CoT-Evo: Evolutionary Distillation of Chain-of-Thought for Scientific Reasoning
Authors: Kehua Feng
Keyan Ding
Zhihui Zhu
Lei Liang
Qiang Zhang
Huajun Chen
Venue: ICLR 2026 Poster (2026)
Keywords: Long CoT Distillation
Scientific Reasoning
Evolutionary Algorithm
Primary area: foundation or frontier models, including LLMs
TL;DR: We propose CoT-Evo, an evolutionary distillation framework that constructs diverse CoTs from multiple LLMs and iteratively refines them into high-quality CoTs for scientific reasoning.

Abstract: While chain-of-thought (CoT) distillation from advanced large language models (LLMs) has proven effective in general reasoning tasks, it struggles in scientific domains where even advanced models often produce incorrect or superficial reasoning due to high complexity and specialized knowledge requirements. Directly distilling from such flawed outputs results in low-quality training data and limits the performance of smaller student models. To overcome this, we propose CoT-Evo, an evolutionary CoT distillation framework. It begins by constructing a diverse pool of reasoning trajectories from multiple LLM thinkers, enriches them with automatically retrieved domain knowledge, and iteratively refines the trajectories using novelty-driven selection, reflective recombination and mutation. The refinement is guided by a fitness function that evaluates answer correctness, coherence, and effective knowledge utilization. This results in a high-quality CoT dataset tailored for scientific reasoning. We employ this evolved dataset to fine-tune a compact model, which achieves state-of-the-art performance on scientific reasoning benchmarks. Our work establishes a scalable approach to synthesizing high-fidelity scientific reasoning data from diverse and fallible LLMs.

Published as a conference paper at ICLR 2026
CoT-Evo: EVOLUTIONARY DISTILLATION OF CHAIN- OF-THOUGHT FOR SCIENTIFIC REASONING
Kehua Feng 12, Keyan Ding 2 Zhihui Zhu', Lei Liang", Qiang Zhang 22 Huajun Chen
!Zhejiang University >/JU-Hangzhou Global Scientific and Technological Innovation Center "AntGroup
(kehuafeng, dingkeyanjezju.ede edu.co cn
ABSTRACT
While chain-of-thouse (CoT) distillation from advanced large language models (LLMs) has proven effective in general reasoning tasks, it struggles in scientific domains where even advanced models often produce incorrect or superficial rea- soning due to high complexity and specialized knowledge requirements. Directly distilling from such flawed outputs results in low-quality training data and limits the performance of smaller student models. To overcome this, propose CoT-Evo, an evolutionary CoT distillation framework. begins by constructing a diverse pool of reasoning trajectories from multiple LLM thinkers, enriches them with automatically retrieved domain knowledge, and iteratively refines the trajectories using novelty-driven selection, reflective recombination and mutation. The refine- ment is guided by a fitness function that evaluates answer correctness, coherence, and effective knowledge utilization. This results in a high-quality CoT dataset tailored for scientific reasoning. We employ this evolved dataset to fine-tune a compact model, which achieves sfute-of-the-arr performance on scientific reasoning benchmarks. Our work establishes a scalable approach to synthesizing high- fige-fidelity scientific reasoning data from diverse and fallible LLMs. Code available htttps://githus cwm/co//////eeoec htw.ttubb...cc/iii/ee////////D Fenggg/DDDD--
INTRODUCTION
Recent advances in reasoning large language models (LLMs), such DeepSeek-RI (Guo et al. and OpenAl-o 1lo3 (Jaech et al. 2024), have demonstrated that leveraging long and structured chains of thought (CoTs) leads remarkable improvements in complex reasoning tasks. CoT distillation from advanced teacher models has proven effective in general domains (Ye et al.] 2025 Hu et al. 2025 However, when applied to scientific domains, even the strongest L.MMs frequently generate erroneous or superficial reasoning paths due to the increasing complexity and specialization of scientific tasks (Liu et al., 2025 Li et al.) 2025). This raises critical need for more fine-grained CoT distillation approaches tailored to the unique requirements of scientific reasoning.
2025
Existing work has made significant progress in optimizing CoT distillation. Some approaches focus on enhancing intra-chain quality in single-teacher settings by compressing reasoning token length (Wang et al., 2025 Lu et al., 2025) or identifying intermediate error states {Luo et al. 2025). Others employ multi-teachar to aggregate diverse reasoning paths and seleet the most suitable CoT for each sample (Zhu et al. 2024 Xu et al. 2025). While these methods have enriched the landscape of CoT distillation, they overlook critical aspects that are particularly consequential in scientific reasoning tasks: 1) single-teacher optimization may introduce bias (Xu et al. 2025), and merely pruning redundant or erroneous steps does ensure accurate knowledge usage in the core thought; 2) multi-teacher frumework increases diversity but lacks the flexibility to refine the internal logic of CoTs a fine- ane-grained level.
To address these limitations, we propose CoT-EvO, an evolutionary CoT distillation framework. Distinct from prior work that merely selects or transfers single promising reasoning path per sample, CoT-Evo performs intra-chain aggregation, dynamically integrating thoughts from multiple
"Corresooniigg author.

---

Published as a conference paper at ICLR 2026
Multi-Thinker CoT Initialization
Novelty-Driven Candidate Selection
Initial Candidate Pool
Question
Answer
Behavioral Embedding
Fitness Function
Stage 1: CoT Generation
Stage Knowledge Augmentation
Reasoning LLMs
Question
Answer
Prompt Strategies
Model +
Nearest Neighbors
Knowlodge
Chain of Thought
Rellective Reasoning
Correctness
Local Compefition Score
Backward Think
Knowledge Snippets
Tree of Thought
KNN Embedding Space
Novelly Soore
Internal Knowledge
Additional Context
Pareto-Based Selection
Initial Candidate Pool
V(U=(N() L(U)
800
800
Higher NIt) <> More noval
Candidalos
c. Reflective Recombination and Mutation
Recombination
Mutation
Targef CoT
Apply
Apply Offspring Trajactory
Add
Offspring
Trajectories
Targel CoT
Mutation Operator
Strategy Provider
Identify Binding Point
Cross-chain Recombination
d. CoT-Evo Optimization Loop
Fitness
Novelly Reward
Recombination & Mulation
Candidate Pool
Selection
Figure 1: Overview of CoT-Evo. (a) Multi-thinker CoT initialization constructs diverse pool of candidates. (b) Novelty-driven candidate selection evaluates them via a composite fitness function and retains promising trajectories. (c) Reflective recombination and mutation generate new offspring CoTs through targeted operations. (d) These modules form the iterative CoT-Evo optimization loop, which evolves compact, accurate, and domain-reliable CoTs for downstream training.
CoTs to synthesize a single, high-quality chain. Specifically, CoT-EVO begins by generating a diverse candidate pool of CoTs using multiple LLMs and prompting strategies, optionally augmented with external knowledge. Each candidate is then scored by a fitness function measuring answer correctness, reasoning length appropriateness, and knowledge usage accuracy. Rather than greedily picking the top candidates, CoT-Evo employs a novelty-diven selection mechanism that jointly rewards quality and behavioral diversity. Finally, reflective recombination and mutation operators integrate or revise reasoning steps across candidates to produce improved offspring chains. Iterating this evaluation ieslection-variatioo-uplpp loop yields a compact yet high-fidelity set of evolved CoTs for downstream training.
Our contributions be summarized follows:
We introduce the first intra-chain multi-trajectory aggregation framework for CoT distillation, enabling fine-grained integration of reasoning steps within a single chain.
We propose evolutionary CoT distillation approach that integrates novelty selec- tion, reflective recombination, and mutation to iteratively refine reasoning trajectories.
We construct an evolved CoT dataset and demonstrate that our method significantly improves the performance of student models on scientific reasoning tasks.
2

---

2) Published as a conference paper at ICLR 2026
2 RELATED WORK
Long CoTs have been shown to significantly enhance LLMs' reasoning ability, as evidenced by models like DeepSeek-RI (Guo et al. 2025) and OpenAl-ol/o3 (Jaech et al. 2024). Distilling such trajectories from strong teacher models into smaller ones has become a common strategy to boost reasoning efficiency under limited computation (Ye et al., 2025 Hu er al. 2025). To improve quality, prior work has explored intra-chain optimization, e.g. compressing reasoning token length or pruning erroneous steps (Wang et al. 2025) Luo et al. 2025), and inter- chain (i.e., multi-teacher) strategies, e.g., aggregating multiple reasoning paths from different teachers or prompting paradigms or Program-of- Thhouhhht (Chen et al.. 2022 (Zhu al. 2024 Xu et al. 2025 Lei et al. 2025
Long CoT Distillation
(Wei et al., (022). Prce-of-Thoughy Yao et al. 2023).
Despite these advances, existing methods remain limited in scientific domains, where ensuring both factual accuracy and logical rigor is critical. To this end, we introduce CoT-Evo, which applies an evolutionary, fine-grained intra-chain aggregation strategy to combine and refine reasoning steps across CoTs, yielding more reliable and domain-accurate scientific reasoning trajectories.
Reasoning in Scientific Domains With the rapid progress of LLMs in mathematics and code, recent efforts have turned to evaluating their capabilities in scientific domains. Benchmarking
efforts have shifted focus from high school-level exams such as MMLU (Hendrycks et al., 2020).
CEval (Huang et al. 2023), and AGIEval (Zhong al., (023), to more advanced scientific tests including GPQA (Rein et al. 2024), SciEval (Sun et al. (024), and SciKnowEval (Feng et al. 2024).
and further domain-intensive tasks such BioMaze (Zhao al.) 2025a), BioProBench (Liu
et al. 2025). and ChemCoT Bench (Li et al.) 2025), which emphasize reasoning over memorization, covering areas from biological protocols molecular design. Moreover, developing specialized scientific LLMs to tackle complex downstream tasks has emerged as a promising direction (Zhao et al.
2025b Bai al. 2025). In this paper, we aim to provide generalizable CoT distillation framework that generates high-quality reasoning trajectories adaptable to diverse scientific applications.
3 CoT-Evo: EVOLUTIONARY COT DISTILLATION
In this section, present CoT-Evo, a novel evolutionary framework tailored for CoT distillation in scientific reasoning tasks. Let Dan { y:) 1 denote the original training dataset without COT. For each vi, the goal of CoT-Evo is generate high-fidelity, compact Co'I' for downstream training by leveraging diverse candidate pool p = { .,,,,,,,,t... ) produced from collection of LLM thinkers L. Through iterative refinement guided by carefully crafted reward signals, CoT-Evo evolves these candidates into more accurate and domain-reliabee reasoning chains.
Following the principle of genetic algorithm, CoT-Evo consists of four core modules: 1) multi- thinker CoT initialization (Section (.1]). 2) novelty-driven candidate selection (Section (3.3 3) reflective CoT recombination and mutation (Section 3.4), and 4) fitness function definition (Section
3.2). We summarize the optimization loop of CoT--Vo in Section 3.5 Figure| | provides an overview of CoT-Evo, and the full CoT-Evo algorithm is formalized in Algorithm
3.1 MULTI--HINNKR COT INITIALIZATION
key to the success of evolutionary algorithms lies constructing an initial candidate pool P that both diverse and promising. To this end, we employ a two-stage approach.
CoT Generation We first assemble a collection of L.M thinkers -= (2,12,.... hm where each 1, may represent: 1) reasoning-based L.LMs from different model families or scales, e.g., DeepSeek-R1 (Guo al. 2025). Owen3-235B-A222) (Yang al.) 2025). and Qwen3-32B: instruction-tunel LLMS with varying prompting strategies, e.g., Tree-of-Thouge (Yao et al. (023). Chain-of-Thoughh (Wei al. 2022), and backward reasoning. Formally, for query D Don. each
trajectory t E PG is generated by
t 4=4(x)
i= 1,2,..,
Knowledge Augmentation Considering the high specialization of scientific domains, model's internal knowledge alone is often insufficient. Therefore, collect additional knowledge required for
3

---

Published as a conference paper at ICLR 2026
each query z using a prompt- automated approach. Specifically, for each QA pair (z, y) E Doni we prompt an advanced proprietary model to perform reflective reasoning from to identify the knowledge necessary for solving and then abstract it into general, contextiindependent snippets Kg. We then randomly select a subset of thinkers, and provide each chosen thinker I3 with Krr as additional context, resulting in a knowledge-enhanee
CoT t, E pp represented as
1 = Ko,, j = 1, ..., m.
This approach results in an initial candidate pool pG pk that maximizes both cognitive difficulty (Cai et al. 2025) and strategic diversity, simulating a broad coverage of the solution space.
3.2 FITNESS FUNCTION
We evaluate each candidate trajectory using a composite fitness score that captures 1) answer correctness, 2) reasoning-length appropriateness, and 3) correctness of knowledge usage.
Exact Match We use a task-specific external script to check whether the candidate's 's final answer exactly matches the ground truth. The exact match score is binary:
exact match,
SEM
otherwise.
Length Appropriateness We compute token lengths from scientific reasoning datasets (e.g., Llama- Cemotron-Science (Bercovich et al., 2025 ) and set the 15% and 85% percentiles lower and upper bounds, since responses shorter than the 15% threshold often miss key knowledge, while those beyond the 85% threshold tend be verbose. Thus, the length appropriateness score defined as
0.0
if len(t)
15% percentile,
SLEN
0.5
if len(t)
85% percentile,
1.0
otherwise.
This encourages concise reasoning while avoiding under-explained outputs.
Knowledge Usage Correctness We employ an LLM-as-a-Judge (Zheng al. 2023) evaluator to assess the accuracy of the knowledge applied in the core thought of f. Given the reference knowledge K., and the CoT f, the judge assigns categorical score
SKNOW Judge(Kg, t), SKNOW E (1,2,3,4,5)
(5)
The final fitness function of combines the three components with weighted contributions:
R(t) SEm \1SLEN A25KNOW
(6)
where A and Å2 control the relative importance of length and knowledge usage.
3.3 NOVELTY-DRIVER CANDIDATE SELECTION
While the initial pool P obtained in Section 3.1 offers substantial diversity in reasoning trajectories, selecting candidates solely based the highest fitness scores can lead to premature convergence toward narrow set of CoT's. To mitigate this, COT-EVo employs a novelty-driven selection mechanism, inspired by Novelty Search with Local Competition (NSLC) (Lehman Stanley 2011 which simultancously promotes two complementary objectives: (i) encouraging distinct reasoning patterns, and (ii) rewarding local quality improvements.
Behavioral Embedding We first embed each CoT E P into d-dimensional behavioral spuce through a mapping b: P Rd capturing its structural or semantic reasoning features:
2, = b(t) e Rd
In practice, instantiate b(.) using Qwen3-Fimbeddingg-8 Zhhng al. 2025
4

