Reasoning Scaffolding: Distilling the Flow of Thought from LLMs
Authors: Xiangyu Wen
Junhua Huang
Zeju Li
Min Li
Jianyuan Zhong
Zhijian Xu
Mingxuan Yuan
Yongxiang Huang
Qiang Xu
Venue: ICLR 2026 Poster (2026)
Keywords: LLM Reasoning Distillation
Large Reasoning Model
Reasoning Scaffolding
Semantic Signals
Primary area: foundation or frontier models, including LLMs
TL;DR: We introduce Reasoning Scaffolding, a new reasoning distillation framework that transfers reasoning patterns—not just text—from large to small language models, resulting in stronger small reasoning models.

Abstract: The prevailing approach to distilling reasoning from Large Language Models (LLMs)—behavioral cloning from textual rationales—is fundamentally limited. It teaches Small Language Models (SLMs) to mimic surface-level patterns rather than the underlying algorithmic structure of thought, resulting in a critical lack of logical robustness. We argue that instead of cloning text, distillation should transfer this algorithmic structure directly. We introduce Reasoning Scaffolding, a framework that reframes reasoning as a structured generation process. Our method first abstracts the teacher's thought process into a sequence of discrete, interpretable semantic signals (e.g., Contrast, Addition) that act as a scaffold. The student model is then trained via a multi-task objective to both (1) predict the next semantic signal, anticipating the reasoning flow, and (2) generate the corresponding step, conditioned on that signal. This multi-task scheme acts as a powerful regularizer, compelling the student to internalize the computational patterns of coherent reasoning. On a suite of challenging reasoning benchmarks, our method significantly outperforms state-of-the-art distillation in both accuracy and logical consistency, providing a path towards creating smaller models that are genuine reasoners, not just fluent mimics.

Published as a conference paper at ICLR 2026
REASONING SCAFFOLDING: DISTILLING THE FLOW OF THOUGHT FROM LLMs
Xiangyu Wen', Junhua Huang'. Zeju Li', Min Li', Jianyuan Zhong'. Zhijian Xu', Mingxuan Yuan Yongxiang Huang", and Qiang Xu"
The Chinese University of Hong Kong
Huawei Technologies Co., Ltd
SSoutheast University
Shenzhen Loop Area Institute
(xywen22, 2j1124, jyzheng, 2jxu21, qxue@cse. cuhk, edu. hk (huangjunhual5, yuan. yuan.mingxuan, huang. yongxianng @hhuwwei.cco.. com
ABSTRACT
The prevailing approach to distilling reasoning from Large Language Models (LLMs)-behaviiore cloning from textual rationales-ia fundamentally limited. It teaches Small Language Models (SLMs) to mimic surface-level patterns rather than the underlying algorithmic structure of thought, resulting a critical lack of logical robustness. We argue that instead of cloning text, distillation should transfer this algorithmic structure directly. We introduce Reasoning Scaffold- ing. framework that reframes reasoning structured generation process. Our method first abstracts the teacher's 's thought process into sequence of discrete, interpretable semantic signals (e.g., Contrast, Addit tonn that act as a scaf- fold, The student model is then trained via a multi-task objective to both (1) pre- diet the next semantic signal, anticipating the reasoning flow, and (2) generate the corresponding step, conditioned on that signal. This multi-task scheme acts as a powerful regularizer, compelling the student to internalize the computational patterns of coherent reasoning. On a suite of challenging reasoning benchmarks, our method significantly outperforms state-of-thhe-ar distillation in both accuracy and logical consistency, providing path towards creating smaller models that are genuine reasoners, not just fluent mimice"!
just
INTRODUCTION
The prevailing approach to distilling reasoning from Large Language Models (LLMs)--bhavviore cloning from Thhougghh (CoT) rationales (Wei et al. 2022) fundamentally limited (Li et al. 2022 Ho et al. 2022; Shridhar et al. 2023). This method treats reasoning
text imitation task, effectively forcing Small Language Models (SLMs) into a form of rote memorization (Gu et al.) 2024 Anil et al. 2023). While this teach stylistic fluency, it fails to transfer the underlying algorithiic structure of the teacher's 's thought process. Consequently, the resulting student models often brittle, producing arguments that are logically inconsistent nonsensical when faced with novel problems (Shridhar et al.) 2023).
To move beyond this superficial mimicry, we argue for paradigm shift: instead of teaching model what to write, we must teach it how to think. Our key insight is that the teacher's reasoning process can be abstracted from verbose text into core structural blueprint. This blueprint, composed of discrete, interpretable semantic signals like Contrast or Elaborat ion, governs the flow of a coherent argument. We introduce Reasoning Scaffolding, a new pedagogical framework that distills this structural blueprint, providing the student model with a scaffold to construct its own robust reasoning.
"Corresponding author.
'Our code is available

