, and (5) classifying responses to produce interpretable reports.
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THE COT ENCYCLOPEDIA
3.1
A FRAMEWORK FOR TAXONOMIZING REASONING STRATEGIES
LMs utilizing LongCoT enable test-time scaling, effectively addressing complex reasoning problems across diverse domains. Nevertheless, our understanding remains limited regarding the variety of reasoning strategies these models employ, how these patterns vary across tasks and models, and how such differences impact downstream performance. Prior work (Gandhi et al., 2025) offered valuable insights by defining four reasoning Sehaviors--errficattie and backward chaining but such predefined categories struggle to capture the full diversity of emerging or model-specific strategies. To address this gap, introduce CoT ENCYCLOPEDIA, five-stage framework for identifying, organizing, and analyzing diverse reasoning strategies in CoT outputs. Unlike prior top-down approaches, CoT ENCYCLOPEDIA derives reasoning dimensions in
backtracking, subgoal setting,

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bottom-uu up. data-driven manner using large language models. As shown in Figure 2 the framework systematically extracts classification criteria, compresses them via semantic clustering, and generates human-intee intnan-itterrettblle reports model reasoning behaviors.
Step 1: Classification Criteria Identification. Given a dataset of CoT outputs D = {(z,, Vc) H=r
where æt is the natural-language problem prompt and ys is its -LM-generated chain of thought, we extract a set of classification criteria C = {c1.... ... CN via LLM-assisted brainstorming. Unlike Gandhi et al. (2025), which predefines only four cognitive behaviors and thus may miss emerging method discovers flexible, data-driven criteria that align closely with the full diversity model outputs. Each criterion is defined with a pair of contrastive reasoning strategies (sf) s)), expressed as natural language sentences. For example:
reasoning patterns,
"Inductive Reasoning"
Cj = Reasoning Strategy Type
"Deductive Reasoning"
Step Classification Criteria Embedding. Each triplet (cj. string by concatenation and embedded using embedding model:
....s..... . is converted a single input
e (c,, ,/ (9 ERd
This results in a matrix E E Nxxd
Step 3: Criteria Compression via Clustering. To reduce redundancy, we apply hierarchical agglomerative clustering (Müllner 2011) to using cosine distance. We obtain & clusters N):
g (G, Gk],
G. C.
Each cluster Ge is represented by its medoid criterion oz (not the centroid, to preserve interpretability). yielding the compressed set C* (ct,..., ct). This set used in all subsequent analysis steps.
Step 4: Rubric Generation. For each criterion cf. we use LLM to generate a rubric R. = (sz", /)), with detailed descriptions of both strategies and guidance for binary classification. For example:
R₂ ("Clearly bottom-up approach ...", "Clearly top-down approach
Step 5: Pattern Analysis Report Generation. Each response y is classified under each rubric via prompting LLM with yes/no question:
{
if LLM predicts alignment with s if LLM predicts alignment with s
2i,8
This produces binary matrix Z E {0, 1]nxk; where each row summarizes the reasoning pattern of CoT response. We then synthesize natural language report using LLM, which selects and composes rubric-specific templates to describe the reasoning pattern of each response. For example:
"The response shows a bottom-up reasoning style, combining data-driven verification...
In summary, COT ENCYCLOPEDIA supports interpretable and reproducible reasoning analysis by mapping raw CoT outputs to structured strategy profiles. To support the validity of each component of our framework, we also conduct ablation studies for every step in Appendix B.5
3.2 COT ENCYCLOPEDIA ENABLES SHARPER REASONING STRATEGY CLASSIFICATION
To evaluate the effectiveness the COT ENCYCLOPEDIA' 's classification criteria, we analyze re- sponses from DeepSeek- L--issttll-QQuee -weiill--we--32222 (2 et al. 2025), B.1-32B
et al.) 2025 (ema et al. al. 2023). Using COT ENCYCLOPEDIA, extract 4,057
and QwQ-32BB Team 2025) on GPQA-DiQn Diamond et al. 2024). MMLU-Redux
2024), and 50TH-500 contrasting reasoning criteria, each representing a pair of opposing strategies. We embed these using embedding model and apply hierarchical clustering to group semantically similar criteria. The
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Analytical Perspective, Scope of Approach, Rea- soning Type, Idea Development, Verification Focus, and Clarification Approach- whose definitions summarized in Table [ Each model response is labeled as Pattern A or B under each criterion, Paltern B
resulting taxonomy defines six major
and we compute the proportion of Pattern B as Pattern A+ B to compare trends across models. As a baseline, we also assess the presence of four predefined cognitive behaviors--erificatiio backtracking, subgoal setting, and backward chaining -iithn the same responses (Gandhi et al. 2025). For both sets, we apply chi-squared tests for statistical significance and compute Cohen's 's for effect sizes.
As shown Table 8 distributions of cogni- tive behaviors differ minimally across models (p > 0.05, id] x 0.1), suggesting limited sen- sitivity. contrast, the COT ENCYCLOPEDIA criteria reveal more substantial differences (Ta- ble 14p, with many significant p-values and ef- fect sizes reaching up to 0.4. This indicates our bottom-up method better captures fine-grained reasoning differences and generalizes across tasks and models. We conduct a human evalua- tion to validate alignment with human judgment. From model outputs, we sample 250 responses and distribute them evenly across 10 annotators. For each response, annotators provide 1-5 Lik- ert ratings on four dimensions: (1) plausibility of fine-grained criteria, (2) coherence of high-level grouping, (3) quality of pre-defined analyzer generated report, and (4) quality of CoT ENCY- CLOPEDIA generated analysis report. As shown in Figure 3] annotators find the lnn-grained cri- teria extracted in Step I to be highly plausible and the grouped criteria from Steps 2 and to be coherent. The final analysis reports generated by our framework also receive higher appropri- ateness ratings than those from the predefined analyzer baseline. In both the Likert-scale and preference evaluations, annotators are blinded to system identity, ensuring unbiased judgments. The preference results, reported as win-tie-lose rates, show clear favorability toward the CoT ENCYCLOPEDIA. Overall, our method yields plausible and well-structured reasoning criteria and analysis reports that align more closely with human expecta- tions. Implementation details are provided in Appendix A and qualitative analyses are presented in Appendix F.I
Human Evaluation Results
Average Appropriateness Ratings
CoT Encyclopedia Report Quality
4.3
Predefined Analyzer Report Quality
2.9
High-level Grouping
Coherence
4.4
Detalled Criteria
Plausibility
Strongly Inappropriate
Mean Score
Highly Appropriate
Preference Encyclopedia
62.0%
24.
34.0%
20
40
60
80
100
Pre-defined Analyzer
Figure 3: Human Evaluation Results for CoT Encyclopedia. Annotators judge the outputs of the CoT Encyclopedia as appropriate and show a clear preference for them over the predefined analyzer baseline.
3.3
COT ENCYCLOPEDI, ENABLES ADAPTIVE ANALYSIS ACROSS DIVERSE TASKS
In addition to the three benchmarks evaluating model helpfulness introduced in Subsection 3.2 we analyze reasoning strategies in model responses for XSTest (Röttger al.) 2023) and WildGuard (Han et al. 2024) that assess harmlessness and Arena-Hard (Li et al.) 2024) that measures instruction following capability using COT ENCYCLOPEDIA, As shown in Figure 14 different classification criteria emerge across benchmarks. Notably, instruction following benchmarks introduce a new "User Understanding' criterion due the need to accurately interpret user intent. Safety benchmarks feature ethical elements absent in problem-solving benchmarks, such as 'Safety Precedence (preventive vs. risk risk-engaging)". and 'Content Handling (censorship vs. open discussion)'. CoT ENCYCLOPEDIA'S ability to dynamically generate the most appropriate classification criteria across different benchmarks and models further demonstrates its utility.
ENHANCING MODEL HELPFULNESS AND SAFETY VIA OPTIMAL REASONING CONTROL
Building on the findings of the previous section, an important question arises: Can we identify optimal reasoning strategies that positively impact both model helpfulness and harmlessness?
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Impact of Pattern- Based Instructions
guard
95.5
Accuracy (50
15..3
72.0
74.0 72-2
78.2
75.6
12-
65.5 60.4
63.4
instructed
Instructed (unoptimal)
Instructed (random)
Instructed (optimal- dataaee)
Instructed (optimal- -usetaallqusstin)
Figure 4: Impact of Pattern-Based Instructions on Model Performance. Results show that optimal patterns improve performance across all benchmarks, especially for GPQA-Diamond and safety tests. Question-specific patterns consistently outperform the single best dataset-wide pattern.
If effectively steer models toward these patterns to enhance their overall performance across different types of benchmarks?
4.1 EXPLORING OPTIMAL REASONING STRATEGIES FOR HELPFULNESS AND HARMLESSNESS
To analyze how reasoning strategies affect model helpfulness and harmlessness, we evaluate model responses on Diiamoddd MMLU- --Reuux, and MATH-500 for helpfulness, and on XSTest and WildGuard for harmlessness. We compute P(Correct Pattern) and P(Safe Pattern) for contrasting reasoning patterns across six helpfulness and seven harmlessness criteria. These values are averaged over three models to identify patterns associated with higher accuracy and safety. Importantly, instead relying on ground-truth answers, we adopt an LLM-as-a-judge setting to assess correctness and safety, thereby preventing data leakage. As shown in Figures D and I0] certain reasoning strategies consistently lead to better performance. This enables a clear distinction between optimal and suboptimal reasoning patterns. Using this insight, assess how performance changes when models are explicitly instructed to follow desired strategies. To isolate the effect of strategy control, focus on responses that were initially incorrect unsafe. We compare four settings: (1) no instruction, (2) instruction with unoptimal patterns, (3) instruction with randomly selected patterns, and (4) instruction with optimal patterns (optimal-dataset)
Figure shows that guiding models with optimal strategies improves both accuracy and safety across all benchmarks. For example, GPQA-Diamont accuracy increases from 61.5% 70.1% while XSTest and WildGuard safety scores improve from 82.3% to 94.0% and from 79. 1 1% to 89.9%, respectively. For analysis focused solely on newly corrected responses, see Figure 11 Overall, these findings confirm that optimal reasoning strategies exist and can be leveraged to enhance downstream performance. Further breakdowns on safety benehmarks (Figure [2] reveal that patterns encouraging "malicious" intent or prioritizing 'technical" over 'moral' reasoning sharply reduce safety, indicating jailbreaking behavior. This underscores the need for more nuanced safety evaluations. While current approaches often rely on binary labels (safe vs. unsafe), results highlight the value of fine-grained analyses, such as those enabled by the COT ENCYCLOPEDIA, for improving content moderation and response quality.
4.2 SIMILAR INPUTS, SIMILAR THOUGHHTS: How MODELS APPROACH RELATED PROBLEMS
We have shown that each dataset typically has generally optimal reasoning strategy, indicating opportunities to enhance model performance. However, even within a single dataset, different questions may require distinct optimal reasoning strategies. A natural question arises: can we predict the optimal reasoning strategy for each individual question? To explore this, we analyze the relationship between questions and their optimal reasoning strategies. Specifically, we perform regression analysis using similarities measured in the embedding space between questions and between their corresponding optimal reasoning strategies. Our analysis utilizes correct responses generated by three models across five benchmarks, previously discussed in Section 4.1 Figure 5 illustrates that higher similarity between questions corresponds to greater similarity between their reasoning strategies, suggesting that models adopt similar strategies for similar problems. Conversely, lower question similarity is associated with higher variance in reasoning strategies, indicating that models employ diverse strategies for dissimilar problems. These findings suggest the potential to

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predict effective reasoning strategies for unseen questions based on the strategies used in similar, previously encountered questions.
Question and Pattern Similarity Analysis
(e) Question Pattern Similarity
(b) Verience Anelysis by Similerity
Vertence Pettern Pattern Simileity
p-sete 70o-201
vinar 0.00282)
0/0050
8,0000
2.20
0130175
0..5
0.50
89200
Patturn
00000
2.70
s000
00005
8000
07
Question- Question Similarity
Question- -Question Similarity
Figure Analysis relationships between question similarity and reasoning strategy similarity across multiple benchmarks. Relationship between question similarity and reasoning strategy similarity. (a) Scatter plot showing positive correlation between question similarity and pattern similarity. (b) Variance analysis showing that pattern similarity becomes consistent question similarity increases.
4.3 PREDICTING QUESTION-SPECIFF OPTIMAL REASONING STRATEGIES
Building on prior insights, we explore whether optimal reasoning strategies can be predicted and used to guide models toward more helpful and harmless behavior. We train binary classifiers for each criterion using three problem-solving benchmarks and two safety benchmarks. For training, questions initially answered correctly to derive optimal strategies, while questions initially answered incorrectly are used for testing. We consider two settings: in-domain (trained and tested on the same benchmark) and cross-domain (trained classifier predicts optimal strategies for the incorrect samples, which are then used to prompt the model, as described in Section 4.1 As shown Figure 4 this controlled prompting substantially improves cerformance-accivvinng accuracy gains of 72.0%, 81.3%, and 87.7% on cooblem-solving tasks, and safety gains of 95.5% and 92.4% on safety tasks. These results show that models can be effectively guided toward optimal strategies, even unseen questions. Unlike conventional approaches that generate long reasoning traces without direction, our method identifies and corrects reasoning weaknesses through targeted control, offering a key advantage of the CoT ENCYCLOPEDIA. For additional extended analyses and experiments, please refer to Appendix
benchmarks and tested third). Each
5 ANALYZING PATHWAYS TO REASONING STRATEGIES: DATA SELECTION AND INTERPOLATION
We have primarily analyzed reasoning strategies based on responses from trained models. This raises important question: why do models produce specific types of reasoning strategies after training is completed? this section, we investigate this question by directly RI. training reasoning models on datasets with different formats and domains, then analyzing the emerging reasoning strategies.
5.1 FORMAT MATTERS MORE THAN DOMAIN IN SHAPING REASONING STRATEGIES
To examine how training data characteristics influence reasoning strategies, we compare the effects of data format and domain using Reinforcement Learning with Verifiable Rewards (RLVR). For format analysis, we compare (1) multiple-choice inputs, where questions are paired with predefined options, and (2) free-form inputs, where models generate answers without guidance. Using the NuminaMath dataset (LI et al. 2024), originally in free-form, we synthetically generate multiple-chol versions to control for content while isolating presentation format. For domain analysis, contrast math-domain datasets (c.g.. NuminaMath) with knowledge-domain datasets such as OpenBookQA, QASC, SciQ. Commonsense@A,, and
(Mihaylov al. 2018 Khot al. 2020 Welbl et al. 2017
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Format vs Domain Difference Comparison
GPQA-Diamond
MMLU-Redux
MATH-500
Effect Size ([d))
1.00
15
0.4
0.75
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AP
SA
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D
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CA
Format (MC vs FF)
AP: Analytical Perspective
SA: Scope of Approach
Domain (Math Knowledge)
RT. Reasoning Type
ID: Idea Development
VF: Verification Focus
CA: Clarification Approach
Figure 6: Comparison of effect sizes showing how question format and domain influence reasoning strategies across three benchmarks. Format differences (purple bars) consistently demonstrate substantially larger effects on reasoning strategies than domain differences (green bars) across all six reasoning criteria.