---

Published as a conference paper at ICLR 2026
Novelty Score To quantify distinctiveness, compute trajectory t's average distance to its k nearest neighbors (t) in behavioral space:
(t) k ('ENN((1
Σ
Zr
(8)
Larger N(t) values correspond more differentiated reasoning styles.
Local Competition Score
Given a fitness function R.(t) (defined in Section 3.2 that assesses the correctness and quality of trajectory evaluate t's relative improvement over its neighbors:
Ltt)
1
Σ - +(t)) (a)+ max(a, 0).
MENA())
Here, I(t) rewards local superiority within the same behavioral region.
Pareto-Based Selection We treat each (N((), L())) pair a bi-objective performance vector g(t) = (t))), L(t)). Define (strict) pareto-dominacc relation g(t') > g(t), if N(t)) 2 N(()) A
L(t') 2 L(t) with at least one strict inequality. The Pareto front then
F. = {t E P 7t' E E s.t. g((') > g(t) }.
(10)
From Fe, parent candidates sampled with probability
+(t)+
p(t)
E>0,
(11)
(L()+)))
FEF:
where the parameter ensures numerical stability and slightly favors trajectories with higher local performance while maintaining diversity.
3.4 REFLECTIVE COT RECOMBINATION AND MUTATION
To further evolve reasoning trajectories, COT-EVO adopts reflective approach for recombination and mutation. enabling models to incorporate useful strategies from peers or revise their own reasoning patterns.
Recombination is triggered only to yields an incorrect final answer (i.e., (t.) 0). Unlike standard genetic algorithms, crossover operates single target CoT to with guidance from strategy provider lp. Let C, denote the recombiner (defaulting to lo that produced l..).
CoT Recombination.
Step 1: Identify binding point. We decompose ip into distinct thoughts using transition keywords (Chai al. 2025) (see Appendix A6 for details), then apply C, to select the endpoint of the last reasonable thought as the binding point B:
B = Cr (tp. transition keywords).
(12)
Step 2: Cross-chain recombination. We employ Cr to extract unique steps and knowledge from lp absent los denoted by I, and let C, generate new CoT conditioned on the prefix lof: B and Z:
=o B3] (t.l::
(13)
Owing to the limited instruction-folloiing capability of currently reasoning models, if C, a reasoning model, we explicitly insert guiding immediately after C,'s initial "<think>" token, including: 1) "I can receive externally provided information through "<info></info>" and 2) "Upon receiving information, should switch new thought and verify and use that information."
Reflective Mutation. Mutation aims to alter to's strategy, logic, expression. Given t, and mutation operator M,, (defaulting Io), we generate new variants via three modes:
(1) Additive mutation: enrich logical detail, explanations, and domain knowledge:
(()) Mullaa Add);
(14)
5

---

Published as a conference paper at ICLR 2026
(2) Deletive mutation: prune redundancy, unproductive exploration, extraneous knowledge:
f/3) = MM (to Delete);
(15)
(3) Innovative mutation: diagnoses erroneous logic in t, using the correct answer y,, then generates a new trajectory that attempts to avoid the identified mistakes:
{(o> = MMu Innovate), Delete).
(16)
3.5 CoT-Evo OPTIMIZATION LOOP
Putting the above modules together, COT-Evo proceeds in an iterative evolutionary loop that progres- sively refines the candidate pool, which is similar to the standard genetic algorithm [Holland (T992). At each generation, the current pool P produced by the multi-thinker initialization (Section 3.1) is first evaluated by the fitness function R(t) (Section 3.2) to obtain the quality scores of all trajectories. Rather than greedily selecting only the top-scoring CoTs we apply the novelty-driven selection mechanism (Section 3.3) to choose a set of parent trajectories that are both diverse in reasoning behavior and locally competitive. These parents are then passed to the reflective recombination and mutation operators (Section 3.4) to generate improved offspring trajectories, which inherit useful strategies or undergo targeted revisions of their reasoning steps. The resulting offspring are merged with the previous pool, with the towest-fitness. trajectories removed to maintain the population size popp forming new candidate set for the next iteration of the seliuattioinsllecioo--iiiie This iterative process continues until convergence or a predefined budget B, yielding an evolved CoT dataset Devo { i 1 with t arg maX4eP,, (t)) for downstream model training.
cycle.
4 EXPERIMENTS
4.1 IMPLEMENTATION OF COT-EVO
Our pool of LLM thinkers includes Qwen3-322 B-en3--3BBthhe 22B-think Yangg et al. 2025). DeepSeek-RR (Guo et al. 2025), and
2-5---22------2-BB- (Yang et al., 2025), together with three prompting strategies based on Llama4-Scour Sccoutt17--666 17B-16E (Meta 2025): backward reasoning (Chen et al.] 2024), Chain-of- Thought (Wei et al. 2022). and Tree-of-Thouge
Yao al. 2023). ). For knowledge augmentation in Section 3.1 we employ GPT-5-min to generate the knowledge snippets Kz, In deploying the fitness function, we set A 0.3 and A 0.1. The optimization loop of CoT-Evo uses fixed population size of Ppp = 6 per epoch with computation budget of B 5 epochs. During novelty-driven candidate selection, we set the k-nearest neighbors parameter to k front Fe, parent trajectories randomly sampled (three per iteration by default) for recombination and mutation. Consequently, each query can theoretically yield up to + 3 x 5 = 21 distinct CoTs.
and from the resulting Pareto
We apply COT-EVO to three popular open-source LLMs: Qwen3-8B Yang et al. 2025). Qwen2.5- 7B-Instruct (Team 2024), and Llama3. / --B--Inttruct (Grattafiori al. 2024).
4.2
EXPERIMENTAL SETUP
4.2.1
DATASETS
To comprehensively evaluate CoT-Evo, we focus on two representative scientific reasoning datasets, Dattaet and BioProBench, that capture the challenges of molecular editing and optimization, and experimental protocol design.
ChemCoT (Li et al. 2025): This dataset contains 14K samples tailored for chemical reason- ing. Complex tasks (e.g., molecular design) are decomposed into modular, verifiable operations (e.g., substructure addition, deletion, replacement), ensuring that the reasoning process is transparent and step-wise. encompasses four tasks, including molecular understanding (Und.), molecular editing (Edit), reaction prediction (Reaction), and molecular optimization (Opt.). We use ChemCo DieemooTDaaase TDataset for training data construction and evaluate on its associated benchmark, ChenCoTBench.
BioProBench (Liu al. 2025): This benchmark assesses LLMs' ability reason over biological experimental protocols. transforms 27K real-world protocols into 306K training samples and 3.6K test samples covering protocol QA (PQA), step ordering (ORD), and error correction (ERR) tasks.

---

Published as a conference paper at ICLR 2026
Table I: Performance comparison of CoT-Evo against bascline distillation methods and original LLM teachers across BioProBench and ChemCoTBBench. Best results are marked in bold, and second- becond-best results are underlined.
BioProBench
ChenCoTBench
Method
PQA
ORD
ERR
Und.
Fdit
Reaction
Opt.
Acc.
EM 1
Acc.
FI
MAEL
TMS1
Acc.t
Acc.f
SRT
FISt
LLM Teachers
DeepSeek R1
0.683
0.448
0.625
0.600
0.560
0.314
0.680
0.783
0.576
0.756
Qwen3.32R-think
0.628
0.434
0.510
0.575
0.225
0.691
0.472
0.454
Qwen3-238B-A22B-B00
0.669
0.625
0.600
0.683
0.565
0.227
0.880
0.689
0,473
0.658
0.595
0.202
0.625
0.480
0,850
0.145
0.655
0.650
0.402
0.706
Llamaf-Scout-CC Scout-Co''
0.588
0.208
0.600
0.392
0.680
0.187
0.625
0.650
0,364
0.675
Llama4 Scout TTo
0.593
0.181
0.626
0.539
0.805
0.172
0.610
0.589
0.340
0.634
LLM Stidents
Llama3. Llama31-88--nsz 1-8B-Inxt
0.468
0.077
0.580
0.452
1.860
0.143
0.615
0.261
0.147
0.173
+ Single Teacher
0.431
0.667
0.707
0.495
0.640
0.527
Multi Teacher
0.474
0.353
0.616
0.665
0.530
0.247
0.573
0,549
0,208
0,504
Best-of-K
0,508
0.329
0,527
0.609
0,461
0.226
0.599
0.600
0,294
0.534
+ Retro-Scarch
0.488
0.121
0.623
0.635
0.533
0.247
0.613
0.492
0,274
0.456
+ TwT
0.499
0.397
0.570
0.459
0.607
0.238
0.597
0.506
0.278
0.433
CoT- Evo
0.512
0.419
0.698
0.375
0.250
0.707
0.597
Qwen2.5-7B-Inst
0.519
0.227
0.564
0.398
0.620
0.086
0.575
0.304
Single Teacher
0.518
0.354
0.593
0.649
0,929
0.162
0.533
0.445
0.186
0.538
Multi Tencher
0,505
0.370
0.608
0.621
0.536
0.246
0.573
0.548
0.270
D.516
+ Best-of-K
0,538
0.339
0.619
0.570
0.440
0.116
0.487
0.445
0.294
0.460
+ Retro-Search
0,519
0.178
0.613
0.596
0.508
0.187
0.562
0.450
0.248
0.417
IWT
0.558
0.358
0.589
0.438
0.752
0.132
0.632
0.442
0.448
CoT-Evo
0.551
0.448
0.675
0.671
0.497
0.306
0.664
0.602
0,332
0.577
Qwen3-8f-think
0.602
0.371
0.590
0.419
01.40
0.139
0.612
0.422
0,278
0.352
+ Single Teacher
0.601
0.368
0.616
0.534
0.405
0.268
0.583
0.629
0.375
0.599
+ Multi Teacher
0.603
0.434
0.637
0.616
0,395
0,250
0.647
0.623
0.455
0.424
+ Best-of-K
0.603
0.369
0.608
0.457
0.395
0.173
0.651
0.600
0.365
0,516
Retro-Search
0.583
0.279
0.552
0.540
0.163
0.303
0.528
+ TwT
0.475
0.401
0,563
0.466
0.865
0.067
0.540
0,281
0.319
0,300
+ COT Evo
0.649
0.544
0.645
0.677
0.351
0,358
0.674
0.625
0.4.7
0.629
For computational efficiency, we use 20K subset of the training QA pairs for CoT construction while retaining the full test set for evaluation.
4.2.2 BASELINES
For comprehensive and fair comparison, compare CoT-Evo with the following baselines:
LLM Thinkers (Teachers). We also directly evaluate the six LLM thinkers used in our initialization stage, including DeepSeck-R1, Swen3-235B-AAe Qwen3-32B, and Llama4- Scout-17B-16E with three prompting strategies. These serve as the upper bound references for evaluating the distillation quality of CoT-Evo.
Base Models. We directly evaluate the original instruct or reasoning LLMs without addi- tional fine-tuning, serving reference to measure the overall gain of CoT-Evo.
Single Teacher (ST). For each LLM thinker, we apply the fitness function (Section 3.2) to filter its CoTs and retain only those with exact-match correct answers (SgM = 1). We repeat this process for all thinkers and report the performance of the best individual teacher.
Multi Teacher (MT). For each query, aggregate CoTs from all thinkers and directly select the correct trajectory with the highest fitness score. This representative CoT used for training, thereby capturing diversity across teachers. If no correct CoT exists, the query is discarded.
Best-of-K (BoK). For each LLM thinker, we sample K = 21 trajectories (matching the maximum number produced by CoT-Evo for a single query), ), apply rejection sampling based on the fitness function, and select the correct COT with the highest score.
7