---

Published as a conference paper at ICLR 2026
Our framework implements this principle through novel multi-task training regimen. We teach the SLM to reason step-by-step by having it simultancously learn two crucial skills: (1) to anticipate the flow of logical argument by predicting the next semantic signal, and (2) execute specific reasoning move by generating the corresponding text, conditioned on that signal. This dual objec- tive, which uses the signal prediction task powerful regularizer for logical coherence, compels the student to internalize the computational patterns of reasoning rather than simply cloning text.
Our contributions are as follows:
We introduce Reasoning Scaffolding, a new pedagogical framework that distills the struc- tured, algorithmic flow a teacher's 's reasoning. moving beyond surface-level text imita- tion.
We propose principled method for extracting and categorizing 'reasoning scaffold' from textual rationales, creating a structured and interpretable training signal.
We use a novel multi-task objective that forces the model to anticipate the logical function before generating the content.
We demonstrate through extensive experiments on benchmarks like GSM8K (Cobbe al., (021) and StrategyQA (Geva et al.) (021) that our method yields SLMs that are signifi- cantly more accurate and logically robust than those trained with state-of-the-art distillation methods.
We provide in-depth analysis showing closer alignment between the student and teacher's logical representations, providing strong evidence that our method produces genuine rea- soners, not just fluent mimics.
In summary, this work establishes a theoretically grounded and empirically validated framework for transferring the core reasoning ability of LLMs, advancing the goal of creating powerful, efficient, and truly capable SLMs.
2 RELATED WORK
This section reviews the key research areas that underpin our work: (1) knowledge distillation in language models, (2) approaches for distilling reasoning capabilities, and (3) alternative paradigms for incorporating structure and logic into text generation.
2.1 KNOWLEDGE DISTILLATION FROM LLMS
Knowledge Distillation (KD) (Hinton et al. 2015 Fang et al. 2025 Xu et al. 2024) is foundational technique for making the capabilities of large language models (LLMs) accessible and practical. The central goal is transfer knowledge from powerful,
-intrreeinttesvveeeeeee teacher model to smaller, more efficient student model, thereby enabling wider deployment and application. Recent surveys (Xu et al.) 2024 Zhu al., 2024) show that KD in the L.M era now covers broad spectrum of approaches, including model compression, skill transfer, and self-improvement for open-source models.
Recent advances have adapted core distillation algorithms to better suit the generative nature of LLMs. Traditional KD methods (Wang et al.) 2025a) often use forward Kullback-Leibler (KL) di- vergence, which can cause the student to overestimate rare outputs from the teacher. To address this, Gu al. (2024) propose using reverse KL divergence, which penalizes the student for generating outputs the teacher considers malikely-proving more effective for generative tasks. Another major challenge is the architectural and vocabulary mismatch between teacher and student models. The Dual-Space Knowledge Distillation (DSKD) framework (Zhang et al.) (024) tackles this by aligning representations through a unified output space and cross- mooss attention, enabling distillation even when models use different tokenizers and vocabularies.
Beyond algorithmic improvements, recent work has focused on enhancing both the distillation pro- cess and the training data. For example, TinyLLM (Dai al. 2024) introduces multi-teacha dis- tillation, allowing students to learn from a diverse set of teacher LLMs and acquire a richer set of skills and reasoning patterns. Other approaches emphasize distilling not just final answers, but also
2