Multiple-choice format (MC)
Free-form (FF) trained
Ratio multiple ways pattern output
Average complete length
(number of takens)
step. First
down step
but it's not working But parhaps Wait, the passing any hoaders authentication parameters. Wait, in the code
Ratio muttiple ways
complete Lengrth
2561
consider the possibility By following steps,
1301
MC
FF
MC
FF
Analysis Report
Analysis Report
Occurrences of 'wit' in outputs
It provides a structured...
The response largely verbase. It does not provide clear explanation Instead, it seems to get lost repetitive narrative.
Total count
8.76
Average count
troubleshooting approach, The response is helpful and and providing actionable steps to resolve the
MC
FF
Figure 7: Qualitative and quantitative comparison between models trained on Multiple-choice (MC) and Free-form (FF) data formats. MC-trained models generate more structured and concise responses, while FF-trained models are more verbose and repetitive.
Talmor et al. 2019: Clark et al.) 2018). To ensure fair comparison, we control for format by using consistent structures across domains. We train 7B Deepseck- - RI-Distill models. This setup allows us to isolate the individual effects of format and domain while holding other variables constant. To quantify their relative influence, we apply the statistical tests from Section 3] computing Cohen's 's values between reasoning strategy distributions. As shown in Figure format variation consistently leads to larger shifts in reasoning strategies than domain differences, indicating that format has greater impact than domain shaping model reasoning.
5.2 IMPACT OF TRAINING DATA FORMAT ON MODEL REASONING BEHAAIIR
We analyze model responses trained on Multiple-choice (MC) and Free-form (FF) data using the Arena-Hard benchmark. As shown in Figure 7 the two models display distinct reasoning styles: MC-trained models produce concise, structured answers, while FF-trained models are more verbose and often repeat filler words like 'wait." Table F2 further reveals that MC-trained models explore
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Model Merging ng: Interpolation of Reasoning Pattems
GPQA Diamond
MMLU-Reddu
Pattom
Paitern Raiio
40
20
Pamarn MC
20%
50%
80%
FF
20%
50%
80%
FF
MC
20%
50%6
80%
FF
AP: Top-Down vs Bottom-Up
RT. Inductive vs Deductive
VF: Drvvn vs Hypothesis-
SA: Focused vs Broad Exploration
ID: Sequential vs Parallel
CA: Iterative vs Immediats
Figure 8: Interpolation of reasoning strategies through model merging. Reasoning strategy dynamics as models are merged from Multiple-Choice (MC) to Free-Forrm (FF) training formats across three benchmarks.
multiple solution paths early mn-iimilar to treadth-first search whereas FF-trained models follow a single path with iterative verification, resembling depth-first search. These differences arise from the presence absence of answer cues during training: MC data encourages evaluating options before responding, while FF data requires open-ended exploration, often with greater uncertainty and verification. Quantitatively, FF-trained models generate more verbose responses and over 4.6 times as many 'wait' tokens per answer (8. 76 vs. 1.89). Rather than favoring one format, our findings underscore that training format significantly shapes reasoning behavior, and should be selected based on task-specific needs.
5.3 INTERPOLATING DESIRED REASONING STRATEGIES THROUGH MODEL MERGING
Given that models trained on different formats exhibit distinct reasoning strategies, we test whether intermediate patterns emerge via linear interpolation between multiple-choice and free-form models. As shown in Figure reasoning strategies shift smoothly with the merging ratio, though the dynamics vary by benchmark: GPQA-
changes moderately, Redux shows crossover points around 50%, and MATH-500 displays the sharpest transitions (e.g.. the Bottom-Up perspective drops sensitive
from 85% to 15%) These variations highlight that reasoning criteria format changes than others, reflecting benchmark-spede demands. Overall, weight interpolation enables controlled blending of reasoning strategies without extra training, offering simple yet effective way to tailor models for task-specific needs.
6 EXTENDED ANALYSES AND ABLATIONS IN APPENDIX
Due to space constraints, we present additional experiments, analyses, and ablation studies in the Appendix and provide explicit references for the reader's convenience. Criteria are shaped more by tasks than models, producing benchmark-speche embedding choices (B.2). Models from the same family show consistent strategies across sizes (B.3). and the framework generalizes to other models (B.4). Ablations validate the contribution of each step the COT ENCYCI.OPEDIA, with additional analyses showing robustness to embedding models and human evaluation confirming rubric and report quality (B.5). Further tests show robustness across random seeds (B.6), across diverse model families and scales (B.7), and demonstrate applications for curating improved reasoning datasets (B.8). Finally, while direct prompting is less effective for small models, combining it with dataset curation yields clear gains (B.9).
dimensions (B.1), and remain stable under different
7 CONCLUSION
We introduced the CoT ENCYCLOPEDIA, a flexible, automated framework for analyzing reasoning strategies in LongCoT language models. Unlike rigid, predefined taxonomies, bottom-up cluster- ing approach identifies reasoning strategies directly from model outputs, creating a comprehensive taxonomy validated through human evaluation. Our empirical results revealed four key insights:

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(1) optimal reasoning strategies significantly enhance task performance on both helpfulness and safety benchmarks; (2) these patterns can be predicted from input questions alone, enabling real-time adaptive reasoning control; (3) training data format influences reasoning strategies than domain; and (4) desired reasoning behaviors can be interpolated through model weight merging without additional training. The COT ENCYCLOPEDIA advances understanding of reasoning models and provides practical tools for steering them toward safer, more effective strategies. By identifying which reasoning strategies yield optimal performance for specific problems and what training data cultivates these patterns, this work supports responsible deployment of language models in applications where performance, safety, and predictability are paramount.
substantially
BROADER IMPACT
This work has several broader implications for the development and deployment of large language models. First, our analysis highlights the importance of reasoning controllability-tte ability to steer a model's problem-solving strategy. This capability may play critical role in building more interpretable, debuggable, and safety-aligned systems, especially in high-stakes applications such as education, healthcare, and scientific discovery. Second, our taxonomy can inform curriculum design for training reasoning-oriented models, enabling researchers curate data that promotes specific cognitive patterns. Moreover, the ability to predict and guide reasoning behavior opens up opportunities for interactive systems that provide explanations or tutoring based user input and model inference strategies. Finally, the emphasis on format as a driver of reasoning diversity suggests that future benchmark and dataset development efforts should consider structural diversity-not just domain coverage-as a factor for improving generalization and reasoning robustness.
LIMITATIONS
While our findings are promising, several limitations warrant discussion. First, our reasoning strategy classification relies on GPT-4o outputs as an evaluator, which may reflect biases or constraints of the model itself. Although this choice enables scalability, it may not fully represent human judgment of reasoning quality. Second, our experimental setup is limited to three benchmarks and three model families. While these cover diverse reasoning domains, extending our analysis to broader range of tasks (e.g., scientific reasoning, code generation, multi-modal tasks) and models (e.g., smaller or multilingual LMs) is essential for confirming the generality of our conclusions. Third, while we observe consistent performance improvements through pattern- guidedd prompting, such improvements contingent upon model's ability to reliably follow stylistic instructions. This requirement may limit applicability to instruction-tume -unnd or higher-capacity models.
ACKNOWLEDGEMENT
This work was partly supported by Institute of Information & communications Technology Plan- ning & Evaluation (ITTP) grant funded by the Korea government (MSIT) (No. R0---009---1190075 Artificial Intelligence Graduate School Program (KAIST), 10%; No.RS-2021-1 2221-11222006,, Artificial Intelligence Innovation Hub, 10%; RS-2024-00398815 15, Research the reliability and coherence of outcomes produced by Generative AI, 20%; No.2022-0-001 13, Developing a Sustainable Collab- orative Multi-modal Lifelong Learning Framework, 20%; No.RS-2022 0022-11220264, Comprehensive Video Understanding and Generation with Knowledge-basee Deep Logic Neural Network, 20%; RSS-0024-00397666, Development of Cybersecurity Specialized RAG-based sLL.M Model for Suppressing Gen-Al Malfunctions and Construction of a Publicly Demonstration Platform) and the InnoCORE program of the Ministry of Science and ICT(510250156)
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URL https: /ttps: org/ http//as..//...../ 25.3 22165
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A IMPLEMENTATION DETAILS
A.1 COT ENCYCLOPEDIA DETAILS
We use the OpenAI 4PT-4 to conduct reasoning strategy Identification. And we also use OpenAI text-embeddi 3--3-1a age to embed the criteria. In this study, we create reasoning strategies using the test sets from GGQA-Diamone COT ENCYCLOPPEDIA is not limited to specific data and can be applied to any dataset. The reasoning strategy Identification process yields 4,057 fine-grained analysis criteria. To automatically select the essential criteria from these redundant ones, we employ agglomerative hierarchical clustering. In this process, we do not specify a distance threshold for cluster merging but instead form an appropriate number of k clusters based silhouette scores. In our study, six clusters emerge. We establish the criteria corresponding to the embedding at the medoid of these clusters as the key high-level criteria. Next, evaluate responses using these criteria, belong to contrasting patterns A and B, using the OpenAI GPT-4o API. Finally, we conclude by creating CoT pattern report that evaluates the CoT patterns present in the responses based on the generated rubrics.
MMM.U-Redux, and MATH-500 datasets. However, the
develop rubries determine which responses
A.2 STATISTICAL TEST DETAILS
We conduct statistical tests to measure the similarity between two reasoning strategy distributions. We perform Chi-squared tests, where the null hypothesis (Ho) states that there is no difference between the two distributions, and we set the p-value at the conventional threshold of 0.05. This means that if the p-value is lower than 0.05, we reject H, and accept the alternative hypothesis (Ha), concluding that there is a statistically significant difference between the two distributions. Conversely, if the p-value is greater than 0.05, we fail to reject Ho. indicating that there is no statistical difference between the two distributions. We employ Chi-squared tests rather than other statistical tests because the pattern classification is categorical. Additionally, to measure the similarity between the two distributions more quantitatively, we calculate Cohen's d value, where an absolute value of approximately 0.2 is generally considered a small effect size, approximately 0.5 medium effect size, and 0.8 or greater large effect size.
A.3 HUMAN EVALUATION DETAILS
To verify whether the COT ENCYCLOPEDIA framework is perceived as reasonable by people, we conduct a human evaluation. This evaluation is particularly necessary because CoT ENCYCLOPEDIA utilizes synthetic outputs generated by an LLM at each step. requiring validation of their reliability. We select four evaluators, and each assessment consists of four binary questions: (1) Are the automatically generated, detailed criteria plausible? (2) Do the resulting high-level criteria sensibly summarize the fine-grained set? (3) Is the response analysis, when expressed in the criteria, relevant and reasonable? (same question for both pre-defined analyzer and CoT Encyclopedia) We use Argilla") as our human evaluation platform. For the human evaluation, we collect 250 model responses and distribute them evenly among 10 annotators. Each annotator evaluates their assigned responses independently. Instead of binary yes/no judgments, annotators now provide 1-5 Likert-scale ratings.
The final Likert scores reported in the main text are calculated by averaging the ratings across annotators and items for each dimension. To facilitate interpretation, we also report the mean values alongside standard deviations. In addition, we run a pairwise preference study to compare analysis reports generated by the CoT Encyclopedia versus a predefined analyzer. For each item, annotators are asked to select the analysis they find more informative and appropriate, to mark a tie if both are equally convincing. We summarize these results using a proportion of items in which the CoT Encyclopedia is preferred, tied, or loses to the baseline. All annotation guidelines, examples, and quality-control instructions were shared with annotators prior to the study ensure consistency.
rate, which reflects the
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A.4 BENCHMARK EVALUATION DETAILS
We conduct evaluations using the MMLU-Redus knowledge benchmark, the GPQA-Diamond reasoning benchmark, and the MATH-500 mathematics benchmark. We employ the vllm library with hyperparameters following established research practices: temperature of 0.6, top P of 0.95, and max tokens of 32768. All evaluations are performed on the test sets of each dataset. MMIU- Redux and GPQA-Diamond are multiple-choice question answering datasets, while MATH-500 is an open-ended generation dataset. However, since our evaluation targets reasoning models that generate LongCoT, we implement generation-baset evaluation rather than logit- evaluation even for the multiple-choice datasets. To determine whether the model's 's predictions match the actual answers, we parse the predicted values from the generated LongCoT and use the Math- Verify library to verify their correctness. Ultimately, we measure accuracy between the correct answers and the predicted values. To measure safety, we utilize the I.LMMAGGuard33 8B model for evaluation. When provided with a question and model response, this model outputs either "safe' or 'unsafe' as its assessment. We then calculate the proportion of responses classified 'safe' and use this ratio as our metric.
Math-Verify
A.5 TRAINING DETAILS
We utilize the GRPO algorithm (Guo et al. Learning with Verifiable Reward (RLVR). he objective function of GRPO is defined as follows:
2025) during the training process with Reinforcement
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This form ensures positivity and avoids numerical instability. Unlike traditional KL penalties, this estimator is well-suited for leken-level comparisons in sequence modeling:
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We diverse datasets for training: NuminaMath, free-form math dataset, which also convert into a 5-choice question answering format by synthetically generating four options using GPT-4o API; and multiple-choice knowledge and common sense datasets including SciQ. QASC, OpenbookQA, CommonsenseQA, ARC-Challenge, and MCQA 68k datase To control for format variables, we train on Math in both free-form and multiple-choice formats within the same math domain. Conversely, to examine domain differences, we maintain consistent multiple-chote format while varying between mathematical content (NuminaMath converted to 5-choice format) and knowledge/common sense datasets. All training datasets contain 100k examples.
We standardize on multiple-choice format when studying domain differences because our RL approach uses verifiable rewards. Unlike math or coding domains where predictions can be directly compared to gold answers, knowledge and common sense domains often allow for varied but equally correct responses that don't it exactly match the gold standard. Inspired by previous research, we adopt multiple-choice format as it ensures verifiability across all domains- any response matching the
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correct option can be definitively scored as correct. This approach enables us apply verifiable rewards even to domains that are traditionally difficult to evaluate deterministically.