---

Published as a conference paper at ICLR 2026
TwT. TwT (Xu et al. 2025 is a recent multi-teacher distillation framework that uses Dual- Criteria Rejection Sampling to build a high-quality and diverse CoT corpus from multiple teacher LLMs, and then progressively distills these reasoning patterns into the student model. We implement TwT with the same set of LLM thinkers as teachers as in CoT-EVo.
Retro-Search (Retro). Retro-Search (Lu et al. 2025)
MCTS- search algorithm that retrospectively explores alternative continuations of a teacher's 's reasoning trajectory to mitigate under-thinking and over-thinking while preserving the correct final answer. We apply vetro-Search separately to each LLM thinker and report the best student performance.
4.2.3 EVALUATION METRICS
For BioProBench, we evaluate the protocol QA (PQA) task using Accuracy (Acc), the step ordering (ORD) task using Exact Match (EM), and the error correction (ERR) task using both Acc and FI score. For ChemCoTBench, we adopt task-specific evaluation metrics. molecular understanding (Und.), we apply mean absolute error (MAE) for functional group counting, Tanimoto molecule similarity (TMS) for Murcko scaffold extraction, and accuracy for the remaining subtasks. Molecular editing (Edit) is evaluated with accuracy, reaction prediction (Reaction) is assessed by fingerprint similarity (FTS) with reference molecules, and molecular optimization (Opt.) is measured by success rate (SR), indicating the generated molecules that achieve the desired property improvement.
4.3
MAIN RESULTS
CoT-Evo delivers consistent performance gains over distillation baselines. Table | reports the performance of CoT-EvO compared with existing distillation methods. Our approach consistently outperforms both single-teacher (ST) and multi-teacher (MT) baselines across the two benchmarks. On BioProBench, CoT-Evo yields relative gains of 12.6% over ST and 8.4% over MT. while on ChemCoTBench the improvements reach 27.0% and 19.3%, respectively. CoT-Evo further surpasses recent strong process-level distillation baselines, including Retro-Search (Retro) and TwT. Notably, on several tasks, CoT-Evo even rivals the performance of the LLM teachers themselves. Such gains stem from COT-EVO not only filtering out erroneous or redundant reasoning from teachers but also integrating complementary reasoning strategies across multiple thinkers, yielding distilled CoTs that are often more accurate and task- aligned than the raw outputs of the teacher LLMs. These results highlight the overall advantage of evolutionary CoT distillation in producing stronger student models.
The performance gains of CoT-Evo go beyond the effect of increased sampling, As described in Section 4.1 COT-Evo can theoretically generate up to 21 candidate CoT' per query. To examine whether its superior performance merely stems from this enlarged sampling budget, we compare CoT-Evo with the Best-of-K (BoK) baseline, where each teacher independently samples K 21 CoTs and selects the best one according to the fitness function. Results in Table I demonstrate that COT-Evo substantially outperforms BoK, confirming that the improvements arise from higher-quality CoT evolution rather than brute-force data scaling.
CoT-Evo improves both data utilization and reasoning quality. To validate the source of these improvements, we analyze how CoT-Evo compares with baseline approaches in terms of usable data and CoT quality. For data utilization, we measure the proportion of distilled trajectories that are correct and usable. For reasoning quality, we employ GPT-5 as a judge to score CoTs across five dimensions: knowledge diversity, knowledge accuracy, reasoning diversity, logical coherence, and step redundancy. In addition, we conduct pairwise comparisons between COT-EVO and baseline CoTs, reporting win rates to capture relative quality. We do not report results for TwT, as it does not directly select CoTs with correct answers, leading to an unfair comparison. As shown in Table 2 CoT-Evo maintains over 70% usable data while producing CoTs that are more knowledge-rich and logically compact. Furthermore, strongest baseline achieves a win rate below 40% demonstrating that its gains come not just from more data, but from better data.
Table 2: Comparison of data utilization (Pass), reasoning quality (Quality) and win rate (WR) across distillation baselines and CoT-Evo.
BioProBench
Chemeo/DDatnel
Method
Pass
Quality
WR
Pass
Quality
WR
0.375
0.329
0.349
0.319
MT
0.536
6.776
0.374
0.524
5.935
0.390
BoK
0.498
6.763
0.353
0.389
5,571
0.335
Retro
0.446
7.024
0.362
0.413
5.857
0.354
CoT-Evo
0.729
8.230
0.704
7.847
the
8

---

Published as a conference paper at ICLR 2026
75
Selection Greedy Selection
ND Sel Selection
1.8)
Pass (%)
60
Fitness Score (max
1.2
55
Random Avg
0.8
Random Max
Greedy
40
Greedy Max
Novelty driven Aug
Novelt-drrvven Max
5
Qwen3-88
Qwen2.5-7B
Llama3.1-88
Generation Epach
Figure 2: Comparison selection strategies. Left: Impact of selection strategies on BioProBench (average Pass @ across all tasks). Right: Fitness dynamics across generation epochs, showing both average and maximum fitness.
4.4 ABLATION STUDY
In this section, we explore the key components and hyperparameters of CoT-Evo through series of ablation studies. More analysis provided in Appendix A2.2
Effectiveness of Selection Strategy. To assess the effectiveness of proposed novelty-driven selection (NDS) strategy, we compare it with two straightforward baselines: 1) greedy selection, which always chooses the candidates with the highest fitness score R; and random selection, which samples candidates uniformly at random. Average Pass results on BioProBench are shown in (igure([((eft) Across all three base models, NDS consistently surpasses the baselines. This trend can be explained by the evolution of fitness scores (Figure 2 right): random selection yields steady but slow improvements; greedy selection saturates within the first few epochs and often converges to local optima; in contrast, NDS drives faster and more stable gains, producing progressively higher-quality CoTs. Importantly, the budget of suggesting further room for improvement.
remains well below the saturation point of CoT-Evo,
Necessity of Recombination and Mutation. To evaluate the effectiveness of the core mod- ules for CoT optimization. experiments by testing 1) CoT-Evo without recombination, and 2) CoT-Evo without mu- tation on BioProBench. As shown in Table removing either module leads to noticeable performance drop. However, the roles of recombination and mutation differ in important ways. Recombination primarily enhances the diversity of reasoning trajectories and promotes better utilization of knowledge; thus, removing this module degrades data quality and in turn weakens the performance of the student model. Mutation, on the other hand, is designed to correct errors and reduce redundant reasoning within CoTs. Without this module, the convergence of COT-EVO is hindered, resulting in fewer usable correct CoT's and consequently more significant decline student models' performance.
Table 3: Ablation on recombination and mutation.
Method
Qwen3-8B
Qwen2.5-77
Llama3.1-8B
conduct ablation
0.612
w/o Recombination
0.591
0.564
0.553
w/o Mutation
0.568
0,548
0.534
Algorithm Scalability We aim to vali- date whether the scale of our algorithm is a key factor affecting distillation perfor-
6.52
022
mance. Specifically, Figure 3 investigates two major hyperparameters controlling the scale of CoT-Evo: the iteration budget and the population size Npop- As shown in Figure 3 (left), increasing the iteration budget initially leads to clear performance gains (B < 3), but these improvements gradually level off in later stages (in
824
652
Budget (Nac Ganeration Epoch)
Popudat on zu gur Generation
Figure 3: Impact of budget (left) and population size (right) on CoT-Evo's distillation performance.

---

Published as a conference paper at ICLR 2026
BioProBench (Llama3.1-89)
BinProBench (Qwen2.5-78)
BioPro (Qwen3-88)
0.7
0.7
NT
BoX
CoTEvo
HT
Bok
CoT
MT
Box
+
CoT
0.6
0,6
0.6
0.5
0.5
0.4
0.4
30K
50k
70k
30K
50K
70k
Budget
Burget
Budget
Cher CheeCCoBencch 3-188)
ChenCoTBench (-77)
ChemCoTBench (Owen3-88)
0.6
DoX
Colltve
0.6
MI
DoK
Cal-bvo
0.6
MT
Bog
Col-tvo
5con
0.5
Scure
0.5
0.5
0.4
0.4
0.4
0.3
0.3
30K
30K
50K
Tokan
Takan
Taken Budget
Figure 4: Performance comparison under equal token-budget constraints on BioProBench and ChemCoTBende across three LLMs, 1-ama..1-8B-Imm Instruuttt,, Swen2.5-7B-Instruue and Qwen3-8B.
trast to Figure 2 This may be because we always select the highest-fitness CoTs from the candidate pool; after several epochs, correct and high-fitness CoT's are already obtained, reducing the marginal benefit of further iterations. A similar trend can be observed in the population-size curves (Figure 3 right). Empirically, when Pop < 5, enlarging the population size enhances the diversity of the initial candidate pool at each iteration, which facilitates more effective recombination. Overall, increasing the scale consistently improves CoT-Evo's performance, and near-optimal gains can be achieved under relatively modest budgets.
Boken-Buddet Controlled Comparison. To verify that the gains of CoT-Evo do not simply stem from using more tokens, we further compare with Multi-Teacher (MT) and Best-of- (BoK) under the same total distillation token budgets (30K, 50K, 70K, 90K). For BoK, we repeatedly sample CoTs from a single teacher until the budget exhausted and then select the best CoT using the same fitness function as in Section 3.2 reporting the best result across all teachers. For MT, cycle through all six teachers in rounds until the same budget consumed, aggregating their CoTs and keeping the highest- fitnesss-ssssssseeee correct trajectory. For CoT-Evo, terminate the loop immediately when the token budget is consumed, selecting the best candidate from the current population. As shown in Figure CoT-Evo consistently surpasses both MT and BoK at all budget levels, despite operating under identical token constraints. Notably, the performance gap is already clear in the low- and medium-budget regimes, indicating that evolutionary refinement can extract substantially more value per token than simple over-sampling and selection. As the budget grows, all methods improve, but CoT-Evo maintains a stable advantage, suggesting that its gains come from systematically improving CoT quality rather than merely generating more trajectories. These results confirm that the evolutionary design CoT-Evo provides more compute-efficient route to high-quality reasoning traces.
the full evolutionary pipeline but
5 CONCLUSION
In this paper, we introduced CoT-Evo, an evolutionary framework for thain-of-thought (CoT) distil- lation that goes beyond prior methods by performing intra-chain aggregation, integrating reasoning steps from multiple Co''s through an iterative evaluation- selection-variation design yields distilled CoTs that are more accurate, rigorous, and diverse while remaining compact and efficient for training smaller scientific models. Extensive experiments show that CoT-Evo consistently outperforms existing distillation approaches. Looking forward, we aim to evaluate its generalization across broader scientific domains. and enhance the knowledge augmentation stage by incorporating external resources such as domain databases or structured knowledge graphs, making CoT-EVo more scalable, knowledge-groundde and practical for real-world scientific applications.
process. This
10

---

Published as a conference paper at ICLR 2026
LIMITATIONS
While CoT-Evo demonstrates strong performance scientific reasoning distillation, is not without limitations. First, leveraging multiple LLM thinkers introduces substantial computational and time costs, as generating and refining diverse trajectories requires repeated sampling and evaluation. This cost may hinder scalability to very large datasets cesource-constrained environments. Second, evolutionary process currently relies on LLM-based reward signals to evaluate reasoning quality; while effective, these signals may still carry biases, and future work could explore integrating more verifiable reward signals (e.g,, rule-based) to further enhance robustness.
ACKNOWLEDGEMENT
This work is funded by New Generation Artificial Intelligence National Science and Technol- ogy Major Project (20552D0122803, K.D.), NSFC62301 (K.D.), NSFC62302433 (Q.Z.). NS- FCU23A20496 (Q.Z.), and Ant Group Research Fund (K.D.).
ETHICS STATEMENT
This research aims to enhance the reliability of AI for scientific reasoning. Our experiments are conducted exclusively on public scientific benchmarks, which contain no sensitive or personally identifiable information. While we utilize pre-trained LLMs, framework is designed to filter and refine their outputs to improve factual accuracy and logical rigor. We have made every effort to mitigate potential risks, such as the generation of incorrect scientific content, and therefore foresee no significant ethical issues arising from this work.
REPRODUCIBILITY STATEMENT
We committed the full reproducibility of research. We will release source code for the COT-EVO framework, fine-tuning scripts, and evaluation protocols. The paper provides comprehensive details on the public datasets, models, and hyperparameters used. Furthermore, all prompts required to replicate our evolutionary process are documented in the appendix. These resources will enable the community to verify our findings and build upon our work.
REFERENCES
Lei Bai, Zhongrui Cai, Maosong Cao, Weihan Cao, Chiyu Chen, Haojiong Chen, Kai Chen, Pengcheng Chen, Ying Chen, Yongkang Chen, al. Intern-S1: scientific multimodal foundation model. arXiv preprint wwXhh:2508.15766 2025.
Akhiad Bercovich, Itay Levy, Izik Golan, Mohammad Dabbah, Ran El- Yaniv,,y, Omri Puny, Ido Galil, Zach Moshe, Tomer Ronen, Najeeb Nabwani, al. Llama-nemotron: Efficient reasoning models. arXiv preprint arXiv:2505.0044 0004999999009,,, 2025.
Wenrui Cai, Chengyu Wang. Junbing Yan, Jun Huang, and Xiangzhong Fang. Reasoning with omnithought: A large CoT dataset with verbosity and cognitive difficulty annotations. arXiv preprint arXiv:2505. 10937, 2025.
Jingyi Chai, Shuo Tang, Rui Ye, Yuwen Du, Xinyu Zhu, Mengcheng Zhou, Yanfeng Wang, Yuzhi Zhang, Linfeng Zhang, Siheng Chen, et al. SciMaster: Towards general-purpose scientific AI agents. part i. x-master foundation: Can we lead humanity's 's last exam? arXiv preprint arXiv:2507.05241, 2025.
Justin Chih- Yao Chen, Zifeng Wang, Hamid Palangi, Rujun Han, Sayna Ebrahimi, Long Le, Vincent Perot, Swaroop Mishra, Mohit Bansal, Chen-Yr Yu Lee, et al. Reverse thinking makes L.MMs stronger reasoners. arXiv preprint
2024.
Wenhu Chen, Xueguang Ma, Xinyi Wang, and William W Cohen. Program of thoughts prompt- ing: Disentangling computation from reasoning for numerical reasoning tasks. arXiv preprint arXiv:2211.12288, 2022.
11