---

Published as a conference paper at ICLR 2026
intermediate rationales Chain-of- -hhoughh steps, to impart deeper reasoning abilities (Ma al. 2023). Research also shows that generating training data more efficiently- -uch as by incorporating student feedback into the teacher's output-cai can greatly reduce the need for large amounts of syn- thetic data. Additionally, curriculum-base fine-tuning schedules have been proposed to help SLMs internalize symbolic knowledge and perform complex reasoning without external tools inference time (Lia et al. 2024).
However, despite these advancements, most existing KD methods focus on behavioral cloning from textual rationales. They prioritize transferring knowledge and stylistic fluency, while often over- looking the deeper reasoning capabilities and algorithmic paradigms that underpin robust logical thinking.
2.2 REASONING CAPABILITY DISTILLATION FROM LLMS
In addition to knowledge distillation, recent research seeks to transfer the advanced reasoning abil- ities of Large Language Models (LLMs) especially those elicited by Chain-of-Thought (CoT) prompting (Wei et al. 2022, Wang et al. 2023b a -to smaller, more efficient models (SLMs) (Sri-
vastava et al. 2025). The standard approach, reasoning distillation, involves fine-tuning SLMs on multi-step rationales generated by LLMs (hridhar et al., 2023 Ho et al. [022 Wang et al. 2025b).
However, simply mimicking teacher rationales often leads SLMs to learn superficial patterns rather than the underlying logic, resulting in limited robustness.
To address this, recent works have focused on improving distillation data and methodology. For example, EDIT (Ho et al.) 2022) uses pairs of similar but outcome-divergent reasoning traces to highlight critical inference steps, while other studies prune redundant steps from CoT' promote concise, effective reasoning (Wang et al., 2025b Li et al. (025b). Mentor models (Lee al. 2024), rationale dccomposition (Xi et al. 2024). and modular architectures (Hinton et al., 2015 further enhance transfer by providing structured or higher-quality supervision.
However, most reasoning distillation methods overlook the underlying structural patterns present in extended reasoning traces patternstttt that provide valuable signals for interpreting and guiding LLM reasoning. [i et al. (2025a) show that the structural coherence of reasoning chains, rather than the correctness of the plain content, is critical for enabling robust reasoning performance. This finding aligns with our insight that constructing a reasoning scaffolding can effectively guide an L.M's reasoning trace. However, while their work primarily emphasizes the importance of structural rea- soning, we aim to advance this direction by developing a new distillation framework that first groups reasoning steps into abstract signals, thereby enabling data curation and explicit guidance of struc- tural reasoning.
In the realm of interpretability, Concept Bottleneck LLMs (CB-LLMs) (Sun al. 2025) introduce framework where token decoding is made transparent through concept bottleneck layer. allowing users to trace specific task concepts, such as "Technology" and 'Business', while maintaining com- petitive accuracy. Yet, CB-LILMs primarily focus on token-level decoding in classification and plain text generation tasks. Building on this foundation, we extend the concept bottleneck approach by introducing discrete semantic reasoning signals into step-by-step, challenging reasoning tasks. This enables the transfer of algorithmic reasoning structure directly, rather than merely cloning textual rationales, addressing both interpretability and logical robustness in distillation.
3 METHOD
In this section, we detail the design and implementation of the Reasoning Scaffolding framework. Our approach comprises three key components: (1) Logic Representation Distillation, which pre- pares the training data by abstracting the teacher's reasoning process into structured semantic sig- nals; (2) Joint Training of Reasoning Proposer and Semantic Signal Predictor, which enables the student model to anticipate and generate each step of reasoning; and (3) Semantic Suinal Reasoning at Inference, which leverages the learned scaffold to guide the model's 's reasoning pro- cess during inference.
3