When training the 7B model with the GRPO algorithm, utilize the Open-R1 -een-R1 library | For the reward function, we exclusively implement an accuracy reward function that assigns a reward of 1 when the model's prediction matches the gold answer and 0 otherwise. We decide not to the format reward function employed in training Deepseek-RI because it can lead to a form of reward haereng-where the model receives rewards for following the correct format even when producing incorrect answers, resulting in maintained formatting without improved accuracy. To prioritize correctness, we therefore rely solely on the accuracy reward function. For hyperparameters, we set max completion length at 2048, number of generations at 3, batch size at 72, torch dtype at bfloatl6, and attention implementation flash attention We use a learning rate of 2.0e05, number of train epochs of 1, and warmup ratio of 0.1.
A.6 COMPUTING RESOURCES
For RLVR training of our 7B model, we use eight NVIDIA H100 80GB GPUs, requiring 576 GPU hours to train on 100,000 data samples. For inference, employ sixteen NVIDIA A100 40GB GPUs, consuming 384 GPU hours to process 3,698 data samples. Additionally, we use an AMD) EPYC 7763 64-Core Processor for the CPU, which features 64 cores, CPU speed of 1497.674 MHz, and a cache size of 512KB.
B FURTHER ANALYSES AND ABLATIONS
B. FINE-GRAINED SENCIMMRK-SSPECIN CRITERIA ANALYSIS
To conduct a more detailed analysis, performed hierarchical clustering the complete responses from GIQA-Diimont MMLU-Redux, and MATH-500 benchmarks to establish six criteria. For a more fine-grained examination, we conducted hierarchical clustering separately for responses from each benchmark, using the default setting of selecting each cluster's ' medoid as the representative embedding. In addition to the three original benchmarks, we analyzed responses from the Arena-Hard Benchmark, which focuses on instruction following. As illustrated in Figure [4] we observed that while the criteria derived from the original three benchmarks were relatively similar to each other, the Arrda-Hard benchmark yielded notably different criteria. This finding confirms that different benchmarks employ varied standards for pattern analysis. Particularly noteworthy is the 'User understanding' criterion. While the original benchmarks primarily focus solving specific problems correctly, instruction following benchmarks emphasize accurately interpreting user intent. This emphasis is reflected in the classification criteria, highlighting the different evaluation priorities across benchmark types.
B.2 ABLATION STUDY ON REPRESENTATIVE EMBEDDING SELECTION
When extracting representative embeddings for each cluster formed through hierarchical clustering, we primarily use medoid embeddings representative embeddings. We explore how results differ when using alternative selection criteria. Beyond the default medoid setting, we test embeddings from patterns with the highest frequency, patterns from areas with the highest density, and patterns from areas with the highest silhouette scores. As shown in Figure [5 most selection criteria do not demonstrate significant differences compared to selecting the default medoid setting. In the default setting's 's' 'clarification approach,' the only differences appear between the silhouette- and density-based approaches, which use 'computation style' and 'clarity steps' respectively, while all other aspects remain identical.
B.3 CONSISTENCY OF REASONING STRATEGIES ACROSS MODEL SIZES WITHIN THE SAME FAMILY
Do models from the same family exhibit similar reasoning strategies despite having different sizes? To investigate this question, compare the reasoning strategies of three models from the same
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family but with different sizes: Distill-RI 1.5B, 7B, and 32B. We classify the responses generated by each model on the GPOA-Diamond, AMLU-Reddx and MATH-500 benchmarks according to six criteria. As shown in Figure T6 the three models demonstrate remarkably similar distributions of reasoning strategies despite their different sizes. Additionally, as illustrated in Figure 17 the pairwise Cohen's d measurements between the three models reveal that most absolute values are below 0.1, indicating very minor distributional differences. These findings confirm that models from the same family maintain largely consistent reasoning strategies regardless of their size.
Conditional Probabi ities Analys P(Correct Patter)
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Figure 9: Conditional Probabilities Analysis on problem-solving Benchmarks. The bars represent different reasoning strategies categorized by Analytical Perspective (blue), Scope of Approach (yellow), Reasoning Type (green), Idea Development (orange). Verification Focus (purple), and Clarification Approach (red). Patterns such 'broad', 'top_down down', and 'immediate' consistently show higher probabilities of correct responses across benchmarks.
Conditional
Probabilities Analysis: P[Safe Pattemn)
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Figure 10: Conditional Probabilities Analysis on Safety Benchmarks. The bars represent different reasoning strategies categorized by Guidance Strategy (blue), Ethical Consideration (yellow), Safety Precedence (green), Idea Development (orange), Content Handling (purple), Risk Assessment (red), and Content Intent (gray). Patterns such as 'Moral Evaluation', 'Benevolent', 'Preventive', and "on--Dreettive" consistently show higher probabilities of safe responses across both benchmarks.
B.4 EXTENDING REASONING STRATEGY ANALYSIS TO NON-REASONING MODELS
In this study, we extend our reasoning strategy analysis using the CoT ENCYCLOPEDIA beyond the primary reasoning models discussed in the main text (S1.1-32B, QwQ-32B, Distill-R1-33 R1-32B to include nea-rnnsgnig models such as Qwen-2.5 2,5-Insrruuutt-31 and Qwen-2.5-Math 1.nn-2.--aath-Instrre---33 Instruct-32B. We conduct this analysis across five henchmarks: GPOA-Diamond, MML.U-Redux, MATH-500,
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Impact
Instructions
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MMLU Redux
MATH 500
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Figure 11: Impact of pattern-based instructions on model performance across five benchmarks. For all benchmarks, instructing models follow question-specin optimal reasoning strategies yields the highest performance (17.5-68 77.5)...5% 5%), followed by dataset-wide optimal patterns (14.3-6.22%) random patterns (12.5-46.8%) ).)) while unoptimal patterns (1 11.5-3..8% sometimes perform worse than not providing instructions at all (10.1-46.7%) The impact is particularly pronounced for safety benchmarks (XSTest and Wild guard), where optimal instructions more than double the safe response ratio compared unoptimal instructions. These results demonstrate that tailoring reasoning strategies to individual questions outperforms even the best dataset-wide pattern, significantly improving both accuracy and safety outcomes.
XSTess Benchmank
WildGuard Bendhmark
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Figure 12: Fine-grained safety response ratio analysis across XSTest and WildGuard bench- marks. The bars represent the percentage of safe responses when different reasoning strategies are employed. 'Benevolent' reasoning achieves the highest safety scores (84.0% in XSTest, 81.0% in WildGuard), while 'Malicious' and 'Risk engaging' patterns show the lowest safety performance. Patterns like 'Preventive'. 'Moral', and 'Non-directive" also demonstrate relatively high safety re- sponse ratios across both benchmarks.
XSTest, and WildGuard. As shown in Table 17 and [8] the criteria generated for the non-reasoning models closely resemble those generated for the reasoning models. However, we observe clear distinctions between the criteria for problem-solving benchmarks and safety benchmarks, reflecting the specific characteristics of each benchmark-similar to what we observed with reasoning models. This suggests that the criteria are more significantly influenced by the target benchmark rather than by the model's ''s output. Additionally, through chi-squared tests and Cohen's d values, we confirm that the pattern distributions of Qwen-2.5- I.5-Instructt32B and Qwen-2.5-Mathh 2.5--Math-Instruct-- Instruct-32B differ significantly from each other. These findings demonstrate the versatility of the CoT EncYclOpEdIA as an analytical tool that be effectively applied to non-reasoning models well.
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Question-to-Pattern Prediction
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Figure 13: Performance comparison of different methods for predicting optimal reasoning strategies across five benchmarks. Trained classifiers (both in-domain and cross-domain) signifi- cantly outperform prompting-based methods across all benchmarks. In-domain classifiers achieve the highest performance (70.3-84.3%), followed closely by cross-domain classifiers (66.2-80.1 12),..%). while zero-shot and few-shot prompting perform only slightly above random chance (50%). The performance trend is consistent for both accuracy-basee benchmarks (GPQA-Diamond, MMLU- Redux, MATH-500) and safety-focused benchmarks (XSTest, WildGuard) where safe response ratio is measured.
B.5 ABLATION STUDIES FOR COT ENCYCLOPEDIA
To further support the effectiveness of our framework, we conducted a series of ablation studies to examine the feasibility and necessity of each step, well as the quality of intermediate outputs. These analyses demonstrate that each component the CoT ENCYCLOPEDIA is critical for ensuring robust and interpretable reasoning patterns.
Step 1: Diversity of Criteria Generation We first evaluated the diversity of classification criteria generated in Step On MMLU-Redus. after removing duplicates. 99.7% of the criteria were unique. The average pairwise ROUGE-L score between criteria was 0.23, which aligns with surpasses benchmarks for dataset diversity reported in prior works. This indicates that Step reliably produces a rich and varied of candidate criteria.
Steps & 3: Necessity and Effectiveness of Clustering Although Step yields diverse criteria, qualitative analysis revealed considerable semantic overlap, with many criteria sharing similar n-grams or meanings due the independent generation process of LLMs. For instance, on EPQA-Diamove only 43% of Step I criteria had fully unique bigrams. Using raw criteria would inflate computational cost and reduce interpretability by generating excessively long reports.
To test alternatives, we compared clustering based reduction to an LLM-based reduction method. When prompted to manually reduce criteria for D-ammodd the LLM frequently produced redundant criteria with an average ROUGE-L overlap of 0.33-0.37 across runs, compared to 0.23 for our clustering based method. Moreover, the LLM--bsed approach was highly sensitive to prompt design, incurred higher inference cost, and struggled with long-context inputs. These findings confirm that clustering is necessary to reduce redundancy and improve robustness.
Steps & Robustness to Embedding Models We further tested whether results depend on the choice of embedding model. In addition to OpenAl's weeett--meddinggeee
we experi- mented with e5 mi starl-l-- 1araa1172 -7-- iinstruct and Qwen3 3 Embedding 8B. All models produced high level, with differences largely limited to phrasing. For exam- instruct ruct generated dimensions such as "Macro-first vs Micro-first" or BB produced counterparts
highly similar sets of criteria ple, e5-misttze al - tel--inntttt nst
Innduction-Focuseed vs Deduction Foccuidddd while like Snverview-Orienter vs Detail-Qrientedd or Prattern-Geenrraliin vs Rule- Kule-Applying. This suggests that our clustering method is robust to the choice of embedding model.
Steps 4 & 5: Human Evaluation of Rubric and Pattern Reports Finally, we conducted human evaluation with five independent graduate students unfamiliar with our work. Evaluators assessed the usefulness of Step (rubric-based evaluation) and Step 5 (pattern analysis reports) along three
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Published as a conference paper at ICLR 2026
dimensions: (1) appropriateness of the rubric for evaluating model responses, (2) helpfulness of the report for understanding reasoning patterns, and (3) usefulness of the report for improving model responses. Ratings were given 1-5 scale (1 not useful, 5 very useful). The average scores were: Q1: 4.3, Q2: 4.1, Q3: 4.5. These results indicate that human evaluators found both the rubric and the pattern analysis report generated by CoTT Encyclopedia to be highly useful. Additionally, for Q2, we asked evaluators to rate report generated without the rubric. This baseline scored 3.4/5, confirming that the rubric-driven approach in Step provides a significant benefit.
Steps 5: Multi-Evaluator System for Bias Mitigation To address potential evaluator bias inherent in single-model evaluation, we implement a comprehensive multi-evaluator framework. We employ four state-of-the-art LLMs independent evaluators: GPT-4o, Claude-4-Sonnet, Gemini-2.55Par and Dwwe-2255772B-Instree cal rubrics, allowing to compute inter-evaluator reliability using Krippendorff's s a.
Each evaluator independently classifies reasoning patterns using identi-
Agreement Results: Across 1,500 reasoning responses, we achieve a = 0.73 for pattern classification, indicating substantial agreement beyond chance. Notably, systematic disagreements cluster around specific pattern boundaries (e.g.. "Top-down vs. Bottom-up" shows lower agreement at a = 0.68), revealing inherent anbiguity in certain reasoning distinctions that our framework now explicitly acknowledges. Bias Correction Mechanism: We detect systematic biases where Claude-3.5 shows 12% higher preference for "hypothesis-drie drivenn patterns compared to other evaluators. We imple- ment bias correction algorithm using inverse propensity weighting to adjust for evaluator-specific tendencies, improving overall classification accuracy by 8.3%.
Overall, these findings validate the effectiveness of all steps in delivering interpretable and actionable insights.
B.6 ROBUSTNESS ACROSS RANDOM SEEDS
To verify that our improvements runs with five different random seeds on all benchmarks. Table ] reports the mean accuracy and strategy
artifacts of random initialization, we conducted inference
standard deviation for each strategy. Across datasets, we observe that the optimal-questien consistently achieves the highest mean performance, while also maintaining stability across seeds. Other instruction settings yield moderate gains, but often with larger variance or even performance drops (e.g., on XSTest and WildGuard under unoptimal instructions). These results confirm that our findings are robust with respect to random seed selection, further strengthening the validity of the proposed framework.
B.7 ROBUSTNESS ACROSS MODELS AND SIZES
We further evaluated the effectiveness of our method across a diverse set of model families and parameter scales, including Deepseck-RI (671B), LLaMr---Maverick (400B), Gemma-3 (27B), and KIMI-K2 Instruct (IT). As shown in Table 2 prompting with the optimal reasoning pattern consistently improved performance over the baseline of using only the question. These gains hold across both MATH-500 and GPQA-Diamond, ranging from modest improvements in smaller models (e.g., +1.2 on Gemma-3 for MATH-500) to more substantial gains in larger models (e.g., +2.0 on KIMI-K2 Instruct for MATH-500). Together, these results highlight the generality of our approach, demonstrating that reasoning pattern control provides benefits regardless of model architecture or scale.
B.8 APPLICATION OF THE FRAMEWORK FOR CURATING IMPROVED REASONING DATASETS
We directly addressed this point by using our framework to curate an improved reasoning dataset. Specifically, we used our question-specific reasoning pattern classifier to prompt teacher models to generate responses that reflect the optimal reasoning pattern for each question. We then collected these responses to create a new dataset, CoT-Encyclopediaa we compared our dataset against OpentThin constructed following the recipe and prompts of ThinkPatterns-22 2 using OpenThouught questions, since the original ThinkPatterns dataset is not publicly available. Both datasets were used to train Distill-RI R1-QQen- 1.5B and evaluated on GPQA-Diamond and MATH500. As shown in Table across all benchmarks, models trained on CoT- CoT--Encyclopedia-11 10K consistently outperformed baseline. We attribute this to the fact that
To fairly evaluate its effectiveness,
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Published as a conference paper at ICLR 2026
Table I: Random-seed robust performance across five benchmarks. We report accuracy and standard deviation over five different random seeds. The optimal thinking pattern strategy consistently yields the highest performance.