---

Published as a conference paper at ICLR 2026
Tri Dao. Flashattention-2: Faster attention with better parallelism and work partitioning. arXiv:2307.08611, 2023.
Kehua Feng, Keyan Ding, Weijie Wang, Xiang Zhuang, Zeyuan Wang, Ming Qin, Yu Zhao, Jianhua Yao, Qiang Zhang, and Huajun Chen. ScilnowEval: Evaluating multi-level scientific knowledge of large language models. arXiv preprint (rxxiv2446.090990 2024.
Aaron Grattafiori, Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Alex Vaughan, et al. The Ilama 3 herd of models. arXiv preprini arXiv:2407.22 27740777217.,,.. 2024.
Daya Guo, Dejian Yang, Haowei Zhang, Junxiao Song, Ruoyu Zhang, Runxin Xu, Qihao Zhu, Shirong Ma, Peiyi Wang, Xiao Bi, et al. Deepseck-RI: Incentivizing reasoning capability in LLMs via reinforcement learning. arXiv preprins arXiv:2501.12945 2025.
Dan Hendrycks, Collin Burns, Steven Basart, Andy Zou, Mantas Mazeika, Dawn Song, and Jacob Steinhardt. Measuring Massive Multitask Language Understanding. arXiv:2009.0m 030000, 2020.
John Holland. Adaptation in natural and artificial systems: an introductory analysis with applica- fions to biology, control, and artificial intelligence. MIT press, 1992.
Xiao Hu, Xingyu Lu, Liyuan Mao, YiFan Zhang, Tianke Zhang, Bin Wen, Fan Yang. Tingting Gao, and Guorui Zhou. Why distillation can outperform zero-rl: The role of flexible reasoning, arXiv preprint arXiv:2505.21067 2025.
Yuzhen Huang, Yuzhuo Bai, Zhihao Zhu, Junlei Zhang, Jinghan Zhang, Tangjun Su, Junteng Liu, Chuancheng Lv, Yikai Zhang, Yao Fu, et al. C-Eval: A multi-level multi-discipline chinese evaluation suite for foundation models. Advances in Neural Information Processing Systems, 36: 2023.
Aaron Jacch, Adam Kalai, Adam Lerer, Adam Richardson, Ahmed El-Kishky, Aiden Low, Alec Helyar, Aleksander Madry, Alex Beutel, Alex Carney, et al. Openai ol system card. arXiv preprint arXiv:2412.167200 2024.
Joel Lehman and Kenneth O Stanley. Exolving diversity of virtual creatures through novelty search and local competition. Proceedings of 13th annual conference on Genetic and evolutionary computation, pp. 21 1-218. 2011.
Zhenyu Lei, Zhen Tan, Song Wang, Yaochen Zhu, Zihan Chen, Yushun Dong, and Jundong Li. Lear- ing from diverse reasoning paths with routing and collaboration. arXiv preprint arXiv:2508. 16861, 2025.
Hao Li, He Cao, Bin Feng, Yanjun Shao, Xiangru Tang. Zhiyuan Yan, Li Yuan, Yonghong Tian, and Yu Li. Beyond chemical qa: Evaluating LLM's chemical reasoning with modular chemical operations. arXiv preprint a38.v 2025.
Yuyang Liu, Liuzhenghao Lv, Xiancheng Zhang, Li Yuan, and Yonghong Tian. BioProBench: Comprehensive dataset and benchmark biological protocol understanding and reasoning. arXiv preprint 2rXiv:2505.07889, 2025.
I Loshchilov. Decoupled weight decay regularization. /7X 2017.
Ximing Lu, Seungju Han, David Acuna, Hyunwoo Kim, Jaehun Jung, Shrimai Prabhumoye, Niklas Muennighoff, Mostofa Patwary, Mohammad Shoeybi, Bryan Catanzaro, et al. Retro-search: Exploring untaken paths for deeper and efficient reasoning. arXiv preprint arXlv:2504.04383, 2025.
Yijia Luo, Yulin Song, Xingyao Zhang, Jiaheng Liu, Weixun Wang. GengRu Chen, Wenbo Su, and Bo Zheng. Deconstructing long chain-of- oftthhuggttttt A structured reasoning optimization framework for long cot distillation. arXiv preprint arXiv:2503. 16385, 2025.
AI Meta. The llaaa 4 herd: The beginning of a new era of natively multimodal ai innovation. http::/ai.. meta. htt.://mmmm---mmiimmmmmaa--iiiii
checked on, 4(7):2025, 2025.
12

---

Published as a conference paper at ICLR 2026
Samyam Rajbhandari, Jeff Rasley, Olatunji Ruwase, and Yuxiong He. Zero: Memory optimizations toward training trillion parameter models. In SC20: International Conference for High Performance Computing, Networking. Storage and Analysis, pp. 1-16. IEEE, 2020.
Jeff Rasley, Samyam Rajbhandari, Olatunji Ruwase, and Yuxiong He. Deepspeed: System optimiza- tions enable training deep learning models with over 100 billion parameters. In Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pp. 2020.
David Rein, Betty Li Hou, Asa Cooper Stickland, Jackson Petty, Richard Yuanzhe Pang, Julien Dirani, Julian Michael, and Samuel Bowman. GPQA: graduate- moogle-proot q&a benchmark. In First Conference on Language Modeling, 2024.
Liangtai Sun, Yang Han, Zihan Zhao, Da Ma, Zhennan Shen, Baocai Chen, Lu Chen, and Kai Yu. SciEval: A multi-level large language model evaluation benchmark for scientific research. In Proceedings of the AAAI Conference Artificial Intelligence, volume 38, pp. 19053-19061, 2024.
Qwen Team. Qwen2.5 technical report. arXiv preprint arXiv:2412.15115, 2024.
Zhaoyang Wang, Jinqi Jiang. Tian Qiu, Hui Liu, Xianfeng Tang, and Huaxiu Yao. Efficient long CoT reasoning in small language models. arXiv preprint arXiv::505. 18440, 2025.
Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Fei Xia, Ed Chi, Quoc V Le, Denny Zhou, et al. Chain-of thouhht prompting elicits reasoning in large language models. Advances in neural information processing systems, 35:24824-24837 2022.
Jingxian Xu, Mengyu Zhou, Weichang Liu, Hanbing Liu, Shi Han, and Dongmei Zhang. TWT: Thinking without tokens by habitual reasoning distillation with multi-teachers' guidance. arXiv preprint arXiv:2503. 2494,4 2025.
An Yang, Anfeng Li, Baosong Yang, Beichen Zhang, Binyuan Hui, Bo Zheng, Bowen Yu, Chang Gao, Chengen Huang, Chenxu Lv, et al. Qwen3 technical report. arXiv preprint arXiv:2505.08 09388, 2025.
Shunyu Yao, Dian Yu, Jeffrey Zhao, Izhak Shafran, Tom Griffiths, Yuan Cao, and Karthik Narasimhan. Tree of thoughts: Deliberate problem solving with large language models. Advances neural information processing systems, 36:11669-1111 1809-1182111 2023.
Yixin Ye, Zhen Huang, Yang Xiao, Ethan Chern, Shijie Xia, and Pengfei Liu. Limo: Less is more for reasoning. arXiv preprint arXiv:2502.033877 2025.
Yanzhao Zhang, Mingxin Li, Dingkun Long, Xin Zhang, Huan Lin, Baosong Yang, Pengjun Xie, An Yang, Dayiheng Liu, Junyang Lin, et al. Qwen3 Embedding: Advancing text embedding and reranking through foundation models. arXiv preprint 25Xivv2506.05/76 2025.
Haiteng Zhao, Chang Ma, FangZhi Xu, Lingpeng Kong, and Zhi-Hong Deng. BioMaze: Bench- marking and enhancing large language models for biological pathway reasoning. arXiv preprint arXiv:2502. 16660, 2025a.
Zihan Zhao, Bo Chen, Ziping Wan, Lu Chen, Xuanze Lin, Shiyang Yu, Situo Zhang, Da Ma, Zichen Zhu, Danyang Zhang, et al. ChemDFM-R: An chemical reasoner LLM enhanced with atomized chemical knowledge. arXiv preprint 2.XXi:2507.21990 2025b.
Lianmin Zheng, Wei-Lin Chiang, Ying Sheng. Siyuan Zhuang, Zhanghao Wu, Yonghao Zhuang, Zi Lin, Zhuohan Li, Dacheng Li, Eric Xing, al. Judging auddee with mt-bench and chatbot arena. Advances in neural information processing systems, 36:46595-46623, 2023.
Yaowei Zheng, Richong Zhang, Junhao Zhang, Yanhan Ye, Zheyan Luo, Zhanghhi Feng, and Yongqiang Ma. Llamafactory; Unified efficient fine-tuning of 100+ language models. arXiv preprint arXiv:2403. 2024.
Wanjun Zhong, Ruixiang Cui, Yiduo Guo, Yaobo Liang, Shuai Lu, Yanlin Wang, Amin Saied, Weizhu Chen, and Nan Duan. AgiEval: A human-centric benchmark for evaluating foundation models. arXiv preprint 230.00344. 2023.
13

---

Published as a conference paper at ICLR 2026
Xunyu Zhu, Jian Li, Yong Liu, Can Ma, and Weiping Wang. Distilling mathematical reasoning
capabilities into small language models, Neural Networks, 179:106594, 2024.
14

---

Published as a conference paper at ICLR 2026
APPENDIX
A1 ALGORITHM OF COT-EvO
Algorithm 1: CoT-Evo: Evolutionary CoT Distillation Framework
Input: Training data (x, 3) Don. LLM thinkers L, fitness function R (SEM. SLEN, and skNow), budget B, population size Roop
Output: Evolved CoT dataset Devo
// Initialization:
P +;;
for (x,1y) Dai do obtain K₂ via O;
for 4 (4,..... mm do
4 - (x) (Eq.
91 - (t:)) (Eq. 6), P+P (());
end
for
1 {I ml ) do
t, l (x. Kn)) (Eq.
8j R(t,) (Eq. 6 P+PU ((tz,
end
10 end
11
while budget B > 0 and s E P not converged do A NoveltySelec((P)
12
1/ select parents (Sec. 3.3
13
++ ft:
// offspring set
14
for to E do
draw operator op Uniform (Recombine Mutate);
16
op Recombine A 8EM(lo) = then
sample strategy provider tp P; fcand + C,, tp):
18
// recombination (Sec. 3.4
19
else
choose mutation mode {Add, Delete, Innovate):
21
leand f- (M, m)
// Reflective mutation (Eqs. 14 16
22
gandd R(teand)
// evaluate offspring
U (feand, Scand) );
24
end
25
P PUO;
11 Merge offspring into pool
26
keep top-Mppp trajectories from P by fitness to maintain 1;
[P] S npop:
27
B
28
end
return Dovo {1r,, t = arg maxteP,, R(t), 1
29
A2
ADDITIONAL RESULTS
A2.1 RESULTS FOR INDIVIDUAL TEACHERS
In Section reported the performance of the Single Teacher (ST) baseline on BioProBench and ChemCoTBench (Table I. as well as the reasoning quality of CoT's distilled under the ST setting (Table 2p These results were obtained by selecting the best-performing teacher the representative. In this section, we provide the detailed results for all individual teachers. Specifically, Table A1 presents the performance of all teacher models across all tasks in both benchmarks, while Table A2 reports the quality evaluation of the training CoT data distilled from each teacher LLM.
As presented in Table A1 the two most powerful teacher models, Deepseek-RR I and Qwen3-235B- A22B-think, demonstrate a significant advantage. The student models distilled from these teachers outperform those from other teachers on the vast majority of scientific tasks. This suggests that larger and more capable LLMs, with their superior reasoning abilities, can generate more useful and higher-quality data during the distillation process. Consequently. the distilled CoTs exhibit more logical consistency and contain richer knowledge. Furthermore, the results reported in Table A2
15