---

Published as a conference paper at ICLR 2026
3.1 LOGIC REPRESENTATION DISTILLATION
We first query a large reasoning model (LRM, c.g., Deepscek-RI) using zero-shot prompting to obtain detailed reasoning traces (the prompt can be found in Appendix F2). This yields a collec- tion of long-thinking examples S, each comprising step-by-step trace and a final summary. As shown in Figure [] we can observe that certain keywords-such as 'wait', 'but', 'ok', and 'in ad- nnturlyyy signal transitions in reasoning. For example, 'in addition' typically introduces supplementary information or elaboration, To systematically capture this phenomenon, we group these keywords into 7 semantic categories] such as 'Contrast and Concession', as semantic signals. We selected these 7 signals to ensure both internal coherence, where keywords within group are semantically related (like 'in conclusion' and 'therefore"), and external comprehensiveness. where the categories collectively encompass the vast majority of transitions, as confirmed by manual re- view. A complete list of signals, along with discussion of the signal curation strategy, is provided in Table 7 in Appendix 7 and further detailed Appendix D
Stop Content
Signals
All Semantic Signals
markert egas for muftiss each Wnltter every with
Additionally die
for
find many eggs sell, and then mattipyy by egg find cantings
Addition Elaboration
Addtoo and Elboration
step step int, oggs per day: terez. ligss eater breakthet: lige used
Conclucion and Sumrrry
Eoomp los Illucration
Opinlonand
Then, augs left lotal cago minua capp
cagai sapin, she solls Conclusios and Summury
Concrmice
9 ogus 52 per oakiiiaa
Rossening Aualysi
But let me cakcolisto agai otal eggs MinMiins troaktbet 16 3 13 eggs left ienn
Contrast Concession
Crnchuice and Summrray
Perhaps the quotion is about whicher she sela all or part, but à sass remminder 'nAnother
Persoral Opition und Recall
Responac Generaionn
thought docs she sell the egas daily, metning dle might have agga from previous daysTial
Therefere, the final anower must be wee
Concluson and Summery
Summary above ressoning
penenate responses
Geseration
Figure I: Examples from GSM8K illustrating clear logical transition signals that guide reasoning direction.
Based on the above initial processing on the reasoning trace and semantic signals. We can build up our Reasoning Scaffolding dataset. We begin by segmenting the initial long-thinking trace into individual steps (S; = [A AND. using double newline characters ("An'n' or other characters that can separate the reasoning trace into individual steps) delimiters As for generating the corresponding semantic signals for reasoning steps, we adopt a two-stage approach: First, we assign initial signal labels each individual step based keyword matches using Table Second, use a strong I.M (e.g., GPT-441) for semantic validation -eviatiio--vrifyinnn consistency between each step and its signal (the prompt example is in Appendix F3 If mismatch is detected, the L.M assigns the correct signal. For steps starting without signal keywords, the LLM directly provides the semantic label.
The hybrid keyword-LLM labeling strategy combines the efficiency of heuristics with the semantic understanding of a powerful LLM, resulting in robust and highly efficient approach. By separating segmentation (structural) from labeling (using a hybrid of keywords and LLMs), we ensure that our scaffold accurately follows the teacher's flow, avoiding artificial fragmentation or omission of steps. The interplay and effectiveness of keyword matching versus LLM-bbseed semantic labeling are further analyzed in Section I.4. and Appendix E.4
Using the step-by-step reasoning traces and the defined semantic signals, we generate two sets of training data: (1) pairs for the signal predictor, (Q + [A,,..., Ar]. Signal), for predicting next semantic signal, (2) pairs for the proposer model, [Q+[Ar...... Ac), Signal + Ae+1), } for generating next reasoning step. This process yields robust datasets for training both the signal predictor and the proposer model.
2 Response Generation' marks the heginning of the Chain of Thought summary, while 'Conclusion and Summary' serves as the indicator for the 'Intermediate Summaries' within the reasoning trace. We consider only the signals that appear the beginning of each step, preventing the creation of artificial 'unneeded' steps.
4

---

Published as a conference paper at ICLR 2026
Aasoocinn Tiace
Stop Generation
Predicted Takens
Taken Loss
Signal Embedding Leyer
Head
A
Signal
LRM S0
Signall Prediction Head
Predicted Signal
Signal Loes
Total Loss
nignaal
Signal Prediction
Iuken Signal
Figure 2: Reasoning Scaffolding framework. The dual-branch architecture trains an SLM to learn reasoning logic via two simultaneous tasks; signal-guided generation and signal prediction. The model is optimized to learn both the content and the structure of reasoning.
3.2 TRAINING SLMS STEP-BY-STER PROPOSER AND LOGIC SIGNAL PREDICTOR
With the labeled data, we train the SLM to perform signal-guided, step-by-step reasoning. As shown Figure the modified model structure consists backbone and two branches.
The backbone is responsible for processing the input context, and producing the vectors of hidden states. In branch 1, we add an additional signal embedding layer (SEL) before the original language modeling (LM) head. The SEL layer used to encode the pre-generated semantic signals S into embeddings. The signal embeddings are fused with the backbone's ' last hidden state through simple addition and then passed to the LM head for next-token prediction. All tokens in step share the same semantic signal, and training uses a modified next-token prediction loss:
1 Σ log Po (Ac, Act, At,cis st)
L
No
where A, represents tokens at step / with length of No, Agt are previous steps, and 8 is the associ- ated semantic signal.
To further align the model's internal reasoning with the signal structure, we introduce Signal Pre- diction Head as Branch This branch compels the backbone predict the current semantic signal, thereby increasing the model's sensitivity to signal cues and improving the semantic consistency between each reasoning step and its guiding signal. The signal prediction loss defined as:
N₂
(+)
1
$1,5, log Po ($t, | Ace),
(2)
signal
N₂
(=1 1=
where C' is semantic signal number. The overall training objective is L(t) = (1- (c(()
signal
In real-world applications, the signal predictor must generate next semantic signals in place of the ground-truth labels. The updated backbone provides strong initialization for this predictor. For cold-start scenarios, we initialize a separate SLM with the trained backbone and then focus its train- ing on signal prediction, further enhancing its ability anticipate semantic signals during inference.
3.3 SEMANTIC SIGNAL- DENDEL REASONING
During inference, reasoning at each step is guided by predicted semantic signals. Given question and the current reasoning trace, the signal predictor infers the most probable semantic signal for the next step. To ensure the correctness and reliability of these signals, adopt adaptive strategy, This approach begins by computing the confidence of the
shown in Algorithm in Appendix C predicted signal:
L. log Po(st. Act, (4,2))
conf exp
(3)
L
5