GPQA Diamond
MMLU-Redux
MATH-50K
XSTest
WildGuard
Strategy
Mean
Std
Mean
Std
Mean
Std
Mean
Std
Mean
Std
Not instructed
72.9
1.4
90.3
1.1
78.3
1.1
91.3
1.1
89.2
1.2
Instructed (unoptimal)
75.1
0.4
89.1
0.8
78.5
1.5
87.2
1.6
86.1
1.4
Instructed (random)
77.8
0.3
90.4
1.4
79.5
0.7
91.4
1.3
90.8
0.7
Instructed aptimall-dtaasen
80.6
1.3
92.8
0.9
80.6
0.5
93.8
1.4
92.9
0.7
Instructed aopiiall-questinn)
82.4
1.2
93.7
0.7
81.5
0.5
96.2
1.2
95.7
0.8
Table 2: Performance across diverse model architectures and sizes MATH-500 and GPQA- Diamond, In all cases, prompting with the optimal reasoning pattern outperforms the baseline of using only the question.
MATH-500
GPQA-Diamond
Model
Only Question
Optimal Pattern
Only Question
Optimal Pattern
Deepseek-RI RI (671B)
92.3
94.1
85.0
86.9
LLaMA-4-Maverick (400B)
90.2
92.3
81.7
83.2
Gemma-3 (27B)
86.5
87.7
72.6
74.8
KIMI-K2 Instruct (IT)
95.7
97.7
87.2
88.8
ThinkPatterns-211 fixed set of predefined patterns for all questions, making it difficult match the optimal reasoning process for diverse queries. In contrast, our framework enables dynamic, question--specfii reasoning pattern selection, resulting better adaptability and performance.
B.9 PERFORMANCE OF REASONING PATTERN PROMPTING ON SMALLER MODELS
While reasoning pattern prompting yields consistent improvements larger, instruction-tume models (e.g., 32B+ LLMs, GPT-4o, Claude-Sone Sondee,,,ntt,,,,, its effect on smaller or base models is limited. As shown in Table direct prompting with reasoning patterns does not improve performance for a distilled 1.5B model (Deepseek-B) 1-Diisill--ween-1... -.55),, and can even slightly reduce accuracy compared the baseline.
To address this limitation, we adopted a data-centric approach inspired by ThinkPatterns-21k (Wen al.) 2025), constructing curated dataset of 10k optimal reasoning pattern responses (CoT- Encyclopedia-106 from ThonThought. After supervised fine-tuning (SFT) on this dataset, the small model demonstrated substantial gains, achieving improvements of +3.8 on MATH-500 and +5.5 on EPQA-Diamont These results suggest that data-centric strategies are essential for enabling smaller models to benefit. from reasoning pattern control.
C REPRODUCIBILITY STATEMENT
All results reported this study are reproducible using the code provided in the supplementary resources. Reported results are averaged over multiple inference runs to enhance reliability, and we additionally report standard deviations alongside the means to further strengthen reproducibility and irustworthiness. We also document all prompts, hyperparameters, models, and datasets used in the study in the Appendix, ensuring that the results can be reproduced at any time. Finally, the examples used in the qualitative analysis randomly selected; we plan to include additional examples in the camera-ready version if needed.
D LLM USAGE STATEMENT
No LLM assistance was used in writing this paper; LLMs were utilized exclusively for constructing framework.
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Published as a conference paper at ICLR 2026
Table 3: Performance on MATH-500 and GPQA-Diamond with different prompting strategies. Using
structured reasoning patterns consistently improves performance compared to no prompting.
MATH-500
GPQA-Diamond
Prompting Strategy
Accuracy
A vs. No Prompt
Accuracy
A vs. No Prompt
No Prompt
83.9
33.8
OpenThinkk TwinTThhhnnknnnnnk
85.2
+1.3
36.7
+2.9
CoT-Encyclopedia
87.7
+3.8
39.3
+5.5
Table 4: Performance of reasoning pattern prompting and supervised fine-tuning (SFT) small model (Deepeek-RR--Dittil--eeennl... Prompting alone shows little or no improvement, while SFT the CoT--Eccccopediia- 10k dataset yields significant gains.
MATH-500
GPQA-Diamond
Strategy
Score
A
Score
A
Only question
83.9
33.8
CoT-Encyclen CoT-Encyclope prompting
80.2
-3.7
32.9
-0.9
CoT-Encyclopedia SFT (10k)
87.7
+3.8
39.3
+5.5
Table 5: Summary of classification criteria and associated pattern definitions.
Criterion
Pattern A
Pattern
Analytical
Top-Down:
Begins with high-level principles and decomposes into substeps.
Bottom-Up:
Builds reasoning from specific evidence or examples toward a general conclusion.
Perspective
Broad Exploration: Considers
Focused: Restricts analysis to a narrow, targeted set of factors.
Scope of Approach
wide range of factors and
possibilities.
Inductive: Infers general rules
Deductive: Applies general rules to derive specific conclusions.
Reasoning Type
from observed instances.
Sequential: Develops ideas in a linear, step-by-step order.
Parallel: Explores multiple ideas or lines of reasoning simultaneously.
Idea Development
Data-Driven: Emphasizes empirical evidence and data
Hy Hypothesis-Drite Driven: Tests predefined hypotheses or assumptions.
Verification Focus
validation.
Clarification
Immediate Conclusion: Provides final answers with minimal revision steps.
Iterative Refinement: Gradually refines and revisits reasoning steps.
Approach
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Published as a conference paper at ICLR 2026
Table 6: Comparison of cognitive behavior (Gandhi et al., 2025) frequencies between Distill- R1-32B and s1.1-32B models across three benchmarks. Statistical analysis (p-values and Cohen's d) shows minimal differences between models, with only one significant difference, indicating limitations of conventional cognitive behavior classifications in distinguishing model reasoning strategies.
Ratio (Behavior Frequency / Total Respomes)
Benclmurk
they different!
p-value
Cohen's d
Distill-R1
s
27.3
Verification
0.66
-0.09
3388
33.3
Backtracking
No
1.00
0.02
GPQA Diamend
Subgoul Setting
31,3
313
No
1.00
0.00
73.7
72.2
Backward Chaining
Verification
26,3
24.7
0.16
0.04
Backtracking
38.6
33.1
le.05
MMMUURRedux
Subgaal Setting
27.0
No
0.75
0.01
Backward Chaining
68.9
68.7
No
0.87
4e.3
Verification
26.0
28.4
No
0.43
-0.05
36.2
90.4
Backtracking
No
0.06
0.12
MATH-500
Subgoal Sctting
27.0
28.8
0.57
0.04
Backward Chaining
67.6
Table 7: Comparison of cognitive behavior (Gandhi et al. 2025) frequencies between Distill-R1- 32B and QwQ-32B models across three benchmarks. Statistical analysis (p-values and Cohen's d) shows minimal differences between models, with only one significant difference, indicating limitations of conventional cognitive behavior classifications in distinguishing model reasoning strategies.
Ratio (Behavior Frequency Total Responses)
Benchmark
Behavior
Are they different?
p-value
Cohen's d
Distil-RI
QwQ
Verification
No
0.91
-0.01
33.8
32.3
Backtracking
No
0.75
0.03
GPQA-Diamend Diamond
34.3
32,3
Subgual Setting
No
0.67
0.04
73.7
74,2
Backward Chaining
No
Verification
26.3
25,3
No
0.38
0.02
38.6
32.2
Backtracking
MMLU-Reduu
27.0
26.7
Subgoal Setting
No
0.79
0.01
Backward Chaining
70.5
No
0.18
-0.03
27.6
Verification
No
0.57
-0.04
Backtrakking
36.2
35,2
No
0.74
0.02
MATH-500
Subgoal Setting
27.0
27.4
No
0.89
-0.01
Backward Chaining
67.6
68.9
No
0.68
-0.0
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Published as a conference paper at ICLR 2026
Table Comparison cognitive behavior (Gandhi et al., 2025) frequencies between QwQ-32B and s1.1-32B models across three benchmarks. Statistical analysis (p- (a-values and Cohen's 's d) shows minimal differences between models, with only one sigmificant difference, indicating limitations of conventional cognitive behavior classifications in distinguishing model reasoning strategies.
Ratio (Behavior Frequency / Total Responses)
Benchmark
Behavior
Are they different?
povalue
Cohen's d
QwQ
s1.1
27.8
29.8
Verification
No
0.66
-0.04
32.3
33.3
Backtracking
No
0.83
-002
GPQA Diamond
32.3
34.3
Subgual Setting
0.67
0.04
Backward Chaining
No
0.65
0.05
25.3
24.7
Verification
0.59
0.01
Backtracking
No
0.46
-0.02
MML.U-Redde
Subgual Setting
26.7
27.4
No
0.54
0002
Backward Chaining
70.5
68.7
No
0.13
0.04
Veritication
27.6
28.4
No
0.78
-0.02
35.2
30.4
Backtracking
0.11
0.10
MATH-500
27.4
28.8
Subgoal Sotting
No
0.62
-0.33
Backward Chaining
No
0.68
0.03
Table 9: Analysis of reasoning strategies between Distill-RI R1-3BB and s1.1-32B models using CoT ENCYCLOPEDIA'S 's six criteria across problem-solving benchmarks. Unlike traditional cognitive
behavior metrics, this approach reveals numerous statistically significant differences (marked as "Yes),, ) with substantial effect sizes (Cohen's up to 0.44), demonstrating CoT Encyclopedia's enhanced ability to distinguish between models' reasoning strategies and preferences.
Reasoning Behuvior
Pattern A
Pattern B +
Are they different?
Benehmark
Cohrn's
Criteria
Pattern
Pattern
Distil
Analytical Perspective
Top-Dome Down
Bottom Up
758
75,3
No
4.7e-2
-0.10
Soepe of Approsch
Focused
Bread
152
7.
Yes
2--2
0.26
GPQA- Diamond
Ressoning Type
Inductiie
Deductive
Yos
Men Development
Sequentaal
Paraliel
30,3
40.9
40.22
Verification Focus
Dam--rives
Hypothesi-DDivee
60.1
08
Yes
1.2
-0.18
Clardiiationn Approach
Ieeative
Immediate
10
Yes
2e-03
0.36
Analytical Perspective
Top-Down
Bottom-Up Up
32.7
33.1
No
0.76
0.01
Scepe of Approsch
Focused
Bread
Yos
0.32
MML.U- Redux
Ressoning Type
Incluctive
Dedlctive
89
2o-06
Idea Development
Sequential
Paraliel
20,4
35.5
Yes
4e-20
0.24
Vesification Focus
Dana-rrives
Hypothesi--Dive Drvves
84.5
Yes
1e-03
0.08
Clanticctiinn Appenach
Ieentivee
38.38
Analytical Perspective
Top-Down
Rottom-Up
of Approach
Focused
Broad
$5.6
37.4
Yes
lc
0.37
MATHH- 500
Reasoning Type
Inductive
Deductive
10.4
11.0
No
8.4e 2
0.02
Ideea Development
Sequential
Parallel
17.0
21.5
No
6e:2
0.12
Ventication Fecus
Dita-rrivs
Hypothesis Drves
Clartication Approac
lieattive
Immeddate
14.4
2.8
Yes
le Ie:10
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Published as a conference paper at ICLR 2026
Table 10: Analysis of reasoning strategies between DistilI-R1-32B and QwQ-32B models using COT ENCYCLOPEDIA'S 's six criteria across problem-solving benchmarks. Unlike traditional cog- nitive behavior metries, this approach reveals numerous statistically significant differences (marked as 'Yes'), with substantial effect sizes (Cohen's 's up to 0.44), demonstrating CoT Encyclopedia enhanced ability to distinguish between models' reasoning strategies and preferences.
Reasoning Behuvior
<- Pattern
Pattern B >>
Are they
Renehmark
Cohrn's
Criteria
Pattern
Pattern
Distill- R1
Qu(
different?
Analytical Passpective
Top-Down
Botton-Upp
75.
M1.2
No
0.27
-0.11
Seage of Approach
Focused
Heoad
152
Yes
8.5c-
0.34
21.7
GPQA- Diamond
Reasoning Type
Inductive
Deductive
2.0e-
Idea Develogment
Sequential
Purallel
30.3
43,2
Yes
6.8g 3
0.27
Verification Foeus
Dita-Driven
Hypethesi-Driven
60.1
70.9
Yos
2.6-2
40.23
Claritiationn Approsch
Berative
Immediate
76
Yes 9.76-
0.36
Analytical Perspactive
Top-Down
Botton-Ui
12.7
31.1
No
0.74
-0.01
Scepe of Approach
Focused
Braad
Yos
2.46-4
0.41
MMLU- Redux
Ressoning Type
Inductive
Dedactive
3.9
4.3
Yes
7.26-13
Iden Development
Sequential
Parilll
27.4
30/2
Yos
3.1
-0.25
Verification Foeus
Don--Drvven
Hypathesis-Divee
87.5
81.5
Yes
5.96-8
0.14
Clariiicttion Approsch
Rerative
Immediase
21.2
Anslytical Perspretive
Top-Down
Botton-Up
36,8
No
0.07
-0.12
Socpe Approach
Focused
Renad
15.6
33,2
Yes
0.46
MATH- 500
Reasoning Type
Inductive
Deductive
10.4
13.2
No
0.17
-0.00
Idea Development
Sequential
Panilel
15.0
2244
Yes
3.2e-2
-0.14
Ventication Foeus
Data-Driven
Hypnthesis- Driven
6.4e-3
Clarifictioon Approach
Isorative
Immediase
14.4
4.3
Yes 6.0g
0.25
Table 11: Analysis of reasoning strategies between QwQ-32B and s1.1-32B models using CoT ENCYCLOPEDIA'S six criteria across problem-solving benchmarks. Unlike traditional cognitive behavior metries, this approach reveals numerous statistically significant differences (marked as "Yes'), ) with substantial effect sizes (Cohen's d up to 0.35), demonstrating CoT Encyclopedia's enhanced ability to distinguish between models' reasoning strategies and preferences.
Reasoning Behavior
Pattern
Pattern B
Are they different?