---

Published as a conference paper at ICLR 2026
Table Al: Performance comparison of Co against baseline distillation methods (ST. MT. BoK) and original LLM teachers across BioProBench and ChemCoT Best results are marked in bold, and second-best results are underlined.
BioProBenchh
ChenCoTBench
Teacher
PQA
ORD
ERR
Und.
Fdit
Reaction
Opt.
Acc:
EM 1
Acc.
FI
MAEJ
TMS1
Acc.1
Acc.f
SRT
FIS1
Base LLM: Llama3. I AB-Instruct
DeepSeek R1
0.431
0.338
0.500
0.667
0.707
0.249
0.467
0.640
0.236
0.510
Qwen3.32R-think
Qwen3-235B-A22B-hhh
0.427
0.341
0.542
0.665
0.791
0.156
0.495
0.555
0.200
0.527
Sooma---ou-BBawwaaa
0.429
0.193
0,505
0.553
1.276
0.151
0.482
0.512
0.182
0.506
Llamaf-Scou-CCod Scout-CoT'
0.416
0.235
0,512
0.490
1.218
0.214
0.454
0.471
0.170
0,368
Llama4 Scout
0.431
0.208
0.558
0.521
1.095
0.173
0.460
0.539
0.196
0.435
0.512
0.698
0.597
LLM:
@wen2.55-7B Instruet
DeepSeek-RI
0.604
Qwen3-32B-thint
0.506
0.331
0.593
0.584
0,982
0.146
0.500
0.426
0.177
0.414
(wen3-235B-A22B--2
0.518
0.348
0,563
0.649
0,929
0.162
0.505
0.445
0.185
0.503
0.516
0.289
0,571
0.536
1.104
0.129
0.495
0.358
0.174
0.538
Llamad-Scoo
0.502
0.308
0.553
0.494
1,033
0.114
0.468
0.370
0.174
0.417
0.274
0.568
COT-EVO
0.551
0.448
0.675
0.671
0.497
0.306
0.664
0.602
0.332
0.577
Base L.M:: Qwen3 8B shink
DeepSeek-RI
0.601
0.368
0.569
0.532
0.726
0.204
0.558
0.606
0.327
0.554
Qwen3-32B-think
0.567
0.357
0.616
0.521
0,435
0.268
0.583
0.562
0.337
0.548
0.547
0.361
0.525
0.534
0.405
0.183
0.520
0.550
0.375
0.599
Llama4- Saauttt---u---ee Brout-Backward
0.563
0.364
0.577
0.526
0.573
0.165
0.553
0.629
0.534
Llanu4 Col
0.546
0.327
0.475
0.602
0.525
Ilama4. Scout ToT
0.599
0.350
0.590
0.508
0.640
0.187
0.542
0.548
0.324
0.536
CoT-Evo
0.649
0.544
0.645
0.677
0.351
0.358
0.674
0.625
0.437
0.629
Table A2: Comparison data utilization (Pass), reasoning quality (Quality) and win rate (WR) across distillation baselines and CoT-Evo.
BioProBench
ChennoTDautaset
Teacher
Pass
Quality
WR
Quality
DeepSeek-R1
0.371
6.609
0.316
0.349
5.702
0.319
Qwen3-32B-thint
0.261
6.184
0.286
0.275
4.699
0.290
Dwen3-235B-A22B--00
0.375
6.741
0.329
0.309
5.497
0.292
-lama--Scout-- Backward
0.192
5.610
0.218
5.225
-lama4-Scout-CoT
0.127
5.121
0.149
0.251
4.978
0.266
Hlama4-Scout-Tois
0.166
5.119
0.165
0.217
4.516
0.218
CoT-Evo
0.729
8.230
0.704
7.847
confirm that these top-tier reasoning LLMs generally achieve higher data utilization (i.e., pass rate) and superior CoT quality. contrast, other L.M thinkers that rely on specific prompting strategies, such as Jlama4-Scout Co'T, show clear gap in data utilization, indicating that reasoning LLMss may be better eliciting more comprehensive and complete reasoning.
An interesting nuance can be observed between the top two teachers. On BioProBench, DeepSeek- RI's reasoning quality and win rate are slightly lower than those of (0wem3-335B-A22B--0
We attribute this to DeepSeek-RI occasionally generating redundant steps, tasks related to experi- mental protocols prioritize the causal relationship between steps over the exploration of multiple possibilities. Conversely, for tasks requiring more fine-gra ameinndieed deliberation, such molecule editing ChemCoTBench DeepSeek-RR R1 showcases richer ideas and more rigorous thinking, resulting in a higher overall quality score on that benchmark.
16

---

Published as a conference paper at ICLR 2026
Table A3: Sensitivity of CoT-Evo to & (k-nearest neighbors) on Llama3. 1-8-:..1-----nntttee Best results are marked in bold.
BioProBench
ChemCoT
Teacher
PQA
ORD
ERR
Und.
Edit
Reaction
Opt.
Acc.
EM
Acc. f
FI
MAF.
TMSt
Acc.f
Acc.f
SR1
FTSt
0,508
0.395
0.638
0.681
0.427
0.230
0.631
0.653
0.339
0,567
2 (default)
0,512
0,419
0.657
0.698
0.375
0.250
0.639
0.707
0.340
0,597
0.502
0.426
0.648
0.693
0.405
0.348
0.669
0.684
0.348
0.595
Table A4: Sensitivity CoT-Evo to A2) on Llama3. bold.
Best results are marked in
BioProBench
ChemCoTBench
Teacher
PQA
ORD
ERR
Und.
Edit
Reaction
Opt.
Acc.
EM 1
Acc.
F1
MAE!
TMS1
Acc.7
Acc.7
SR1
FTST
0.1.
0.471
0.408
0.624
0.679
0.415
0.281
0.680
0.618
0.311
0.591
0.3, 0.1 (default)
0.512
0.419
0.657
0.698
0.375
0,250
0.639
0.707
0.340
0.597
0.5.
0.514
0.415
0.653
0.480
0.268
0.619
0.656
0.368
0.586
0.3, 0.2
0,525
0.410
0,681
0.668
0.417
0.257
0.607
0.680
0.349
0.567
0.3, 0.3
0.484
0.398
0.533
0.678
0.287
0.168
0.519
0.656
0.268
0.539
A2.2 HYPERPARAMETER ABLATION STUDY
Sensitivity to Population Size and Iteration Budget. To assess the robustness of CoT-Evo to hyperparameter choices, conduct an ablation study on the population size nopp and iteration budget B. Our default settings, such as pop = 6, are based on two principles: (i) matching the initial CoT sample size used in the multi-teacher (MT) baseline, that the initial diversity is comparable without increasing cost in the first stage, and (ii) empirical evidence (Figure [3] left) suggesting that performance gains plateau when rlpop 2 and B improvement diminishes while computational cost rises sharply. This trade-off motivates our choice of 'ppp
Beyond these points, performance
practical balance between performance and cost. The results are shown in Table 3 where we observe that increasing Noop and B improves performance but only yields marginal benefits after the saturation point.
Sensitivity k-Nearest Neighbors (k). For the novelty-driven selection (NDS) strategy, we set the default A 2 for the k-nearest neighbors parameter, as it provides a good balance between stability and discriminative power. Larger values of k tend to overly smooth local structures, potentially overshadowing novel, low-frequency strategies, while smaller values (e.g.. k = 1) make the distance metric overly sensitive noise. As shown in Table A3 we experimented with A: E 2,) and observed minimal performance variation across different settings on both BioProBench and ChemCoTBench, supporting & = 2 as a robust and reproducible default choice.
Sensitivity Fitness Weights (A1, A2). The fitness weights A= and X2 in Eq. T6) reflect the relative importance of different evaluation criteria in our fitness function. As shown in Table we performed coarse grid search over \ 10.1, 0.3, 0.5) and A2 E indicating that performance remains stable as long as SEM (exact-match correctness) is given the highest weight, and BLEN and skNOw are given comparable smaller weights. When X2 is too large (e.g., 0.3), the model tends to select CoTs that use knowledge correctly but do not always reach the correct final answer, slightly hurting performance. Based on these findings, we chose λ1 = 0.3 and X 0.1 stable, low-sensitivity default.
0.3), with results
A2.3 GENERALIZATION TO NON-SCIENTIFIC DOMAINS
While our primary focus remains enhancing LLM performance in specialized scientific reasoning tasks, we also acknowledge the potential for CoT-Evo to be applied in more general domains. To validate the generalizability of approach, conducted additional experiments mathematical
17

---

Published as a conference paper at ICLR 2026
Table A5: Comparison of model performance (passl) across various general reasoning benchmarks. Best results are marked in bold.
Task
hase
ST
MT
BoK
LIMO
CoT-Fvo
AIME24
13.33
23.08
20.00
25.00
10.00
45.00
AMC23
47.50
70.59
75.00
75.00
85.71
MATH500
75.40
80.11
86.67
89.20
91.80
88.80
OlympiadBench
36.89
52.17
64.66
67.87
70.75
66.14
CHMMath
13.33
37.50
43.33
50.00
Gaokao
29.11
59.15
70.27
68.97
72.15
73.41
Kaoyan
30.15
41.14
44.81
40.74
47.24
46.10
GradeSchool
40.48
49.46
54.01
71.31
59.21
60.00
Minerva
49.63
48.36
49,46
51,03
58.22
60.54
GPQA
47.47
40.21
40.96
42.86
50.00
52.87
AVG.
38.33
50.18
51.73
59.64
62.19
64.21
and STEM tasks, using the LIMO dataset Ye et al. 2025). a curated collection 800 mathematical reasoning questions. Following the "Less More' principle, LIMO's limited training data has demonstrated the ability to match the performance of OpenAl's ol -preview model (Jaech et al. 2024). which utilizes reinforcement learning.
In these experiments, we used the Owwen..5-7B-Instie model as the base model and compared several distillation baselines mentioned in Section 4.2.2) (1) the base model without training, (2) Single Teacher (ST), (3) Multi-Teacheer (MT), and (4) Best-of-K (BoK). The results are summarized in Table Notably, ST and MT approaches, due lower data utilization rates (40.75% and 59.87%, respectively), showed significant performance gaps compared to CoT-Evo. On the other hand, BoK demonstrated higher data utilization rate (78.5%) and notable improvements in performance. particularly in general reasoning tasks, highlighting the importance of more granular distillation strategies non-scientific contexts.
Lastly, although the data utilization of LIMO and CoT-EvO was similar (100% vs. 95.75%).
CoT-EVo outperformed LIMO in terms of reasoning quality. This underscores the crucial role of data quality in achieving better performance, with COT-Evo demonstrating that the evolutionary refinement process can generate higher-quality CoTs, even when working with dataset similar to that used in LIMO.
A3 IMPLEMENTATION OF FINE-TUNING
In this work, to efficiently fine-tune LLMs, we leverage LLaMA- Factory (Zheng et al. 2024), Deep- Speed (Rasley al. 2020) with ZeRO Stage 2 (Rajbhandari al. 2020). and FlashAttentinn2 (Dao) 2023) across four NVIDIA A100 (80G) GPUs. We adopt AdamW (Loshchilov 2017) as the optimizer with 0.9, B2 0.95, and weight decay of 0.1. The peak learning with 10% warm-up steps followed by cosine decay, batch size of 32. We set the batch size to 32 and the maximum sequence length 16,384. Training is conducted for epochs ensure optimal performance.
is
2 10
A4 DETAILS OF COT QUALITY EVALUATION
While the student models distilled with CoT-EvO achieve the best overall performance, this does not directly verify the quality of the data generated by CoT-Evo. To comprehensively assess the quality of the synthesized CoTs, we adopt two complementary evaluation strategies: 1) absolute scoring of individual methods; and 2) pairwise comparison between CoT-Evo and baselines. These two strategies capture both absolute and relative perceptions CoT quality. The compared distillation baselines include Single Teacher (ST), Multi Teacher (MT), and Best-of-K (BoK).
18

---

Published as a conference paper at ICLR 2026
A4.1 ABSOLUTE SCORING
Absolute scoring provides a quantitative measure of how CoT's perform across dimensions of interest. Motivated by the design and objectives of CoT-Evo, we define the following five dimensions for evaluating reasoning quality:
Knowledge Diversity: Whether the model recalls introduces sufficient concepts, theo- rems, or knowledge fragments to support reasoning or verification.
Knowledge Accuracy: Whether the knowledge retrieved eited in reasoning is factually correct, so as to avoid propagating errors into the student model.
Reasoning Diversity: Whether the CoT explores meaningful alternative hypotheses
solution paths, promoting multi-perspective thinking and comprehensive understanding.
Logical Coherence: Whether the CoT follows clear, consistent, and error-free logical progression, avoiding excessive leaps or confusion.
Step Redundancy: Whether unnecessary repetitive steps minimized, yielding concise yet complete reasoning.
For each CoT under evaluation, we employ GPT-5 as an LLM judge to assess performance along the above five dimensions and assign an overall integer score ranging from 10. The full prompt provided in Prompt 1
Prompt 1: Prompt for Absolute Scoring
You strict evaluator. Given a reasoning process that leads the correct answer, your task evaluate quality this reasoning process across five dimensions: diversity knowledge, accuracy of knowledge application, diversity of thinking, logical coherence, and redundancy of steps. Finally, provide quality score.
[Reasoning Start] [reasoning] [Reasoning End]
You should strictly follow the instructions below:
1. First, identify all knowledge retrievals and citations within the reasoning chain. Then, leveraging your extensive knowledge and possibly external resources, judge their accuracy. Simultancously, determine whether the knowledge involved in this reasoning chain is diverse enough to help students learn more. If there is no knowledge application in the reasoning chain, you can ignore this aspect during the evaluation.
2. Next, read the reasoning process step by step and consider whether logic between each step is coherent (e.g.. there are causal relationships). At the same time, judge thinking methods are employed in the reasoning process, which can contribute to students' thinking development.
judge whether different
3. Then, determine whether there are any unnocessary or redundant steps. These steps may merely repcat previous ones or be mcaningless. If they exist, what is the proportion of rodundant steps? You can make rough estimate.
4. Finally, based on the analysis of the above five dimensions, provide an integer score between and 10. A score of 0 means the reasoning chain has no learning value, indicating issues such as large number of reasoning hallucinations, incorrect knowledge, and redundant steps. A score of represents the highest quality reasoning chain, with accurate knowledge application, diverse thinking, coherent logic, low step redundancy. As you are strict evaluator, please give a score < for reasoning processes with obvious flaws or those you're not satisfied with, and a score >= for qualified reasoning processes.
Please carefully analyze the given reasoning process. First, output your evaluation process step by step, and then output an integer score between and 10 on the last line. Please strictly follow the format below:
(Your evaluation process here)
[Resul]Scorr(/Resul]]
19