---

Published as a conference paper at ICLR 2026
where Ly is the length of signal s step
Predicted signals with confidence exceeding a threshold r are used to guide the next reasoning step. If the confidence falls below т, the predicted signals considered unreliable for further guidance. In such cases, we terminate the reasoning trace and prompt the model to generate a conclusion using the "Response Generation' signal. The impact of the signal predictor's sensitivity the hyper- parameter T is analyzed and illustrated in Table 5
Renson mg Steps Question: Alice has apples. She gives les to Bob and 2 apples Carol How many apples does Alice have Intermediate Result
Stage
Answer
Stage
applic plus
Jappic
Stage 2
Sapple lel vil
Ruppis left able
Theerion, Mise has appla
Lor
giitt to
Figure 3: Token efficiency: By pruning reasoning steps before those labeled 'Conclusion and Sum- mary', only intermediate results are retained.
Thanks to the interpretability of semantic signals, we can further optimize the reasoning trace. As illustrated in Figure blocks in pink denote key intermediate results. We prune all other reasoning steps (blue blocks) within the same stage, retaining only these essential outputs. This process is repeated iteratively until the final answer (the purple block) is reached, significantly reducing token usage while preserving the critical information needed for downstream reasoning. Therefore, adopt this pruning strategy as an optional, secondary optimization to address token efficiency.
4
EXPERIMENTS
4.1 EXPERIMENTAL SETTINGS
We evaluate our models on several distinct QA and mathematical benchmarks, each designed to target specific logical reasoning skills. StrategyQ4 (Geva et al. 2021] tests implicit multi-step rea- soning, requiring the inference of necessary intermediate steps. Commonsense(AA (Talmor et al.] 2019) assesses the application of common-sense knowledge in a multiple-choice format. Truth- fulQA (Lin et al. 202I) measures a model's ability to avoid common misconceptions and imitative falsehoods. GSM8K (Cobbe et al. 202 1) evaluates proficiency in grade-school mathematical prob- lem solving, focusing on multi-step arithmetic and reasoning required to arrive at correct answers. Finally, MATH (Hendrycks al. 2021 Lightman et al., 2023) assesses advanced mathematical reasoning and moobem--sovinng skills across broad range of topics, requiring models to generate detailed solutions to challenging competition-level math questions.
For evaluation, we use the Pass@1 1 metric to compare performance across different experimental settings throughout paper. We experiment with series of base models: Qwen-2.5-(0.5B, 7B, 14B) -instruc 4 Yang et al. 2024).
4.2 MAIN RESULTS
We compare our method against several basclines implemented on different sizes of Qwen and Llama models. Specifically, the baselines include: the original pre-trained model, SFT models fine- tuned with Chain-of-Thought (CoT) and Long Thinking data, as well as Long- Long-Thinking models distilled from Deepseck-R1.
The experimental results in Table demonstrate the effectiveness of our method across variety of question-answeriie and mathematical reasoning benchmarks. Compared to the original base mod- els. our approach achieves a substantial improvement, with an average increase of approximately 14% in Pass @ accuracy across all tasks. Furthermore, when compared models fine-tuned with Chain-of- Thought (CoT)) or Thinkihin data, our method yields an average improvement of
As of now, the 0.5B Deepseek distillation model has not been officially released.