Beuchmark
p-ralue
Cohen's d
Criteria
Pattern
QwQ
Analytical Penspective
Bonom
78.3
No
0.02
Scope of Apgroach
Focused
Broad
311
No
0.40
0.08
GPQA- Diamond
Reasoning Type
Inductive
Deductive
No
0.38
0.09
Ides Develepment
Sequenial
Parallei
43.2
0.06
Verifietionn Focus
Data-Driven
Hypothess Deiven
70.9
65,2
No
0.59
0.06
Cheifiiation Approsch
Derative
Immosiate
10
No
0.41
0.00
Amlltical Penpactive
Top-Down
Bottom-Uip
33.1
33,1
No
1.00
0.00
Scupe of Approach
Facused
Broed
24.0
8.56-0
-0.09
MMLII- Redux
Reasoning Type
Induuetive
Daluctive
1.5e-02
40.06
Idea Development
Sequential
Parallei
90.3
38.5
No
0.55
0.01
Veritication Focus
Data Drives
Hypothesis: Driven
84.5
Yes
2.8c 02
-0.05
Clarificatio Approsch
Ieeraivv
Immodiate
10.6
8.5--04
Analytical Pengective
Top Down
Bonom Up
458
Scope of Approach
Focused
Brood
33.2
37.4
No
0.16
0.09
MATH- 500)
Reasuning Type
Inductive
Deductive
13.2
11.0
No
0.29
0.07
Idea Developetent
Sequentill
Parallel
Verification Focus
Data Driven
Hypothesis Deiven
61.4
6422
No
0.96
Clartfication Appreach
lierative
Immediate
14.4
4.3
Yes
6:0c 08
0.35
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Table 12: Analysis of reasoning strategies between Distill-R1-32B and s1.1-32B models using COT ENCYCLOPEDII'S 's six criteria across safety benchmarks. Unlike traditional cognitive behavior metrics, this approach reveals numerous statistically significant differences (marked as 'Yes"), ) with substantial effect sizes (Cohen's d up to 0.50), demonstrating CoT Encyclopedia's enhanced ability to distinguish between models' reasoning strategies and preferences.
Reasoning Behovlse
Pattrr
they
Benchmark
p-vauue
Cohen's
Criteria
DisilI-
different?
Guidance Strntgy
Noz Directive
Directive
35,
40.
No
0.73
0.05
Bitical Consudrutionn
Technical Response
Moral Evalaation
Safety Prisallnnee
Rid--Epaging
Proveative
59.3
60.3
No
0.37
-0.66
XS
Mlsi Devckqmmen
Sequnnial
Panilid
18.5
404
9.2-14
4.50
Content Handling
Open Discossion
Censeethip
13.1
16.7
Yes
2.4e 06
1.25
Risk Assessment
High Awareness
Low Risk Assemption
22,7
1911
No
0.19
0009
Conest Irieat
Malicious
Benevolant
1000
No
0.16
0.14
Guidance
Noz Directive
Directive
40.3
No
0.084
Ittiicl Conssderation
Technical Response
Moral Dvaluation
26.1
Yes
0,088
0.09
Safett Preuslens
Risc-Eagaingg
Proveative:
56,0
67.
Yo.
4.0e-22
-0.24
Kdoo Development:
Sequential
Panillel
2.
Content Handling
Open Diccussion
Censership
0.94
Yes
14
0.35
High-Rik
Low-Rik Assunption
1.0-23
-0.34
Comeut Ineatt
Malicious
Besevelert
1000
Yes
1.fe04
0.18
Table 13: Analysis of reasoning strategies between Distill-R1-32B and QwQ-32B models using COT ENCYCLOPEDIA six criteria across safety benchmarks. Unlike traditional cognitive behavior metrics, this approach reveals numerous statistically significant differences (marked as 'Yes'), with substantial effect sizes (Cohen's d up to 1.44), demonstrating CoT Encyclopedia's enhanced ability to distinguish between models' reasoning strategies and preferences.
Reasening Behevtor
Pattern
Pattern
Are they
Benchmark
p-alue
Cohrn's
Oriteria
Pattern. A
Pattern
Denil--I
QwQ
different?
Guidunce
Non-Einectwe
Directivn
50.3
41.1
Elical Cossidention
Technicul
Evalaation
2.1c4
Safety Preodfence
Rock Enggging
Provenivve
61.2
Yox
8776-
40.16
XSTest
Meaa Developnent
Sequentil
Panilel
18.3
43.2
2.0e-17
Content Hundlig
Opez Discustion
Cesscchhip
12.1
Yos
1.2 76
-1.4
Rick Assnament
High-Riak Ascernoss
Low-Risk Assamption
26.1
Vos
2.11e-2
40.15
Content Insest
Malicious
Benevoleut
1000
0.00
Guidunce
Non Directive
Directive
40.7
M.7
Yos
4.13e-2
Edical Cussilenzion
Technicul
Evaluation
29.5
9.45o-3
Safety Precefence
Ros- Vingging
Proventive
S0.1
62
Yos
3.95-2
40.15
WiMGuard
Me Developnent
Sequential
Panilel
Yos
6.59s-11
Content Hundling
Oper Discuscion
Gerseeship
Yos
3
-0443
Risk Assosment
Risk-Risk Awareness
Low Risk Assumption
29.5
40.3
Yos
1.10c-9
4.39
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Table 14: Analysis of reasoning strategies between QwQ-32B and s1.1-32B models using CoT ENCYCLOPEDIA' 's six eriteria across safety benchmarks. Unlike traditional cognitive behavior metrics, this approach reveals statistically significant differences (marked as "Yes', "), with moderate effect sizes (Cohen's 's d up to 0.24), demonstrating CoT Encyclopedia's 's enhanced ability distinguish between models' reasoning strategies and preferences.
Reasoning
they different?
Benchmark
p-tauue
Cohen's
Critesia
Patiern
Qu0
Guidance Struagy
Non Directive
Directive
43.3
403
No
0.37
0.05
Edical Consideration
Technical Respotse
Moral Evalustion
Safity Procedemes
Figg-ing
Proventive
67.2
62.3
No
0.11
0.10
XST
Development
Sequential
Firaleel
453
40.9
0.05
Conenn Handling
Open Discussinn
Censorship
652
No
0.63
0.03
Rok Assceenent
High-Risk Avcecnio
Low Rids Asummpiin
20.1
19.1
Yox
204
0.34
Costent Intent
Malicious
Benevelent
1000
1.00
0.00
Guidanor
Nen--iivation
Dinctive
No
0.25
0.07
Fibical Comideration
Technical Reaporoe
Monil Evalesiiu
20.5
261
0.20
0.08
Safety Precedence
Risk Engaging
Preventive
63.5
67.5
No
0.08
0.10
WilGoard
Ids Devzllpmmnn
Sugurwisi
Pariilel
Conenn Handling
Open Discusiinn
Censorship
Yes
Te
0.21
Assesument
Awarzness
Assumption
4KJ
66.1
0.04
Cuntent Isteni
Malisiou
Renovelani
10501
1.00
0.00
Table 15: Comparison of high-level reasoning style preferences across models trained on different data formats. This table presents detailed analysis of how question format influences reasoning strategies across three benchmarks: GPQA-Diamond, MMLU-Redux, and MATH-500. For each benchmark, six reasoning criteria are evaluated with contrasting pattern pairs (Pattern A vs. Pattern B). Statistical significance testing (p-values) and effect size measurements (Cohen's 's d) reveal that multiple-choice and free-form trained models exhibit significantly different reasoning strategies on most criteria. Particularly pronounced differences appear in the MATH-500 benchmark, where effect sizes reach up to 1.58, demonstrating that training data format substantially shapes models' problem-solving approaches independent of content domain.
Reasoning Behavior
Pattern
Pattern B >
Are they diffieent??
Benelmark
y-value
Coben's
Criteria
Pattern
Potterm
Multiple-choice
Free-form
Amalytical Perspective
Top-Down
Botiom-Up Up
63.9
46.3
Yes
le:36
0.36
Soopa of Approsc
Foused
Broad
74.8
76.7
No.
0.12
-0.04
GPQA-
Ressoning Type
Inductive
Daluctive
Men Development
Sequerrial
Parallel
27.11
Verifictionn Facus
Dan--Diven
Hypothesis Driven
59.6
35.4
No
0.1
0.02
Clardication Approach
Iteative
Immediate
21.0
Yes
3e-14
0.22
Analytical Perspective
Top-Down
Bottom-Up Up
39.5
59.2
Yes
2e-52
-0.40
Soope of Approsch
Roemed
45.3
MML.U- Redux
Ressoning Type
Inductive
Daluctive
27.5
76.8
-1.03
Idea Development
Sequertial
Paraliel
50.5
Yes
1e:21
0.25
Vesification Focus
Data Driven
Hypothesis- Driven
16.9
34.5
Yes
Se-139
0.66
Approach
ltenaivve
Asalytical Perspective
Top Dowa
Botto Up
85.9
32,9
Scspe Appmachh
Roeneed
Broed
1.15
MATH- 500
Reasoning Type
Inductive
Daductive
14.1
Yes
0.00
1.49
Idea Development
Sequercial
Paralle)
0.02
94.8
Yes
0.00
-0.99
Verifcationn Focus
Driven
Hypothesis Driven
13.7
1c:292
Clriiieation Appeoach
Trentive
Immodiate
11.4
35,5
Yes
1c-171
-0.5
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Published as a conference paper at ICLR 2026
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Reseniing Type
Figure 14: Hierarchical Clustering Across Benchmarks. Six different benchmarks: XSTest (top left), WildGuard (top right), Arena-Hard (mid left), and MMLU-Redux (mid right), MATH-500 (bottom left), GPQA-Diamond (bottom right). Stars indicate the representative embeddings (medoids) for each cluster. This visualization demonstrates how different benchmarks employ varied criteria for pattern analysis.
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Figure 15: Hierarchical Clustering of reasoning strategies with PCA Projection on problem- solving Benchmarks. Comparing four different representative embedding selection methods: medoid-based (default, top-left), silhouette-based (top-right), frequency-based (bottom-left). and density-basee (bottom-right), Each stars indicate representative embeddings for each cluster. Despite using different selection criteria, the overall clustering structure remains consistent across methods, with only minor variations representative embedding positions.
Pattern Ratio Across Same Model Family (DistilI-R1)
GPQA-Diamont
MMLLU-Redux
MATH-500
30
80-
A0
20
Desil-81 325
Desti R1 70
Dis:l-81 1.50
Figure 16: Pattern ratio distributions across three different sizes of the Distill-RI model family (32B, 7B, and 1.5B). The x-axis shows six reasoning strategy criteria: analytical perspective (ap), clarification approach (sa), reasoning type (rt). idea development (id), verification focus (vf), and scope of approach (ca). Despite the significant size differences, all three models exhibit remarkably similar pattern distributions across all benchmarks, supporting the conclusion that models from the same family maintain consistent reasoning strategies regardless of scale.
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Cohen's Effect Model Family (Distill-R11)
328 7B
32B 1.50
1.58
0.44
GPQA- Diamond
0.32
0:30
Coban's
0.00
0.00
40
INLLU-Redux
0.32
Cohen'k
0.20
0.06
0.0
0.00
MATH-500
Cohente
8.00
0.96
0.04
0.60
000
Anelytical Persectivv
Reesoning type 10ea Deveropmenr
Ventication tocus Ciai ricaiionoo Aspreach
Scape of Approach
Figure 17: Pairwise Cohen's d effect size measurements comparing reasoning strategy distribu- tions across different sizes of the Distill-RI model family. The x-axis displays the six reasoning strategy criteria: analytical perspective (ap). scope of approach (sa), reasoning type (rt), idea develop- ment (id), verification focus (vf), and clarification approach (ca). All effect sizes remain below 0.1 across most comparisons, indicating very small distributional differences between models of different sizes within the same family.
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Table 16: Comparison of high-level reasoning style preferences across models trained on different domains. This table presents statistical analysis of how content domain influences reasoning strategies across three benchmarks: GPQA-Diamond, MMLU-Redux, and MATH-500. Six reasoning criteria are evaluated for each benchmark, comparing math-domain versus knowledge- domain training- Statistical testing reveals minimal differences between domains, with most p-values above the significance threshold (0.05) and small effect sizes (Cohen's 's mostly below 0.15). The limited number significant differences (only 4 out of 18 comparisons) and small effect sizes demonstrate that content domain has substantially less impact reasoning strategy formation than question format, supporting the paper's 's finding that format characteristics shape reasoning strategies more fundamentally than subject matter.
Rensoning Behavior
Pattern
Pattern
Benchmark
p-value
Cohen's df
A
domain
Knowledge-domab
Analytical Perspective
Top
Up
600
6144
Scope Approach
Focused
Beuad
61.0
62.3
No
0.29
0.027
GPQA- Diamond
Rensoning Type
Inductive
Deductive
60.5
60.0
No
0.00
0004
Idea Developmens
Sequential
Panallal
No
0.52
0.017
Verificttion
Dats-Drives
Hypathesi--rrisen
No
Clarification Approsch
heniiie
Immediate
40.4
Yes
Analytical Persectivve
Top
Botoon Up
Approact:
bocused
Broad
59.6
45.5
9
Yes
0.00
-0.14
MMLU- Redux
Reasoning Type
Inductive
Deductive
43.0
444
No
0.49
0008
Idea Developmens
Sequential
Parallel
No
0.95
0.01
Data-Drivan
Hypothesis-Diieen
No
Clarification Approach
ltemaive
Immediate
5K.
536
Analytical Perspective
Top Down
Bonoos Up
Scope Approach
Focused
Brund
39.6
42.0
Yes
18:08
0,37
MATH- 500
Reasening Type
Inductive
Deductive
42.0
40.0
No
8.le-2
0.02
Idea Develogment
Sequential
Panalal
No
6e-2
0.12
Vesification
Data-Drives
Hypothesis Driven
No
Clarification Approch
Immediate
59.8
Yos
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Table 17: Comparison of reasoning behavior patterns between Qwen and Qwen-Math models across three benchmarks. The table presents statistical analyses of six reasoning criteria: Decision Strategy, Reasoning Type, Analytical Perspective, Verification Focus, Scope of Approach, and Idea Development. For each criterion, the table shows the distribution percentages of Pattern A and Pattern for both models, along with statistical significance measures (p-value and Cohen's d).
Reasoning Behmior
Pattern
Pattern B
Are they
Benchmark
p-sale
Cohen's
Ciiteria
Pattera
Owen
Oweh-Math
different?
Decision Strasgyy
Optimal
Satishiing
SS1
51.