---

Published as a conference paper at ICLR 2026
A4.2 PAIRWISE COMPARISON
While absolute scores quantify quality in isolation, they may not fully capture relative improvements over baselines. To address this, we conduct pairwise comparisons between CoTs distilled by CoT- EVO and those generated by baseline methods.
For fairness, only CoT' with correct answers that were selected for training are included in the comparison. We again employ GPT-5 the LLM judge. Specifically, GPT-5 is given pair of CoTs (one from CoT-EVO, one from baseline) and asked to decide which trajectory is superior overall based on the five evaluation dimensions. The prompt is detailed in Prompt Importantly GPT-5 is not allowed to declare tie, i.e,, it must select the relatively better COT. We then report the win rate of each baseline the proportion of comparisons in which it was judged superior to CoT-Evo.
Prompt 2: Prompt for Pairwise Comparison
You striet evaluator. Given two reasoning processes, A and B, both of which lead the correct answers, your task evaluate the quality each reasoning process across dimen- sions:
knowledge diversity, accuracy knowledge application, thinking diversity, logical coherence, and step redundancy. Finally, determine which reasoning process has higher quality (there will be no tie).
[Reasoning Start] (reasoning a) [Reasoning A End]
[Reasoning Start]
(reasoning b)
[Reasoning B End]
Please strictly follow the instructions below:
1. First, identify all knowledge retrievals and citations within each reasoning process. Then, leveraging your extensive knowledge and possibly external resources, determine which has higher accuracy. Simultancously, assess whether the knowledge involved in each reasoning chain diverse enough to help students learn more.
2. Next, read the reasoning processes step by step and consider which one has more coherent logic between steps (e.g.. causal relationships). Additionally, judge which reasoning process employs wider variety of thinking methods, which can contribute students' thinking development.
3. Then, identify if there are any unnecessary or redundant steps. These steps may merely repeat previous ones be meaningless. they exist, estimate which reasoning chain has fewer redundant steps.
4. Finally, based on the analysis of the above five dimensions, comprehensively determine which reasoning process, A B, has higher quality. You should output either 0 or 1, where 0 indicates that A higher quality and indicates that has higher quality.
Please carefully analyze the two given reasoning processes. First, output your evaluation process step by step, and then output integer of 0 or on the last line represent your judgment. Please strictly follow the format below:
(Your evaluation process here)
[Result]O or [[Result]
The results of these two evaluation strategies are reported Table 2 of Section Since CoT-Evo is not compared against itself, its win rate is omitted. CoT-Evo consistently achieves higher absolute scores, surpassing 8.0 on average, reflecting the robustness of its quality. Moreover, the baselines achieve win rates below 40% in pairwise comparisons, confirming the significant relative advantage of CoT-Evo.
A5 PROMPTS FOR COT-EvO
This section details the prompts used in the evolutionary process of CoT-Evo, described in Section These prompts guide the LLMs to perform specific evaluation, recombination, or mutation tasks the reasoning CoT's
20

---

Published as a conference paper at ICLR 2026
A5.1 FITNESS FUNCTION PROMPTS
to evaluate the quality of candidate trajectories, employ an LLM-as- a-Judge assess the knowledge usage correctness.
As described in Section 3.2
Prompt for knowledge usage correctness evaluation This prompt instructs the LLM judge to score given CoT based on its application of the provided reference knowledge, returning score from to 5. The details of the prompt can be found in Prompt
Prompt 3: Prompt for Knowledge Usage Correctness Evaluation
You are meticulous evaluator specializing in scientific reasoning. Given reasoning chain and set of reference knowledge, your task evaluate the quality the reasoning process based solely how accurately and effectively utilizes the provided knowledge. Finally, provide quality score.
|Reasoning Chain Start]
(rcasoning)
[Reasoning Chain End]
[Reference Knowledge Start]
(knowledge]
[Reference Knowledge End]
You should strictly follow the instructions below:
1. First, carefully read the provided reference knowledge to understand the key facts, principles, and data points. Then, read the entire reasoning chain understand its overall logic and conclusion.
reasoning chain against reference knowledge step-hy-step. Assess the following: Is the knowledge used accurately and without misinterpretation? Are crucial pieces of knowledge from the reference correctly applied? Does the reasoning chain introduce any information supported by the provided knowledge?
Next, compare
"facts' that Finally, based your analysis of knowledge application, provide single integer score between I and score of indicates a complete disregard or fundamental misundcrstanding the reference knowledge. A score of 5 represents a perfect application of all relevant knowledge without any exteraa hallucinations. You should adhere to the following scoring rubric:
Score (Excellent): The reasoning chain perfectly and accurately utilizes relevant knowledge from the reference. No misinterpretations or unsupported claims are made.
Score (Good): The reasoning chain correctly most of the key knowledge, but may have very minor omissions or slightly imprecise application that does affect the overall logic.
Score (Acceptable):
The reasoning chain the knowledge from the reference, but noticeable errors, omissions, or misinterpretations weaken the argument.
Score 2 (Poor): There is significant misinterpretation omission of key knowledge. The reasoning relies heavily information outside the reference gets crucial facts from the reference wrong.
Score 1 (Very Poor): The reasoning chain completely ignores the reference knowledge, fabricates information, demonstrates fundamental misunderstanding of the provided facts.
Please carefully analyze the given reasoning process. First, output your evaluation process step by step, and then output integer score between and 5 on the last line. Please strictly follow the format below:
(Your evaluation process here)
[Result]Score[Ressi]
A5.2 CoT RECOMBINATION PROMPTS
The goal of recombination is create superior offspring trajectories that inherit and integrate the most effective strategies from different parent CoTs, promoting the fusion of diverse thoughts and knowledge.
21

---

Published as a conference paper at ICLR 2026
Prompt for Identifying the Binding Point This prompt tasks the recombiner model (C,) with analyzing strategy provider CoT (tp) to identify the endpoint of the last reasonable thought, which serves the crossover point. The specific prompt is detailed in Prompt
Prompt 4: Prompt for Identifying the Binding Point
You are rigorous scientific evaluator. When facing scientific problems, you excel at judging whether the chain of thought for solving the problem is sufficiently correct and logical, and can keenly identify occur but
the point where thought (CoT), and correct answer, your task is to preserve the longest reasonable prefix from CoT (i.c., the correct or logically sound skeleton) and delete the portion starting from where errors or deviations from rcasonable reasoning occur. Therefore, you need to locate the first sentence that exhibits logical errors significant deviation from correct reasoning and output that sentence exactly appears (ensuring it completely matches the content in the given thought, without rewriting summarizing).
longer corrected. Given problem, its corresponding chain of
[Query Start] {query}
[Query End]
[CoT Start] (thought) [CoT End]
[Answer Start]
(answer)
[Answer End]
#H# Instructions
You must strictly adhere the following instructions:
1.
Carefully read and analyze the entire reasoning trajectory and logic of the thought, ultilizing the correct answer to judge the correctness and reasonableness of each step.
2. After analyzing all steps, carefully determine from which sentence reasoning begins to exhibit obvious errors and the subsequent reasoning trajectory significantly deviates from the correct reasoning path (i.e.. no longer returns to reasonable reasoning trajectory). This sentence is the first sentence that needs to be deleted.
3. Note that if errors occur during reasoning but are eventually corrected through reflection or other means later, it indicates that the subsequent reasoning trajectory has not deviated, and such errors can be ignored!
4. You must ensure that extracted deletion sentence exactly matches the original thought word- for-word, without any rewriting.
#*# Output Format
1. You should first analyze the thought step by step and output the judgment of step accuracy to identify the reasoning prefix to be preserved and the first sentence to be deleted. If the final answer of the given CoT does not match the correct answer, you must find the first sentence that deviates from the correct reasoning path, because there has at least one error. At the end your output, you should output the first sentence to deleted the following format for casy answer extraction:
[RESULT START] First sentence be deleted [RESULT END]
Prompt for Extracting Unique Information This prompt instructs the model to perform a compar- ative analysis between the strategy provider CoT (4,,) and the target CoT (l,)). The goal is to isolate the unique, valuable reasoning steps and knowledge that present only in the provider 4p. The specific prompt detailed in Prompt
22

---

Published as a conference paper at ICLR 2026
Prompt 5: Prompt for Extracting Unique Information
You are an insightful scientific reviewer, adept at discovering and extracting key and uscful knowledge or information. Given scientific problem. chain of thought representing the model's current progress (CoT (CTT_curent]]
chain of thought from external exploration (CoT external), and the corresponding correct answer, your
to organize and extract the guiding information or knowledge CoT__xteraal that can help optimize or improve the reasoning trajectory of CoT cerrent, based on the correct answer. This valuable information will be used to guide CoT_curren to optimize and modify its thinking process facilitate obtaining the correct answer.
[Query Start] (query) [Query End]
[CoT Current Start]
[thought current)
[CoT Current End]
[CoT External Start]
[thought external)
[CoT External End]
[Correct Answer Start] (answer)
[Correct Answer End]
### Instructions
You strictly follow these instructions:
1. The steps, information final answer of CoT_external are partially incorrect. You should justify the correctness of them.
2. Carefully read and analyze _oT_external, and identify all the totally correct knowledge or information that are missing or incorrectly analyzed in CoT current based the correct answer. You need to ensure this information is useful to guide CoT_eurrent optimize improve its reasoning trajectory.
3. Rewrite each knowledge or information extracted from CoT external into self-contained, generalizable sentence.
4. Ensure that the extracted information completely correct (please judge based on the correct answer), genuinely exists, and only exists in CoT_external Ensure that there are no contradictions among the extracted information!!!
### Output Format
1. You should first highlight the correct answer, and then output the analysis of CoT__crreeee _urreet and CoT ext_rxtlmall identify useful knowledge or information in CoT_extema that is missing incorrectly analyzed CoT _urreent.
Next, you should judge the correctness of each knowledge or information extracted from CoT external based on the correct answer. You should delete the incorrect knowledge information after the judgement.
At the end the output, you should output the remaining extracted correct knowledge or information as a list according to the following format:
[RESULT START]
* knowledgeeinformatiion
* knowledge/nfoommatinn
IRESULT END]
Prompt for Generating a New Trajectory This is the final synthesis step of recombination. The prompt guides the model to generate new reasoning suffix, conditioned the stable prefix from the target CoT t, and the unique information extracted from the provider f,, thereby creating a novel, hybrid CoT. The specific prompt is detailed in Prompt
23

---

Published as a conference paper at ICLR 2026
Prompt 6: Prompt for Generating a New Trajectory
<think>
<lips>Before formally considering the user's question, let me reiterate my responsibilities: deeply analyze the user's inquiry. and breakpoints when necessary append additional correct information for subsequent reasoning. Breakpoints will wrapped with "<breakpoint>" and "</breakpoint>" containing key information required for follow-up analysis. will not treat the content within breakpoints as prior knowledge, but will revalidate or re-explain them during remaining reasoning steps. I will ensure contextual continuity before and after brcakpoints. I will detailed and rich thinking after each breakpoint ensure the accuracy and comprchensiveness of my reasoning,</oe </tips>>
(prefix)
<breakpoint>
have received following correct information that should use to continue my reasoning:
(brcakpoint)
I should mention all the information in my follow-up reasoning. I should revalidate re-explain the above correct information (within the "<breakpoint>") in my reasoning later. should continue reasoning from the previous context. </breakpoint>
A5.3 COT MUTATION PROMPTS
Mutation operators designed for local optimization and error correction. They introduce targeted variations into a single CoT to fix flaws, enhance quality, and escape suboptimal reasoning patterns.
Prompt for Additive Mutation This prompt instructs the mutation model (M.) to enrich a given CoT by elaborating on its reasoning. It is used to add more logical details, deeper explanations, or relevant domain knowledge where the original CoT was underdeveloped. The specific prompt is detailed in Prompt
Prompt 7:
Prompt for Additive Mutation
You reasoning expert rich in professional knowledge and good at thinking. Given query and a Chain Thought (CoT), your task add more details to the CoT make the thinking process more complete, coherent, and of higher quality. You should ensure that the final CoT includes more than [word] words.
[Query Start] (query) [Query End]
[CoT Start]
(thought)
[CoT End]
#*# Instructions
You strictly adhere the following instructions: Please read the CoT sentence hy sentence and identify assertions, assumptions, or conclusions that lack substantial evidence, collectively referred to as "unverified elements".
2. Leverage your extensive knowledge to add more evidence and details in the context of these unverified elements, using the same writing style the original text. Make that the final CoT includes more than [word) words!
Ensure that no characters in the reasoning chain are modified, only adding evidence and details. Output the optimized CoT from the beginning.
5. You should first output BHESULT_STARTTE then directly output the optimized CoT. and finally
24