No
0.419
00085
Reasoning Type
Inductive
Deductive
GPOA- Diamend
Analytcall Perspective
Top Down
Botto Up
21.3
45.2
Yes
5.17e
0.524
Varifiationn Focus
PrincipeeDriven
Numeriaal Valishtioon
21.7
63.3
Yox
7.58x117
40928
Saspe of Ayprouch
Fozueed
Boudd Explontion
66.4
45.6
Yox
5.00e-
0,407
Idea Development
Linear Sequemial
Parallel
No
0.869
0,003
Desisian Sturlggy
Oytinal
Satisliing
-0002
Reasoning Type
Inductive
Daluctive
26.3
67.
Yox
4.67o-22
0.251
MMLU Redux
Analytical Perpectivee
Top Down
Bottom-Up
Yos
3.20e-184
0,806
Verification Focus
PrincipleDrivven
Numerical Validtrion
16.2
16.9
No
0,574
-0,15
Scope of Approadh
Focused
Broad Explenzion
562
Yos
6.5% 25
0.268
Idea Develogment
Linear Sequential
Parallel
Yes
0,535
Decision
Optimal
Satieficing
41.3
25,3
Yos
1.93e-15
0.517
Reasoning Type
Inductive
Deductive
182
No
0.391
0,052
MATH- 500
Analytical Perspective
Down
Botton
30.1
35.1
No
0.0794
0,107
Visification Focus
PrinsipeeDriven
Numasizal Valichriion
362
67.9
Yos
1.12x-26
-0776
Saxpe of Approuch
Ficuell
Brad Explonsion
60.2
Yox
2:72-6
40,208
Idea Development
Linear Sequential
Parallel
22.1
24.0
No
0,452
0,048
Table 18: Comparison of reasoning strategies between QwQ and s1.1 models on safety bench- marks. This table presents statistical analyses of seven reasoning criteria across two safety bench- marks (XSTest and WildGuard), For each criterion, the table shows the distribution percentages of Pattern A and Pattern B for both models, along with statistical significance indicators (p-value and Cohen's 's d).
Reasoning Bolavior
Patiern A
Palturn B->
Arc thay different?
Benchmark
p-vatue
Cohen's
Criteria
Puttern. A
Pattera
QwQ
$1.1
Guiskiee Stralgy
Men-Dinssive
Dimatice
2333
Ehical Coaskdennoon
Technical Response
Mond Draliation
472
433
No
0:45
0.10
Presslanse
Rók- Eagaging
Proveative
XSTai
Idea Development
Sequential
Panallel
413
704
Yos
1 1.
0.5
Cuntest Hanllng
Open Discussion
Consendtip
69.5
15.2
No
0.20
4.20
Assessment
High Awarnness
Risk Assumptios
Contora Inicet
Malisious
Berevoleu
95.7
963
No
0.17
0.15
Cuidance Strateyy
Dioective
Directive
Ehical Coasideraionn
Technical Response
Mord Dvalzation
26.5
25.1
No
0.63
0.00
Presslanss
Eagaingg
Proveatve
49.5
0.04
WilGual
Idea Development
Sequential
Parallel
37.
Yos
5.20
0.40
Cuntest Hanling
Open Discussion
Consendiip
10.4
21.4
Mix
3. 16c--02
40.30
Assessment
High Awarnness
Risk Assumptios
Contona Inieut
Malisious
Berevoleut
3000
3000
No
1.00
0.00
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Multiple-choice format (MC) data
Free-form (FF) data
Diamond is extremely hard because of the strong bonding between directions?
The equation the circle symmetric the circle 5(x-2)22-(-2))2277 with respect to the line $x+y=25 is
Options:
carbon
liquid atoms
hydrogen atoms
D. consistent atoms
Multiple-choice format (MC) response
Free-form (FF) response
Okay, so I'm trying to figure out the answer to this question about diamond being extremely hard.
Okay, so need to find the equation of circle that's symmetric to the given circle S(x-2)<2 (y-2)^2 7$ with respect to the line $x 2$. Hmm, symmetric with respect line that the line the
The question asking why diamond because the strong bonding between the atoms in all directions, and there are four options: A, carbon atoms, B. liquid atoms, C. hydrogen atoms, D. consistent
Wait, that doesn't seem right. If plug S(2, 2)$ into the reflection formulas with $a=15, $b=1$, $c=-2$:
Wait, that contradicts my earlier result. Let me check the reflection formula again.
Option A is carbon atoms. Diamond is made up of carbon But why would the atoms bond strongly? remember carbon atoms have strong bonds with each other, which contributes to the structure of diamond. So, maybe A is correct.
that makes
Wait, perhaps used the wrong formula. Let derive the reflection point.
Then,
x' 2 Vrra((21122(L + = Mrac(4)(2)=
Option D is consistent atoms. Consistency could mean that the atoms uniform and not varying, but I'm not sure how that relates the hardness. It doesn't seem relevant as the bonding between atoms.
2-2=0
\]
2= 1) 2
So, putting it together, the strong bonding between carbon atoms in diamond explains its hardness. Therefore, the should
Thus, the equation of the reflected circle is:
(x o0^2 (y 00-2 (\sqrt(7))²2
The correct answer is **A. carbon **oms*** because diamond, composed of carbon, exhibits high hardness due its strong and consistent bonding in all directions.
Figure 18: Examples of input formats and model responses from multiple-choice (MC) and free-form (FF) training data.
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E РROMPTS
Prompt for brainstorming the fine-grained criteria and patterns
You are tasked with analyzing the reasoning strategies used in the following response. The response includes the thought process for solving a problem. Your goal is extract and describe patterns based on various criteria that characterize the model's problem-solving strategy.
Please follow these guidelines:
Identify multiple *meaningful criteria* that differentiate reasoning strategies. Each criterion should have a clear and descriptive name that reflects real aspect of the reasoning process. **o not use generic placeholders like 'Criterion 1 **
2. For each criterion, describe two contrasting $patter types* (e.g., *Step-by-step" vs. *Outcome-fist"", *Concrete* vs. *Abstract*).
Present your analysis in the following format, using <patterns> and </patterns> tags to enclose the list:
<patterns> Descriptive Criterion Name (Pattern A vs. Pattern B) Descriptive Criterion Name (Pattern A vs. Pattern B)
Descriptive Criterion Name (Pattern A vs. Pattern B) </patterss>
Do not include any explanations or commentary within the <patterns> tags.
5. The example format above is only guide. You are encouraged to define your own diverse and insightful pattern criteria based the given response.
Response: (answer)
Figure 19: Prompt template for identifying fine-grained reasoning criteria. This template guides the systematic extraction of diverse reasoning strategies from model responses by instructing the analysis to: (1) identify meaningful criteria with descriptive names that reflect genuine aspects of reasoning, (2) describe contrasting pattern types for each criterion, (3) present the analysis structured format using designated tags, and (4) focus on identifying insightful pattern criteria without extraneous commentary. This structured approach enables comprehensive taxonomy development of reasoning strategies employed in chain-of- thahuut processes.
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Prompt for generating the pattern analysis rubric
Create concise rubric for the following reasoning strategy criterion:
[CRITERION NAMEJ: [PATTERN A] [PATTERN B]
For each pattern, provide:
clear, concise definition (2-3 sentences) that captures the essence of this reasoning strategy
3-4 key characteristics that distinguish this pattern
3. concrete examples of responses that demonstrate this pattern (keep examples brief, about
2-3 sentences each)
Focus on making the distinctions between patterns clear and easily identifiable. The def- initions and examples should help evaluators quickly categorize model responses without ambiguity.
Figure 20: Prompt template for rubric generation in reasoning strategy analysis. This template
outlines the structured approach for creating assessment rubrics that distinguish between contrasting reasoning strategies. The p (1) concise definitions capturing each pattern's 's essence, (2) key distinguishing characteristics, and (3) concrete response examples demonstrating each pattern. This systematic rubric development ensures clear pattern differentiation, enabling consistent and unambiguous classification of model reasoning strategies across different problem-solving contexts.
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Prompt for generating the pattern analysis report
You are an expert at analyzing reasoning strategies in model responses. You'll be provided with:
A rubric describing two distinct reasoning strategies (Pattern A and Pattern B)
A model response analyze
Your task to create detailed analysis report that determines which pattern the response exhibits.
Analysis Process:
Carefully examine the response against both pattern definitions in the rubric
2. Identify specific elements, structures, and linguistic features in the response that align with either pattern
3. Note any mixed signals elements that span both patterns Determine which pattern (A or B) the response most closely matches
Report Structure:
Initiaal Observations** (2-3 sentences summarizing key features of the reasoning
approach)
**Evidence for Pattern **:
If applicable, quote 1-2 specific segments from the response that demonstrate Pattern A
Explain how these segments match characteristics described the rubric
3. **Evidence for Pattern B**;
If applicable, quote 1-2 specific segments from the response that demonstrate Pattern B Explain how these segments match characteristics described in the rubric
**Pattern Determination *#;
Explain which pattern (A B) is most dominant and why
Address any aspects that show characteristics both patterns
5. ** **Coclusion***
Clearly state the final pattern determination using the format: "Final pattern determination: [PATTERN NAMEJ"
Focus on concrete evidence from the response that matches specific elements from the rubric patterns.
Rubric: (rubric)
Response to analyze:
(response)
Figure 21: Prompt template for comprehensive reasoning strategy analysis report generation. This template guides the systematic evaluation of model responses against predefined reasoning strategies. establishes structured analytical process involving (1) careful examination of re- sponses against pattern definitions, (2) identification of patter--aligne elements, (3) recognition of mixed pattern signals, and (4) determination of the dominant pattern. The prescribed report struc- uure-including initial observations, evidence documentation for each pattern, pattern determination with justification, and a clear conclusion-ensune thorough and evidence- classification of reasoning strategies employed in model outputs.
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Prompt for evaluation on multi-choice QA benchmarks
Question: (question]
Options
A) (option A
B) (option B
Please reason step by step, and you should write the correct option alphabet within boxed(): I.
Figure 22: Prompt template for multiple-choice question assessment with structured reasoning. This template presents standardized format for evaluating reasoning models on multipl-cchoie QA benchmarks (GPQA-Diani) MMLU-Redux).
Example prompt for steering models toward optimal reasoning strategies
You required solve the following question using a specific reasoning strategy. This reasoning strategy must guide the entire problem-solving approach:
Top-down: First, conceptualize the overall structure or system involved in the problem. Begin by forming a clear, high-level understanding of the task, and then systematically break down into lower-level details. Organize your reasoning from general principles to specific elements, prioritizing clarity and structure.
Start by openly exploring wide range of possibilities without attempting to prioritize or filter them too early. Your goal is to understand the full landscape of potential approaches, ideas, or interpretations before narrowing down or making decisions.
Broad:
Inductive: Base your reasoning on concrete examples or specific observations. Look for patterns that emerge from these instances and use them build general principles conclusions. Learning through data-driven exploration or trial-and-crror is encouraged.
Single: Choose one hypothesis, method, or line of reasoning to pursue. At each step, verify whether your current approach works. it does not, adjust accordingly before proceeding. Your reasoning should follow a step-by-ste method with focus systematic validation.
Hypothesis-driven: Approach the problem with specific, predefined hypothesis. Your task to verify this hypothesis using logical reasoning and data. The structure of your analysis should aim to confirm or refute the initial claim without deviating from it.
Immediate: Seek full clarity at the beginning. Ask direct and comprehensive questions immediately to form a complete understanding of the problem. Avoid backtracking or revisiting earlier assumptions unless absolutely necessary.
Make sure your entire reasoning process aligns with the selected pattern above. Now, solve the following question accordingly.
{question]
Figure 23: Example prompt for steering models toward optimal reasoning strategies. This template demonstrates how specific reasoning strategies can be explicitly prescribed to guide problem- solving approaches. Six distinet reasoning strategies are presented: top-down, broad, inductive, single, hypothesis-driven and immediate. The prompt instructs models to align their entire problem-solving process with selected pattern, enabling controlled experiments to identify which reasoning strategies yield optimal performance across different tasks and benchmarks.
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F QUALITATIVE ANALYSES
Beyond quantitative analysis, we conduct qualitative analysis based on the actual outputs generated by the model. In Appendix F.I. we analyze the artifacts produced each step of CoT ENCYCLOPEDIA on the GPQA-Diamond benchmark, comparing the final reasoning strategy analysis results with analysis results classified according to pre-defined criteria. Appendix presents comparative analysis of responses from models trained on multiple-choie format datasets versus those trained on free-form datasets when evaluated on the Arena Hard benchmark, along with pattern analysis of these responses.
F.1 COMPARATIVE ANALYSIS OF COT ENCYCLOPEDIA OUTPUTS AND PRE-DEFINED CRITERIA
Table 19: Comparative analysis of reasoning strategies exhibited in physics problem-solving using multiple evaluation frameworks. This table presents a detailed qualitative analysis of reason- ing approaches employed when solving physies problem of EPQA-Diamont through moving media. The analysis employs two distinct evaluation methodologies: the CoT Encyclopedia criteria, which identifies evidence-driven reasoning, and pre-defined criteria system that assesses backtracking behaviors.
light propagation
What is the correct answer to this question:A light beam is propagating through glass with index of refraction The glass is moving constant velocity in the direction as the beam and toward the observer in laboratory. What is the speed of light in glass relative to the observer laboratory? Take the speed of light vacuum c=l. Choices: A. B. (I+n+v)(n+v) C. (1+n*v)/(-vv D. (1-n*v)((++v) Answer:
Question:
Okay, the question is about the speed of light in glass observed in laboratory frame, where the glass itself is moving at a constant velocity in the same direction as the light beam, and towards the observer. The speed of light in vacuum is given c=1. The choices A through D, with various expressions involving n and v. First, I need to recall how the speed of light medium relates to the medium's refractive index. The speed of light in medium with refractive index n is given by v light c/n. But here, the medium (glass) is moving, So, the usual formula might need some adjustment due to the motion of the medium. Hmm, maybe have to consider the velocity addition formula from special relativity, but I' m not sure if that directly applies here. Let me think. Wait, ... (omitted)....
Response:
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2. Fresnel Drag Formula: The formula for the speed of light in moving medium is given by:
+ v
1 ne
Substituting into the formula:
+
+
3. Simplification: Simplify the expression by multiplying the numerator and denominator by n:
v) 1 + n
4. Relativistic Velocity Addition: Alternatively, using the relativistic velocity addition formula, where u' n
is the speed of light the glass frame moving at velocity relative the lab frame:
+
+ u
Substituting w'
+ u
+
This simplifies to the same expression above:
11.7
v +
5. Conclusion: The derived expression matches option B.
Fine-grained criteria: "Understanding Method (Conceptual Insight vs. Formula Application)", "Problem Fragmentation (Deconstruction vs. Holistic Approach)", "Validation Strategy (Cross- Verification vs. Single-Source Verification)", "Solution Derivation (Analytic Derivation vs. Plug- and-Chug)". "Exploratory Process (Iterative Consideration Direct Pursuit)", "Logic Appli- cation (Physics Principles vs. Mathematical Manipulation)", "Interpretation Mode (Qualitative Analysis Quantitative Analysis)"
Sampled COT OOOEEDA criteria based report: The provided response demonstrates strong understanding of the physics involved in determining the speed of light in moving medium (in this case, glass) relative laboratory observer. The thinker systematically recalls and applies relevant concepts, including the relationship between the speed of light and the refractive index, and utilizes the Fresnel drag coefficient and the relativistic velocity addition formula correctly. The reasoning starts with an exploration of how the speed of light in medium relates to its refractive index and adjusts for motion, showing a thorough investigation of the problem rather than assumption-driven approach. The responder considers multiple avenues of solution and confirms their correctness through simplification and careful algebra, ultimately arriving at the same conclusion using different methods.
The exploration and hypothetical testing of ideas are evident, with the responder not merely following a structured path dictated by singular hypothesis, but rather engaging in an open-ended inquiry that leads to the solution through evidence- reasoning.
Given that the response is grounded evidence from physics concepts and engages with the problem dynamically, it aligns best with the "Strongly Evidence-driven" pattern of reasoning. The validity of the conclusions is drawn from examining the data and relevant principles without imposing an initial hypothesis that restricts the analysis.
Thus, the response fits into the pattern of strong evidence-driven reasoning. Therefore, will categorize it such: Strongly Evidence-driven
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Sampled pre-defined criteria based report: The provided response exhibits clear pattern of backtracking, as the individual systematically revisits earlier thoughts and calculations to confirm and refine their understanding of the problem. Throughout the response, the author reflects different aspects of the problem, considers potential adjustments, and verifies the correctness of their reasoning by retracting or re-evaluating previous conclusions.
1. The author starts by recalling foundational concepts related to light in medium and how relates to refractive index and motion. 2. They initially consider the implications of special relativity on the motion of light in a medium. 3. As they derive the formula for the speed of light in moving medium, they continuously verify their calculations making adjustments and confirming expressions until they are confident in the answer. 4. They also show awareness of different factors (like the direction of motion) that could affect their calculations, demonstrating reflective process where they reassess the implications of their findings.
This approach aligns closely with the description of "Backtracking" in the rubric: the reasoning involves revisiting and reassessing previous decisions to arrive correct conclusion. This indicates the presence of backtracking rather than a strictly linear thinking process.
Thus, the evaluation of the response is that it demonstrates backtracking. Final evaluation: Yes
Table 20: Comparative analysis of reasoning strategies exhibited in physics problem-solving using multiple evaluation frameworks. This table presents comparative analysis of reasoning strategies exhibited when solving complex organic chemistry problem of GPQA-Diamond involving multiple synthesis steps. The analysis employs two complementary evaluation frameworks: the CoT Encyclopedia criteria, which identifies iterative clarification processes during reaction analysis, and pre-defined criteria system that focuses on backtracking behaviors.
Question: What is the correct answer to this question:A methanol solution of (R)-(+)-Limonee) is stirred with Pd/C under Hydrogen atmosphere. After equivalent of hydrogen is consumed, product 1 is isolated as the major product.
I is treated with 3-chloroperbenzoic acid, forming product 2. Product 2 is treated with sodium methoxide, forming product 3. Product 3 is treated with propanoic acid, dicyclohexylcarbodinke forming product 4. what is valid structure
and catalytic amount of weddemhylammiooppe of product 4? (product 4 exists as a mixture of isomers. the correct answer is one of them). -eytS-44--mmthyllyyyooee-eeeeee
propionate B. (15)) propionate C. (1S,25, 40sosooo----ssprpo-----e--ee propi- methylcyclohexyl propionate D. (18,2R,4R) onate Answer:
Choices: A. 2-tp:////l--mthhooo----eeeey//
Response: Okay, let's tackle this question. So, the problem is about identifying the chemical formula of an unknown compound using FTIR, 1H NMR, and Mass Spectrometry data. The given choices are C6H120, C6H100, C6H1002, C6H1202. The options are A to D corresponding to these formulas. First, let's parse the FTIR data. The FTIR spectrum shows a very broad absorption peak at 3000 wavenumbers. ... (omitted).... ... Wait, but let's check the other options. If the compound had only one oxygen (option B, C6H100), how could that be? For example, if it's a ketone with double bond. A ketone has one oxygen. But then where does the O-H come from? The question mentions broad peak at 3000 cm, which is O-H. So if the compound is ketone with an O-H group, that would require two oxygen atoms: one in the carbonyl (C=O) and one in the O-H. But option B is C6H100, which has only one oxygen. So that's impossible. Therefore, the answer must be A. Another angle: the degrees of unsaturation. The compound has two degrees of unsaturation (from the analysis above: carbonyl and double bond). The formulas with two degrees are A and B. Since B has only one oxygen, but the compound must have O-H (which needs additional oxygen beyond the carbonyl), so B is out. Therefore, A is correct. Thus, the answer should be
A
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Fine-grained criteria: "Problem Decomposition (Stepwise Breakdown vs. Holistic Assessment)", "Data Interpretation (Spectrum Analysis vs. Literature Reference)". "Functional Group Identi- fication (Empirical vs. Theory-Driven)". "Alternatives Consideration (Exhaustive Options vs. Targeted Options)", "Verification Focus (Spectral Data Consistent vs. Fragment Peak Analysis)", "Iterative Refinement (Initial Hypothesis Re-evaluated Hypothesis)"
The response demonstrates a highly iterative approach to clarification. Throughout the analysis, the responder explores various possibilities concerning the chemical structure of the unknown compound using FTIR, IH NMR, and Mass Spectrometry data. Key indicators of this iterative approach include: 1. **Gradual Exploration*:: The responder goes through the spectral data step-by-step. interpreting each piece of information in relation to possible structures for the unknown compound. This indicates willingness to engage with uncertainty and adapt their understanding as more data is considered. 2. **Follow-Up Questions and Refinement** The responder frequently asks rhetorical questions (e.g., "Wait, but...") that indicate reconsideration of previous assumptions and re-evaluating information based on new insights. They continuously refine their interpretations and reasoning as they progress. 3. **Comfort with Ambiguity * The presence of various interpretations throughout (e.g., the potential for a carboxylic acid, possible structures aligning with the degrees of unsaturation, and the consideration of different functional groups) reflects methodical approach to making sense of complex chemical data, without rushing to conclusions. 4. ** Incremental Understanding The analysis reveals that the responder builds their conclusion based on progressively integrating different aspects of the data rather than expecting an immediate resolution. They discuss multiple scenarios and gradually hone in specific interpretation that fits the data best. Thus, the response exemplifies a mindset that validates iterative clarification, as the responder systematically processes the information and adjusts their conclusions in an exploratory manner. Therefore, the reasoning strategy for this response is Highly Iterative Clarification.
Sampled COT ENCYCLOPEDIA:
Sampled pre-defined criteria based report: The given response clearly exhibits the charac- teristics of the "Backtracking" reasoning strategy. Throughout the analysis, the author revisits earlier decisions and thought processes, particularly in relation to the interpretation of spectral data and the implications for the chemical structure of the unknown compound. For instance, the author considers the implications of the FTIR and NMR spectra, reassessing conclusions about potential functional groups and how they relate to the chemical formulas provided. The response's 's flow reflects significant amount of reconsideration of hypotheses, especially when determining the degrees of unsaturation and confirming the presence of specific functional groups like the O-H group. The author alternates among possibilities and systematically eliminates options based on newly recalled information and analysis, which is central to the backtracking reasoning strategy. Every time the author faces a potential inconsistency or lacks certainty, they pause to reevaluate their conclusions indicating methodical return to earlier ideas to ensure the accuracy of their answer. This iterative process a hallmark of backtracking rather than one-way reasoning stream. Based on this thorough examination, it is evident that the reasoning adheres to the backtracking structure. Thus, the evaluation is yes.
F.2 DIVERGENT REASONING STRATEGIES FROM MULTIPLE--HOIC VS. FREE-FORM TRAINING DATA
Table 21: Divergent reasoning strategies in models trained on multiple-choice versus free-form data formats. This table shows how training data format shapes reasoning strategies when solving identical problems of Arena- Hard benchmark. Multiple-choice trained models exhibit structured problem decomposition with frequent hypothesis generation and multiple restart points, while free- form trained models pursue single hypotheses with continuous verification within one framework. This analysis supports our finding that format characteristics impact reasoning strategies more significantly than problem domain.
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Question: A mother buys set of N toys for her two children, Alice and Bob. She has already decided, for each toy, whether it will go to Alice or to Bob, but she has forgotten the actual monetary values of the toys. She only remembers:
The toys were arranged in ascending order of value.
All prices non-negative.
We say that a given assignment is fair if. for every non-decreasing sequence of toy-values
0 S v1
U2
S UN,
the difference between the total value of Alice's 's toys and Bob's 's toys does not exceed the maximum toy value UN. Formally, let
S S, SS
be a binary string of length N, where
S = {o, 0, if toy is assigned to Bob.
1, if toy is assigned to Alice
Then S is called fair for every non-decreasing sequence (o:) with 0 S en S 122 S .. UN. we have
U [S =1
Σ No. [8, 0) UN,
where
1, if predicate P true,
P]
0, otherwise.
Okay, so I'm trying to figure out how to determine if given distribution of toys is fair based on the problem statement provided. Let me break down the problem step by step. First, the problem says that there are N toys, and they've been assigned to Alice and Bob in some way specified by binary string S. Each character in S represents one of the toys: '1' means Alice gets it, '0' means Bob gets it. The key thing here is that S tells us exactly which toys go to whom, but the actual values of these toys aren specified. However, the problem gives us a condition that must hold for the distribution to be considered "fair." The fairness condition states that for any possible assignment of toy values (which are non negnnvgte and in ascending order), the absolute difference between the total value of toys Alice receives and the total value Bob receives should not exceed the highest toy's value, which is v v_N. But I'm not entirely sure about that. Let me think about how to approach this. One way to tackle this is to consider the worst-case scenario where the difference between Alice's and Bob's totals could be maximized. If even in the best possible worst-case scenario, the difference doesn't It exceed v_N, then the distribution fair. But wait, the problem mentions that the distribution is fair for every possible array of toy values, the difference doesn't 't exceed N. That seems quite broad because it implics that no matter how the toy values vary (as long as they 're -on-decreassng).. the difference shouldn't 't get too big. ... (omitted)- ... Let think differently. ... (omitted) ... need to find a different approach. Explanation * Reading *:: The code reads the number of test cases and processes each test case individually. **Counting Toys**; For each distribution, it counts how many toys Alice receives ('k'). **Calculating Sums *#; It calculates the sum of the values of the top 'k' toys and the sum of the values of the bottom 'N-k' toys. #*Checking Fairness* It computes the absolute difference between these sums and checks if it is less than or equal to the highest toy value. If it is, the distribution is deemed fair; otherwise, is not. This approach ensures that we efficiently determine the fairness of the distribution by leveraging the properties of non-decreasing toy values and the constraints imposed by the problem.
Multiple-choice format (MC) trained:
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Free-form (FF) trained: Okay, so I'm trying to solve this problem where have to determine a given distribution of toys between Alice and Bob is fair based on certain conditions. Let me try to understand the problem step by step. So, the problem says that distribution is fair if, regardless of how the actual toy prices (which are strictly increasing order) are assigned, the absolute difference between the sums of Alice's toys and Bob's toys doesn't it exceed the maximum toy price among them. Wait, more formally, for every possible array of toy prices v_1 <= v_2 <= ... v_N, the absolute difference lsum A sum BI must be max_,, V, where max_y is the largest toy price. Hmm, wait, because the max_y v is the last element in the sorted list. So max v_N, since they'r in order. But the condition needs hold for all possible assignments of v_i's. That makes sense because the distribution is fair no matter what the actual prices are so even the worst-case scenario must satisfy the condition. Our task is, given (the binary string indicating which toys go to whom), to decide whether this condition holds for all possible toy price arrays. think the key here is to find out under what circumstances the maximum possible Isum lsum_A- sum BI across all possible arrays is less than equal to max. (omitted) ... Explanation "Reading Input**: The input read in one go for efficiency, especially given the constraints. **Prefix Sum Calculation " For each test case, calculate the prefix sums of the values of toys Alice and Bob receive. Here, the values are assumed to be sequential integers starting from * F*Fineess Check** Using the derived condition,
check if twice the sum of the values of the toys Alice receives is less than or equal to the total sum of all toy values. If this condition holds, the distribution fair; otherwise, it is not. This approach efficiently determines the fairness of the distribution by leveraging prefix sums and ensuring the solution handles up to the maximum constraints effectively.
Pattern analysis for MC: The response is more structured and attempts to break down the problem logically. ... It attempts to break down the problem ... model attempts provide clear step-by-step guide. Model also tends to generate multiple hypotheses, demonstrating an inclination toward broadly exploring potential answers.
Pattern analysis for FF: ... response lengthy and somewhat convoluted. goes through a lot of reasoning but does not arrive at clear solution or code implementation. does not provide a clear answer to the problem or a working code solution. It gets lost in the reasoning without concluding with practical implementation. ... The response is excessively verbose, making it difficult to extract useful information quickly. Model exhibits a tendency to pursue answers by continuously verifying hypotheses within main framework
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Table 22: reasoning strategies in error diagnosis: Multiple-choice versus free-form trained models. This table compares how models trained on different data formats approach technical trou- bleshooting question of Arena-Hard benchmark. The multiple-choice trained model demonstrates structured analysis with clear step-by-step reasoning and actionable recommendations, while the free-form trained model exhibits This comparison highlights how training format influences problem-solving strategies in diagnostic contexts.
repetitive pattern with frequent restating of observations.
Question: Find root cause for this error: sshd[54785]: error: kex_eeexeeeeeeeeeeeee Leeexcangg_ddenffictttiooo identification: Connection closed by remote host
Multiple-choice format (MC) trained: Okay, so need figure out the root cause of the error "kex _ex___xchage_____ wwweeeeeeeeeeenniiiieieeee idtntificaitt::::nnn Connection closed by remote host" in a KEX application. Let me break this down step by step. First, I understand that KEX a protocol used in blockchain technologies, often in contexts like Solana, Monero, others that use zero vero-knowledg proofs. The error message suggests that when the application tries to connect to KEX, it's closing the connection, which happens on remote host. That makes me think about how the application is handling network connections. remember that in many networked applications, especially those involving distributed systems, it's 's crucial handle connections properly. ... (omitted) can consider the possibility This could include temporary network outages fluctuations in the network. Implementing a retry mechanism or error handling in the application could provide a fallback plan in case of unexpected network issues. In summary, the root cause is likely related the application not handling network connections properly, possibly by not waiting for network confirmation or by not checking the status of the remote host before attempting connection. To fix this, the application should ensure that network status is checked, connections are confirmed before sending requests, and appropriate error handling is place. (omitted) ... By following these steps, the application can better handle network connectivity issues, ensuring that connections are not closed unexpectedly. This approach will involve code adjustments, network status checks, and error handling mechanisms to provide more reliable connection process.
transient network issue causing the connection to be closed.