---

Published as a conference paper at ICLR 2026
outpur "IRESUL.T_NDD Do not output other characters. The format is as follows:
[RESULT START]
Optimized CoT. using the same format the original CoT
[RESULT_END]
Prompt for Deletive Mutation To improve the signal-to-noise ratio of the reasoning, this prompt instructs the model to prune a given COT. removes redundant steps, unproductive explorations, or extraneous information, resulting in more concise and efficient trajectory for student model training. The specific prompt is detailed in Prompt
Prompt 8: Prompt for Deletive Mutation
You insightful scientific critic, adept identifying unnecessary steps and unusual words sentences in complete scientific reasoning process. Given scientific query and its corresponding Chain Thought (CoT), your task is to identify the core skeleton the reasoning trajectory and remove abrupt words and sentences, and steps that are completely unnecessary, meaningless, and do not advance the reasoning further. Finally, directly output the remaining complete, high quality, and clear reasoning trajectory. You should ensure that every character you output truly exists in the original text.
[Query Start] {query]
[Query End]
[CoT Start]
[thought]
[CoT End]
### Instructions
You must strictly adhere to the following instructions:
1. First, carefully read the CoT to find abrupt words and sentences, and redundant and meaningless steps that do not advance the reasoning further. DO NOT delete valuable exploratory steps, necessary information and knowledge obtained and retrieved
middle.
2. should be noted that since the CoT may reference correct answers, tips, or additional information provided by the user, although these external aids are necessary, the sources of this information, such as "the user says" "the tips mention", should not appear in the COТ. Please remove these information sources (c.g., 'user', 'tips', "correct answer') and treat the information the model's internal knowledge. details to ensure coherence.
removing these sources causes contextual incoherence, you can add some
3. Then, directly output the remaining complete, high-quality, and contextually coherent reasoning trajectory from the beginning. You should ensure that every character you output truly exists in the original text, i.c., you cannot modify any characters of the given CoT except for deleted sentences. Use the original format the COT.
4, A complete reasoning trajectory may at least includes 4 core elements: rephrase the query (DO NOT delete the first few sentences), find the solution step by step, validate the solution, and summarize the final result.
You should output "TRESULT_STARTT" START]" the beginning of your response, then directly output remaining reasoning trajectory. and output "[RESULT END]" at the end of your response. The format is as follows:
IRESULT STARTT Remaining reasoning trajectory here, using the same format as the original CoT
[RESULT_END)
Prompt for Innovative Mutation This operator is key mechanism for error correction in framework. The prompt guides the model to first diagnose the logical fallacies faulty CoT by using the ground-truth answer reference, and to summarize them into corrective advice. We then
25

---

Published as a conference paper at ICLR 2026
incorporate this advice into the original query to generate new, correct reasoning trajectory that avoids the identified mistakes. The specific prompt is detailed in Prompt
Prompt 9: Prompt for Innovative Mutation
Given a query, relevant chain thought (CoT), and correct answer, your task is to check correctness of cach step in the CoT based on the correct answer and find all the critical erross that occur in the COT. Finally, write each error as one-sentence advice to prevent the error from recurring.
[Query Start]
{query)
[Query End]
[CoT Start]
(thought current)
[CoT End]
[Correct Answer Start]
(answer)
[Correct Answer End]
### Instructions
Please strictly follow following instructions:
1. First, analyze the vorrectness of each step in the CoT based on the correct answer.
2. Then, identify all the critical errors that occur in the COT. This includes using incorrect knowledge, making wrong inferences, having faulty intuitions. Summarize
one-sentence advice to prevent the same erros from recurring in subsequent attempts. DO NOT mention the correct answer in your summary.
error
4. Output all the summarized errors a list, strictly following the format below:
[RESULT [SARRT]
* Device-I-summary
2-succyy-summmrry
[RESULT_ENT
Please output "IRESULT_S "SAURT"" first, then dircetly output all the summarized advices, and finally output "IRESULT_END]"
A6 TRANSITION KEYWORDS
In CoT-EVO framework, particularly within the CoT Recombination described in Section 3.4 need a systematic way to parse continuous reasoning trajectory into a sequence of discrete, coherent thoughts. To achieve this, we utilize predefined of transition keywords. These keywords act as linguistic markers that signal a shift, pause, or pivot in the reasoning process. By identifying these keywords, our framework can effectively segment long CoT into meaningful, modular thoughts. This segmentation is a critical prerequisite for identifying suitable "binding point", enabling the model to perform more structured and meaningful recombination operations between different reasoning trajectories. Below is the list of transition keywords employed in CoT-Evo.
Transition Keywords in CoT
"Wait", "But wait", "Alternatively", "However" "Let me", "Maybe", "Another", "Let's
see", "Backtrack", "Going back", "Okay", "Alright", "Hmm", "Hmmm", "Not sure", "Let double-check", "I think", "Good", "Got it", "That's correct"
26

---

Published as a conference paper at ICLR 2026
A7 USE OF LLMS
We acknowledge the use of generative Al in this work. Specifically, we employed LLMs to assist with response quality evaluation in Section 4.3 and provide editorial support during the preparation of the manuscript.
A8 CASE STUDIES
To provide more granular understanding of CoT-Evo's capabilities, this section presents two detailed case studies from distinct scientific domains: biophysical protocol sequencing task (Sec- tion A8.1) and complex chemical reaction prediction (Section A8.1). In both examples, we observe that even powerful teacher LLMs fail due to subtle yet critical flaws in their domain-specific knowl- edge or logical application. These cases are chosen to concretely illustrate how CoT-Evo moves beyond simple distillation. By injecting more accurate domain knowledge and refining the logical flow, CoT-Evo demonstrates its ability synthesize superior and correct reasoning path where the original teachers could not.
A8.1 CASE STUDY SEQUENCING PLANAR LIPID BILAYER PROTOCOL.
This case study involves sorting the procedural steps of a complex biophysical experiment (Planar Lipid bilayer), where the correct order depends on understanding the physical and temporal constraints of the technique. The teacher models, DeepSeek-RI and Qwen3-32B-think, both fail due to shared logical error. They incorrectly assume that all physical apparatus, such as the Curved Agar Bridges, must prepared before forming the delicate lipid bilayer. This reflects a superficial reasoning process that overlooks the practical vulnerabilities of the experimental setup.
In contrast, CoT-Evo demonstrates a superior reasoning capability by introducing accurate, domain- specific knowledge about the experiment's s constraints. It correctly identifies that the fragile lipid bilayer must be formed before the agar bridges are put in place to prevent physical disruption. By integrating this key piece of knowledge, COT-Ev Evo improves the overall reasoning logie, correctly sequencing the prerequisites (preparing lipids and protein) and the assembly steps. This allows it to construct a coherent and correct workflow that respects the real-world constraints the technique, showcasing its ability to refine flawed initial hypotheses into logically sound solution.
Case 1: Query
To understand the rolc of the mitochondrial protein MPV17, whose mutations are linked to mitochondrial DNA depletion syndrome (MDS), the following protocol used. The goal is precisely the channel activity of the Drosophila melanogaster version of this protein (dMpv17) in controlled environment using the planar lipid bilayer (PL.) technique.
Please sort the following procedural steps for this experiment in the correct order.
The steps
['dMPV17 17 Protein Preparation', "PLB Formation', "Preparation Curved Agar Bridges', 'Measure- ment of dMpv17 Activity in Presence Uridine', 'Lipid Solution Preparation', 'Channel Activity Recording']
Give the correct order of the steps list of their original indices (start from 0), other words.
Correct Answer: [4, 0, 2, 31
Case 1: Summarized reasoning trajectories of LLM thinkers
DeepSeck-RL
27

---

Published as a conference paper at ICLR 2026
Step 1:
Initial Hypothesis on Core Setup
My initial thought is to figure out the order of the core components. know that to form the bilayer (1), I first need the lipid solution (4). Then I consider the curved agar bridges (2). I reason that since the bridges are part of the physical setup, they should prepared very early, perhaps even before lipid solution made.
Step 2: Incorporating Protein Preparation and First Re-evaluation
Next, try to initially thinking it might happen after the bilayer is already formed. This creates a logical conflict, as the protein must be ready before it can be added to the bilayer. I try to resolve this by con- sidering few different permutations of the setup steps (bridges, lipids, PLB) and the protein preparation.
protein preparation (0) into the sequence. get confused about timing,
Step 3: Seff-Correction on Protein and Experimental Steps
I realize my previous thinking was flawed. It's clear that the protein must be prepared (0) before it is introduced into the system. It also logical that you first have record the baseline channel activity (5) before you can measure any changes caused by adding uridine (3), as you need control to compare against.
Step 4: Formulation of the Final (but flawed) Sequence
With my corrected logic, establish my final proposed order. conclude that the full process is: prepare the protein (0), prepare the agar bridges (2), prepare the lipid solution (4), and then form the PLB (1). Following the setup, the experiment proceeds with recording baseline activity (5) and then measuring the effect of uridine (3). This leads the final, incorrect answer of [0, 1,
Qwen3-32B-think
Step 1: Establishing the Initial Setup Order
started by recalling the general experimental flow. My first step was to order setup components. I decided that preparing the 'Curved Agar Bridges' (2) must be the very first step since they are part of the physical apparatus. After that, I correctly reasoned that the 'Lipid Solution Preparation" (4) must come before 'PLB Formation' (I), because the solution is required create the bilayer.
Step 2: Sequencing Protein and Recording Steps
Once the bilayer formation placed, moved to the protein and measurement steps. My key ervor was thinking that the 'dMPV17 Protein Preparation' (0) happens after the bilayer already formed. Following this step, correctly ordered data collection phase: first, the baseline 'Channel Activity Recording' (5), and then the specific experiment, 'Measurement of dMpv17 Activity in the Presence of Uridine' (3).
Step 3: Final Consolidation and Review
concluded by putting all the steps together into single sequence: bridges (2), lipids (4), PLB formation (1), protein prep (0), recording (5), and the uridine measurement (3). I did final check, and this order seemed logical hased on my flawed assumption about when the protein is prepared. This led finalize incorrect answer (2, 4, 1, 0, 3].
Casel: Summarized reasoning trajectories of CoT-Evo
Step 1: Establishing the Foundational Prerequisites
I began by considcring the standard workflow of PLB experiment. determined that the process must start with the preparation of the essential materials. 1 identified 'Lipid Solution Preparation' (4) as the logical starting point because the lipid biloyer is the foundational structure of the entire experiment.
28

---

Published as a conference paper at ICLR 2026
Next, placed 'dMPV17 Protein Preparation' (0) as a crucial, concurrent prerequisite, as protein must be purified and correctly folded before any attempt to incorporate it into the membrane.
Step 2:
Constructing the Bilayer
With the foundational materials ready, I reasoned that the next stop the formation of the planar lipid bilayer (PLB) itself (I). This critical process involves using the prepared lipid solution to create a stable, high-resistance membrane across the aperture in the experimental chamber, which will serve the host for the protein channel.
Step 3:
Finalizing the Electrophysiological Setup
After the delicate PLB is successfully formed, the next step is to finalize the setup for electrical recording. Crucially, placed 'Preparation of Curved Agar Bridges' (2) after the PLB is formed. This is because the agar bridges are part of the final recording circuit and adding them earlier could physically disrupt the fragile bilayer during its formation. This corrects a major error present in the other reasoning traces.
Step 4: Recording Baseline Channel Activity
Once the bilayer is formed and the agar bridges are in place, the prepared protein can be introduced, allowing it to insert into the membrane. The subsequent step is to record the channel's intrinsic behavior. identified this as 'Channel Activity Recording' (5), which serves the essential baseline measurement against which any changes can compared.
Step 5: Performing the Experimental Measurement
Finally, with baseline activity established, the experiment concludes with the specific test condition. This involves adding uridine to the system and performing the 'Measurement of dMpv17 Activity in the Presence of Uridine" (3). I placed this step last because it is a specific experimental intervention designed test the compound's 's effect on the channel's 's baseline function.
Step 6: Consolidating the Final, Correct Sequence
I summarized the entire logical flow: preparing the foundational materials (lipids, then protein). forming the bilayer, completing the electrical setup (agar bridges), recording bascline, and finally testing the experimental variable. This step-by-step construction, respecting physical and biological constraints of the technique, leads directly to the correct order: [4, 2, 5, 3].
A8.2 CASE STUDY ON CHEMICAL REACTION PREDICTION
In this case, we present a challenging reaction prediction task involving a Sonogashira coupling. Both powerful teacher LLMs,, DeepSeek-R1 and 235-m-3-33--A22--hhe ultimately fail predict the correct product. DeepSeek-RI correctly identifies the reaction type but makes a critical error by misinterpreting the heteroaryl triflate diazonium salt, leading an incorrect final structure. 111---235B-A22B--- performs even more poorly, failing entirely to parse the key reactant and consequently giving up on the problem, returning a starting material as its answer.
In contrast, CoT-Evo demonstrates its ability to synthesize superior reasoning path. It success- fully inherits the crucial initial insight from the teachers- correctly identifying the reaction Sonogashira coupling. However, it then corrects their shared, fatal flaw by accurately identifying the triflate as the leaving group on the heteroaryl electrophile. By combining the correct foundational steps from its teachers with new, pivotal insight, CoT-Evo not only avoids their errors but also creates a more accurate and enriched line of reasoning to arrive at the correct chemical product.
Case 2: Query
Given the reactants SMILES and reagents SMILES, your task to predict the major product(s) SMILES using your experienced chemical Reaction Prediction knowledge.
29