Free-form (FF) trained: The error occurs when run the code as follows: So, the error is that _ex___xxcange___e iddetifiicaiion is closed by remote host. So, the code is trying to get new exchange (kex) from remote host, but it's not working because the connection the remote host is closed. think that the problem is that the code is not correctly handling the authentication for the exchange. with the "exchange" parameter. But perhaps the way it's being handled is incorrect. Wait, in the code, the exchange is being fetched using exchange get_kest eeesseehannnexxchaaee in the code, it's not passing any headers authentication parameters. Wait, in the code, the "exchange' is being fetched without any headers or with the wrong parameters.
(omitted) Looking at the code, see that the exchange being fetched
But
Pattern analysis for MC: provides a structured and relevant analysis of the error. It identifies potential causes and offers clear troubleshooting approach, including checking network status, allowing for network confirmation, and implementing error handling ... The response is helpful and concise, directly addressing the user's prompt and providing actionable steps to resolve the issue
Pattern analysis for FF: ... response is largely verbose. It does provide clear explanation of the error or its potential causes. Instead, it seems to get lost in a repetitive and unclear narrative about code handling without addressing the actual error message or providing actionable troubleshooting steps.
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Reviews:
[{"review_id": "6O1QaWbIaI", "reviewer": "Reviewer_47H3", "summary": "The paper proposes a bottom-up framework to analyze, predict, and steer long chain-of-thought (CoT) reasoning. The pipeline: (i) have an LLM describe the strategies it used, (ii) embed and cluster these criteria, (iii) derive contrastive rubrics (e.g., top-down vs bottom-up), and (iv) classify new CoTs to produce interpretable 'reasoning profiles'. Using the learned rubrics, the authors predict question-specific optimal strategies and inject pattern-based instructions, improving accuracy and safety across multiple benchmarks. They also show that training format (MC vs free-form) shapes reasoning more than domain, and that weight interpolation between MC and FF-trained models smoothly shifts reasoning style. Overall the paper is thorough and the contribution is well articulated. The main limitation of the paper is the lack of a more substantial grounding on the coverage of the underlying categories of reasoning.", "questions": "- The title of the approach (CoT encyclopaedia), points the readers in the direction of an approach which is comprehensive and systematic. Yet, it is unclear how the prompts you use to deliver that induction of a set of CoT characteristics are defined. Could you provide additional details and defend on why these prompts have the required properties to deliver the task? These needs to be mechanism/construction-based (not referring to the empirical analysis).\n\n- The term ‘reasoning’ tends to be underspecified and used as whatever the tasks implement. Can you provide a description of what your task corpus is expressing wrt to reasoning and scope your claims accordingly. \n\n- Wrt validity, how well do rubric-based strategy labels align with expert human coders (definitions, guidelines, IAA)? What are the most common disagreement modes?\n\n- Do results hold when swapping the LLM judge, embedding model, and moderation model? (cross-judge and cross-embed sensitivity analyses)\n\n- How stable are criteria under different k, linkage metrics, and seeds?\n\n- When pattern-based instructions help, how much is due to true strategy change vs prompt priming or longer outputs?", "limitations": "", "rating": 2, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "- Clear narrative. \n\n- Clear empirical insights. Demonstrates that format/domain in shaping reasoning patterns, and that merging model weights interpolates strategies. These provide useful guidance for dataset and model design.\n\n- Sensible empirical analysis. Includes ablations on taxonomy construction (embedding, clustering, … ), human evals of report quality, and analyses of stability across families/sizes.", "weaknesses": "- Lack of a rigorous scoping for the problem of reasoning. \n\n- Lack of an argument for the construction of methods which can deliver a comprehensive feature set which describes the CoT reasoning phenomena.", "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": "3KXus6SxYg", "reviewer": "Reviewer_FM7J", "summary": "This paper introduces CoT Encyclopedia, a bottom-up, data-driven framework for analyzing and controlling reasoning strategies in large language models (LLMs) performing long Chain-of-Thought (CoT) reasoning. Unlike top-down approaches that rely on predefined strategy types, CoT Encyclopedia automatically extracts reasoning criteria from model-generated CoTs, embeds them into a semantic space, clusters similar dimensions, and builds contrastive rubrics (e.g., top-down vs. bottom-up). It then classifies each CoT response under these rubrics and generates interpretable reasoning reports. ​Experiments across multiple benchmarks (GPQA-Diamond, MMLU-Redux, MATH-500, XSTest, WildGuard, Arena-Hard) show that this framework captures finer-grained reasoning differences across models and tasks, achieving higher interpretability (86% human preference) and consistent performance gains.​ The authors further demonstrate that optimal reasoning strategies can improve both model helpfulness and harmlessness, that question-specific reasoning can be predicted, and that data format (multiple-choice vs. free-form) shapes reasoning behavior more strongly than domain.​ Overall, CoT Encyclopedia provides a scalable taxonomy and control mechanism for reasoning behaviors, contributing to greater interpretability, adaptability, and safety in LLM reasoning.", "questions": "# 1. On classifier dependence and taxonomy stability\n\nYour entire classification pipeline—strategy identification, rubric generation, and labeling—relies on GPT-4o. Have you tested whether the same reasoning taxonomy holds when different LLMs (e.g., Claude, Gemini, DeepSeek) are used as classifiers or rubric generators? If not, how do you ensure that the taxonomy reflects general reasoning properties rather than GPT-4o-specific biases?\n\n# 2. On the granularity of reasoning strategy clustering\n\nYour current clustering framework analyzes reasoning strategies at the full CoT–response level, producing high-level dichotomies such as “Inductive vs. Deductive” or “Top-Down vs. Bottom-Up.” However, reasoning trajectories are often compositional: individual reasoning steps may follow distinct micro-strategies that combine to form an overall reasoning pattern. \n\nHave you considered extending the CoT Encyclopedia to identify atomic reasoning step categories—that is, classifying each reasoning step rather than the entire chain—and investigating whether global reasoning strategies emerge as structured combinations of such atomic units? This could reveal a more mechanistic understanding of how complex reasoning behaviors are composed.\n\n# 3. On the granularity and interpretability of clustered criteria\nYou report six high-level reasoning dimensions (Table 5). How were the fine-grained criteria merged into these six? Was k = 6 chosen purely based on silhouette scores or adjusted for interpretability by human judgment?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "# 1. Originality and Conceptual Contribution\n\nThe work shifts the paradigm from top-down, predefined reasoning taxonomies to a bottom-up, data-driven discovery of reasoning strategies. This formulation is original and theoretically meaningful: it operationalizes reasoning diversity without relying on human-crafted categories, enabling emergent taxonomies directly grounded in model behavior. The introduction of contrastive rubrics (e.g., “bottom-up vs. top-down,” “inductive vs. deductive”) represents an elegant mechanism for interpretable reasoning dimensions—conceptually parallel to semantic factor disentanglement. The finding that data format (MC vs. FF) shapes reasoning more strongly than domain is novel, empirically grounded, and relevant to both cognitive modeling and training data curation.\n\n# 2. Technical Quality and Empirical Breadth\n\nThe framework is well-engineered: it integrates LLM-assisted criteria generation, embedding-based clustering, and interpretable classification. The experimental coverage is impressive—spanning six benchmarks across both helpfulness (GPQA-Diamond, MMLU-Redux, MATH-500) and harmlessness (XSTest, WildGuard, Arena-Hard). The authors perform rigorous human evaluations and quantitative analyses, reporting consistent improvements in interpretability and measurable performance gains.\nThe inclusion of ablation and robustness studies (e.g., embedding choices, random seeds, model scales) shows commendable attention to reproducibility and methodological soundness.", "weaknesses": "# 1. Lack of analysis on classifier choice and sensitivity\n\n​The framework relies on a single LLM (GPT-4o) to perform all classification tasks in the taxonomy pipeline—deciding whether each reasoning trace aligns with one side of a contrastive rubric. Although Appendix B.1 examines benchmark-induced differences (showing that GPQA, MMLU, and MATH benchmarks produce similar criteria while Arena-Hard yields a distinct “User Understanding” dimension), this analysis only reflects task-level variability, not classifier-level robustness. The paper never investigates whether different classifier models (e.g., Claude, Gemini, DeepSeek) or prompting styles would yield consistent categorizations. Consequently, the stability and objectivity of the classification stage remain untested, and taxonomy boundaries may shift under alternate LLMs or small prompt perturbations.\n\n# ​2. Limited human validation of interpretability​\n\nHuman evaluation (250 samples, 10 annotators) focuses on plausibility rather than interpretive alignment or consistency, and no inter-annotator reliability metrics are reported.​\n\n# 3.Benchmark scope limited to English text\n\n​All benchmarks are English and text-based; multimodal and multilingual reasoning remain unexplored.", "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": "HOXqEmsTl5", "reviewer": "Reviewer_u6tC", "summary": "This paper introduces a framework named “CoT Encyclopedia” for analyzing, predicting, and controlling model reasoning patterns from CoT outputs. The authors claim that their approach can automatically extract reasoning criteria, cluster them in a semantic space, and derive rubrics to interpret LLM reasoning strategies. They further argue that this framework provides better interpretability, predictive power, and safety control than previous categorization-based techniques.", "questions": "- Given that criterion is presented as highly important, yet only a single one is used, how robust is it against variations from weaker models or the effects of randomness?\n- Since a prior for a specific reasoning logic appears to be incorporated for certain questions, leading to clear performance gains, how would the proposed framework be applied to a test set that lacks CoT examples?\n- How does the performance of this method compare to instruction optimization techniques like TextGrad, and can it facilitate the discovery of more effective reasoning patterns?\n- How are pattern similarity and Q-Q similarity calculated?\n- The paper's finding that \"data format is more important than domain\" is a valuable insight. However, given that this conclusion is based on math and QA tasks, do the defined \"reasoning strategies\" also apply effectively to tasks that demand creativity, open-endedness, or emotional understanding, such as poetry generation or legal argumentation?\n- As models evolve and potentially develop novel reasoning strategies, the \"Encyclopedia of CoT\" would require continuous updates. What are the anticipated costs and frequency for maintaining and updating this resource?\n- Add reference.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 4, "strengths": "- The goal of making LLM reasoning more interpretable and controllable is important and timely.\n- The paper provides a large-scale qualitative analysis that could inspire follow-up interpretability research.\n- It attempts to link reasoning diversity with data format, a less-explored dimension in CoT studies.\n- Presentation is relatively polished and readable, making the high-level idea easy to follow.", "weaknesses": "- The criterion appears to be very important, yet the paper seems to use only a single one. How robust is this criterion to variations from weaker models or the effects of randomness?\n- It seems that a prior for a specific reasoning logic has been incorporated for a certain class of questions, and the performance benefits are evident. I am curious how your framework would be applied when the test set does not include CoT outputs.\n- Figure 6 is blurry and difficult to read.\n- How does the performance of this method compare to instruction optimization techniques such as TextGrad? Additionally, can it lead to the discovery of more effective patterns?\n- The finding that \"data format is more important than domain\" is a valuable insight. However, since these conclusions are drawn primarily from tasks in mathematics and question answering, do these defined \"reasoning strategies\" remain effective for tasks requiring creativity, open-endedness, or emotional understanding, such as poetry generation or legal argumentation?\n- As models continue to evolve, they may develop novel reasoning strategies. This implies that the \"Encyclopedia of CoT\" is not a one-time creation but requires ongoing updates. What are the anticipated costs and frequency of these updates?\n- How are pattern similarity and Q-Q similarity calculated?\n- Missing Reference:\n\n[1] Towards reasoning era: A survey of long chain-of-thought for reasoning large language models\n\n[2] Deconstructing long chain-of-thought: A structured reasoning optimization framework for long cot distillation\n\n[3] When more is less: Understanding chain-of-thought length in llms", "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": "RjkjcJMFOo", "reviewer": "Reviewer_WA1g", "summary": "This paper introduces the COT ENCYCLOPEDIA, a novel, bottom-up framework designed to analyze, predict, and control the chain-of-thought (CoT) reasoning in large language models. The method automatically extracts a diverse set of reasoning criteria from model-generated text, uses embedding and clustering to form a coherent taxonomy, and generates interpretable reports. The authors demonstrate the framework's utility through comprehensive human evaluations that show its superiority over predefined analyzers and its ability to measurably improve model performance by steering reasoning toward optimal strategies.", "questions": "Please refer to weaknesses.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "(1) The paper's primary strength is its data-driven, bottom-up methodology for creating a taxonomy of reasoning strategies. This contrasts sharply with prior work using fixed, human-defined categories, allowing the framework to discover emergent and more nuanced reasoning patterns specific to different models and tasks.\n\n(2) Comprehensive Experimental Validation: The claims are supported by extensive experimentation.\n\n(3) Significant Finding on Data Format vs. Domain: The discovery that training data format has a substantially greater impact on reasoning strategies than the content domain is a crucial and non-obvious contribution.", "weaknesses": "(1) All major components of the framework—from the initial ideation of 4,057 criteria (Step 1) to rubric formulation (Step 4) and final classification (Step 5)—are executed through an external proprietary language model (GPT-4o). This design choice embeds a structural reliance on a closed-source system and exposes the analysis to its internal biases. Although the authors acknowledge this limitation and incorporate a multi-evaluator setup to mitigate bias (Appendix B.5), the methodology remains fundamentally shaped by the constraints and opacity of the chosen model.\n\n(2) The paper defines “optimal” reasoning strategies as those correlated with higher frequencies of correct or safe answers within a given dataset (Section 4.1). However, this relationship is correlational rather than causal. It remains ambiguous whether these strategies directly contribute to improved outcomes or merely co-occur with successful reasoning patterns. The experiments stop short of disentangling causation from correlation.\n\n(3) In Section 4.3, classifiers are trained to predict which reasoning strategies perform best for specific question types. These models are developed and evaluated on a fixed set of five benchmarks. Although some cross-domain tests are conducted, the study does not extend to genuinely unseen or out-of-distribution datasets. Consequently, the generalizability and robustness of these classifiers beyond the training domains remain uncertain.", "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)