---

Published as a conference paper at ICLR 2026
Input:
Reactants SMILES separated by !
Reagents SMILES separated by
Output: Major Product
The output SMILES must be valid and chemically reasonable. Do not provide any additional information beyond the requested SMILES strings. The answer should be json format that includes the major product SMILES:
Question:
Reactants: C#Cclcecoo otC..c/ce.....i.iiiii////ooooooe ccccccccccccccccceeeccccccccce /cccc//ccccccccccc///cccccclllll (oooooooooooooooooooooooooooooo0 bew..e/...eclcooooeeeeeeeeeehhhe
Reagents:
Answer:
"Major Product":
Case 2: Summarized reasoning trajectories of LLM thinkers
DeepSeek-R1
Step 1: Initial Analysis and Key Misidentification
I began by analyzing each reactant to understand its role. I correctly identified the phenylacetylene (C#Cc1ccccc) 1), the palladium complex, and the copper(I) iodide ([Cu]I). Based on these components. I correctly hypothesized that the reaction likely Sonogashira coupling. However, made critical ervor identifying the third reactant, 0cc1cco (OS molecule as a diazonium salt, focusing on the n[nH] moiery, instead of correctly identifying it as heteroaryl triflate where the triflate group (=0) (=0)C(F) (F)F) is the actual leaving group.
(F)
misinterprette this
Step 2: Exploring Consequences of the Flawed Premise
Based on my incorrect "diazonium salt" hypothesis, explored various reaction mechanisms that were not relevant to the actual problem. spent considerable effort trying rationalize how a cyclic diazonium salt would decompose (e.g.. by losing N2 gas) and how the resulting species would couple with the alkyne. This led significant confusion tried parse the SMILES string and visualize ring-opening or rearrangement that would not actually occur.
Step 3: Acknowledging Contradictions and Reassessing the Goal
During my analysis, noticed contradiction prompt's instructions regarding whether to output the "Major Product" or "Byproduct". correctly concluded that the primary goal was to predict the major product, as shown in the example answer format. then returned to the chemical problem but was still hindered by my initial misidentification of the reactant, admitting that the structure complex and confusing under my flawed assumption.
Step 4: Formulating a Final Product Based on Misinterpretation
Despite the ongoing confusion, proceeded formulate final answer. maintained the general idea a coupling reaction. However, because I failed to recognize triflate as the leaving group, my proposed product, 0=c ccc (OS (=0) (F)) (C)F))(CCC22cccCCC [nH]1, incorrectly kept the triflate group on the molecule. Furthermore, incorrectly attached the phenylacetylene group to carbon atom adjacent the nitrogen in the ring, rather than the position of the leaving group.
30

---

Published as a conference paper at ICLR 2026
Qwen3-25BBAA2B-thinn
Step 1:
Initial Analysis of Reactants
began by attempting to identify component in reaction. correctly recognized phenylacetylene (C#Cc1ccccc1 and copper iodide ([Cu]I). also identified the palladium species as a catalyst, though I expressed some minor confusion about the exact SMILES representation of its triphenylphosphing ligands.
Step 2: Critical Failure to Interpret the Heteroaryl Electrophile
My reasoning process completely stalled when I tried to parse the SMILES string becume fixated on trying rocyclic ring system (speculating about triazoles, tetrazoles, etc.) and got lost trying count the atoms to determine the ring size, Critically, I failed to identify the most important feature of this molecule for the reaction: the triflate group (-OS (=0) (=0)C(F) (F)F) F) as an excellent leaving group. My inability to correctly interpret this key reactant prevented me from making any further progress on the reaction mechanism.
(=C (=))
(F)))))) (F)F)
the specific hete-
Step 3: Abrupt and Unreasoned Conclusion
short while was still struggling to understand the heteroaryl structure. Without providing any chemical justification logical path forward, gave up solving the problem. My final answer, C#Cc1 ccccel, simply returns one of the starting materials, which incorrectly implies that no reaction takes place.
My thought process
Case2: Summarized reasoning trajectories of CoT-Evo
Step Initial Reactant Analysis Reaction Hypothesis
My first step is to break down the reactants to understand their roles. identify C4Cc1cccce as phenylacetylene, the palladium complex catalyst, and [Cu]l co-catalyst. Based this combination a terminal alkyne, a palladium catalyst, and a copper co-catalyst, correctly hypothesize that the reaction is a Sonogashira coupling.
Step 2: Correctly Identifying the Electrophile and Leaving Group
Next, analyze the key heteroaryl reactant, C=C (=0))(F)(F)))n(n)))) correctly identify the crucial feature: the sulfonyloxy group (-OTT) is an excellent leaving group in cross-coupling reactions. This singular. correct insight is the pivotal step that allows for successful prediction.
Step 3: Applying the Correct Mechanistic Principles
I then consider the general mechanism for Sonogashira coupling, which involves steps like oxidative addition of the palladium the electrophile, transmetallation with the copper-activated alkyne, and reductive elimination. My reasoning correctly applies this mechanism the actual electrophile, heteroaryl triflate.
Step 4: Deducing the Final Product Structure
From the correct application of the mechanism, deduce that the reaction's 's outcome will replacement of the leaving group. The phenylacetylene group will form a new carbon-carbon bond at the exact position where the sulfonyloxy group was originally attached.
Step Constructing and Confirming Final Product SMILES
Finally, I translate this structural understanding into the final SMILES string. By correctly replacing the OS(=0) (=0))C(F))) F group with the CffCc1 cccce1 group, I construct and confirm the valid, chemically
31

---

Published as a conference paper at ICLR 2026
reasonable SMILES major product: Orclcccccoonnm]))cccccccece This is equivalent to correct answer
32


Reviews:
[{"review_id": "3NKe85kYCP", "reviewer": "Reviewer_9BYm", "summary": "This paper proposes CoT-Evo, an evolutionary distillation framework for generating high-quality Chain-of-Thought (CoT) data specialized for scientific reasoning. Instead of simply selecting CoTs from one or multiple teachers, CoT-Evo iteratively evolves reasoning trajectories through an evaluation–selection–variation–update loop. It combines ideas from genetic algorithms and novelty search to maintain reasoning diversity, integrates reflective recombination and mutation operations, and uses a composite fitness function evaluating correctness, coherence, and knowledge usage. Experiments on BioProBench and ChemCoTBench demonstrate substantial gains over single-teacher, multi-teacher, and best-of-K distillation baselines, with notable improvements even against large teacher LLMs.", "questions": "1. Could you clarify why the proposed evolutionary process particularly benefits scientific reasoning rather than other reasoning domains? Is there empirical or theoretical evidence that the novelty-driven selection aligns better with the nature of scientific reasoning tasks?\n\n2. Since the framework is general, it would be informative to include non-scientific benchmarks to test generalizability and demonstrate the method’s effectiveness beyond science.\n\n3. Regarding efficiency, how does CoT-Evo’s compute cost compare to standard multi-teacher distillation or rejection-sampling pipelines? Could a smaller population or fewer iterations retain most of the gains?\n\n4. In the fitness design, the length appropriateness and knowledge usage scores seem somewhat ad-hoc. How sensitive is the final performance to these weighting hyperparameters (λ₁, λ₂)?", "limitations": "", "rating": 2, "confidence": 4, "soundness": 1, "presentation": 4, "contribution": 2, "strengths": "1. The paper is well-organized, and the pipeline diagram (Figure 1) is visually appealing and instrumental in understanding the full workflow. It clearly depicts the multi-thinker initialization, novelty-driven selection, recombination, and mutation processes, providing an intuitive grasp of the iterative framework.\n\n2. The focus on scientific reasoning is timely and important. This area is under-explored compared with mathematical or commonsense reasoning, and the paper explicitly tackles the difficulty of distilling reasoning traces in scientific domains.\n\n3. Experimental results show large performance improvements across all evaluated datasets compared to strong baselines (single-teacher, multi-teacher, and best-of-K). Ablations also indicate that proposed components contribute meaningfully to performance.", "weaknesses": "1. Although the motivation centers on scientific reasoning, the method itself is very general and could apply equally to other reasoning domains. However, the paper does not include any cross-domain experiments to validate this generality. As a result, it remains unclear why this method uniquely addresses the challenges of scientific reasoning - particularly the lack of verifiable or reliable reward signals. The intra-chain aggregation and evolutionary refinement do not appear to inject additional domain knowledge beyond what the teacher already provides.\n\n2. The evaluation-selection-variation-update process is complex and involves multiple heuristics (novelty search, recombination triggers, mutation modes). The empirical section shows better results but does not convincingly justify why this evolutionary loop is necessary compared with simpler or alternative distillation techniques. Comparisons with other distillation baselines or under the token-budget-controlled settings would make the argument more convincing.\n\n3. The two key points raised in the Introduction: (1) single-teacher bias and pruning insufficiency, and (2) multi-teacher diversity without fine-grained control are not unique to scientific reasoning. These limitations apply to CoT distillation in general. Therefore, the framing as “scientific reasoning-specific” seems somewhat overstated.", "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": "cqcOMVU2vh", "reviewer": "Reviewer_tiKN", "summary": "Existing CoT distillation methods in scientific domains are vulnerable to issues of faulty reasoning and knowledge deficiency. Prior approaches either perform single-chain compression/pruning or select a single chain from multiple teachers, lacking the ability to refine and integrate reasoning at a fine-grained level. This paper proposes an evolutionary CoT distillation framework, COT-EVO, which emphasizes intra-chain recombination and mutation rather than merely inter-chain selection.", "questions": "See weakness.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "Proposes a novel evolutionary CoT distillation framework that introduces the concept of genetic algorithms into reasoning-path optimization. Demonstrates improved performance of small models in scientific reasoning tasks, with ablation studies verifying the effectiveness of the recombination, mutation, and novelty selection components.", "weaknesses": "The authors did not conduct direct comparisons with recent process-level distillation or evolutionary reasoning methods such as TwT, Retro-Search, and BREAD, leaving the unique contribution of COT-EVO unclear.\n\nThe paper does not compare its method with standard CoT under equal compute (equal token count) conditions.\n\nSome of the reported performance improvements are not statistically significant.\n\nThe method is only validated on small-scale models, and it remains uncertain whether the gains would persist for larger models.", "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": "4npLvbWAWc", "reviewer": "Reviewer_pgWS", "summary": "This paper addresses the problem in COT distillation for scientific reasoning: advanced LLM teachers often produce flawed reasoning. Distilling from these flaws limits student model performance.\n\nTo solve this, the authors propose COT-Evo, a novel \"Evolutionary CoT Distillation\" framework. The core idea is to actively \"evolve\" and \"synthesize\" higher-quality reasoning paths rather than just selecting existing ones.\n\nThe framework initializes a diverse pool of CoTs from multiple \"LLM Thinkers.\" It then iteratively optimizes this pool using an evolutionary loop: 1) Fitness Evaluation (correctness, length, knowledge use), 2) Novelty-Driven Selection (balancing quality and diversity), and 3) Recombination/Mutation (integrating strengths and fixing errors). This process generates a high-fidelity \"evolved\" dataset used to fine-tune student models.\n\nExperimental results show that models trained on the COT-Evo dataset achieve better performance on challenging scientific benchmarks (BioProBench and ChemCoTBench).", "questions": "Q1: The COT-Evo framework appears significantly more computationally intensive (e.g., in total tokens or LLM calls) than baselines like MT or BoK, given the iterative evaluation and generation loop. It would greatly strengthen the paper to include a quantitative discussion on this. For instance, could you provide a comparison of the approximate token consumption required to generate the dataset versus the baselines? Alternatively, an analysis of performance under an equivalent, fixed token budget would be very insightful for assessing the method's practical efficiency.\n\nQ2: While Figure 3 helpfully explores the budget ($B$) and population size ($n_{pop}$), could you provide more justification for the selection of other key parameters, such as the fitness weights ($\\lambda_1, \\lambda_2$) and the $k$-nearest neighbors value ($k=2$)? Even a brief explanation of how these were chosen, or a discussion of their sensitivity, would be valuable for reproducibility.\n\nQ3: Since the \"Recombination\" operation is well-defined as a \"guided generation\" process (using a prefix from $t_o$ and information from $t_p$), the analogy to a traditional EA \"crossover\" might not be necessary and could potentially cause confusion for readers familiar with classic EA terminology. Clarifying it simply as a novel, guided operator might be more straightforward.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "Creatively applies evolutionary algorithms and novelty-driven selection to synthesize superior reasoning, moving beyond the traditional \"select-the-best\" paradigm. Clearly identifies and offers a promising solution to the critical problem of distilling from \"fallible\" teachers in complex scientific domains.\n\nRobust validation on challenging benchmarks with comprehensive baselines. In-depth analysis and ablations effectively prove that performance gains come from higher-quality data, not just increased sampling.", "weaknesses": "The framework is computationally intensive, requiring multiple LLM thinkers and repeated LLM calls within the evolutionary loop. The practical overhead compared to baselines is not fully quantified.\n\nThe framework relies on an LLM for critical steps (fitness, recombination, mutation, and quality evaluation), creating a potential point of failure if the judge is biased or flawed.\n\nThe evolutionary process may be sensitive to hyperparameters (e.g., a small population size $n_{pop}=6$ and $k=2$). The justification for these specific choices is limited.", "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": "PNWxUSKD6r", "reviewer": "Reviewer_7Nvu", "summary": "This paper introduces CoT-Evo, an evolutionary CoT distillation framework for scientific reasoning. It generates diverse reasoning trajectories from multiple LLMs, enriches them with domain knowledge, and iteratively refines them using novelty-driven selection and recombination guided by a fitness function. The resulting dataset is used to fine-tune three compact-sized models, achieving strong performance on scientific reasoning benchmarks.", "questions": "See the weaknesses section", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. The paper is well-written and easy to follow.\n\n2. It introduces an evolutionary framework where novelty-driven selection, reflective recombination, and mutation are used to iteratively refine reasoning trajectories, which is shown to be effective and well-motivated.\n\n3. Fine-tuning three 7–8B models with the resulting dataset achieves strong performance, demonstrating the effectiveness of the proposed method.", "weaknesses": "1. Currently, the paper evaluates scientific reasoning only on BioProBench and ChemCoTBench. It would be helpful to include additional benchmarks, such as the well-known GPQA-diamond, to better demonstrate the effectiveness of the evolved CoT dataset.\n\n2. The paper does not report the reasoning performance of the student model after each iteration of CoT evolution. Showing how the selected CoT data at each iteration contributes to model improvement would provide more insight into the co-evolution process.\n\n3. CoT-Evo is specifically designed for scientific reasoning, but the paper does not evaluate its applicability to other complex reasoning domains, such as code reasoning, mathematical problem solving, or logical reasoning.", "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)