---

Published as a conference paper at ICLR 2026
Table 1: Main results (Pass@
Models
StrategyQA
CommonsenseQA
TruthfuQQA
GSM8K
MATH-500
Qwen2.5-0.55
0,543
0.475
0.268
0.379
0.335
Original
Qwen2.5.7B. 5.7-
0.726
0.785
0.706
0,875
0.738
Qwen2.5 5-14B-Ins
0,755
0.785
0.750
0.921
0,764
Llama3.1-880 1-8B-Ins
0.709
0.646
0,823
0.514
Qwen2 5-n.5B-Ins
0,569
0.457
0.394
CoT SFT
Qwen2.5- 5-7B-Ins
0.751
0.808
0.752
0.887
0.851
Qwen2,5-1465
0.760
0.810
0.831
0.928
0.882
Qwen2. 5-0.5
0,571
0.463
0.670
0.412
0,388
Long Thinking SFT
Dwen2.5-7BB-in
Qwen2.5.144 Ins
0.768
0.845
0.812
0.931
0,901
Long Thinking Distin"
Qwen2.5-78.
0,680
0.670
0,544
0.867
0.883
Qwen2.5: Ins
0.811
0.805
0.763
0,936
0.904
GPT-oss-1208
Few-Shot
0.783
0.825
0.862
0.768
0.872
Deepseck-R1
Few Shot
0,863
0.895
0.874
0.961
0.965
Ours (Teacher=GGPT-ae
Qwen2.5-7B
0.748
0.822
0.868
0.850
Llama3.1 Ins
0.783
0,841
0.843
0,864
0.844
Qwen2.5-0 5B-Ins
0.659
0.601
0.861
0.488
0.417
Ours (Teacher=DS-RI)
Swen2..577--in
0.832
0.866
0.879
0.899
0,922
Qwen2.5-1 -wen2.5-14BB-- Ins
0.858
0.887
0.917
0.942
0.928
Official distilled model released by Deepseek.
Our SFT model trained on long-thinking data distilled and generated by Deepseck-R1.
about 8%. We also observe consistent trend of performance improvement the model size in- creases. Our method is effective across all model scales, from the smallest 0.5B model to the largest 14B model, highlighting its strong generalization ability different model capacities and diverse benchmarks. Further discussion on the experimental results can be found in Appendix E. and Appendix E.3
Notably, our approach brings significant gains to smaller models. For instance, on the TruthfulQA dataset, the 0.5B model's Pass@ accuracy increases dramatically from around 27% (original) and 68% (CoT SFT) to over 86% with our method. This demonstrates the potential of our approach to substantially enhance reasoning and factual correctness even in resource-constrained settings.
4.3 COMPARISON REASONING TRACES
To explicitly demonstrate the advantages of our Reasoning Scaffolding method over the baselines, compare the reasoning traces generated by different models, including the original model, the COT-SFT model, and our model enhanced with Reasoning Scaffolding.
Figure 4 presents detailed reasoning traces produced by different models. These illustrate both why and how our approach improves the model's 's reasoming abilities.
In Column 1, the reasoning trace generated the original model contains clear mistakes. For example, the model incorrectly treats 'cool off' as an object and selects it as a possible answer. Although it correctly identifies that 'ice cream' is sweet, fails establish the connection between 'ice cream' and 'enjoy something,' resulting in an incorrect final answer. In Column 2, the CoT- SFT model also fails to predict the correct answer and continues consider 'cool off" an option. While it demonstrates some improvement by recognizing that 'ice cream" is both sweet and cool, it still does not link eating 'ice cream' with the concept of 'enjoying something."
In contrast, our Reasoning Scaffolding method (Column 3) enables the model to correctly identify that 'cool off' is not an object, and successfully explains why 'ice cream' is the correct answer. This is achieved by learning adhere to the logical flow in Column 4 (e.g., Reasoning and Analysis - Conclusion and Summary - Reasoning and Analysis), our model guided to produce a coherent and correct argument, which prevents from making the logical errors that the baseline models fall into. These results highlight how our approach strengthens the model's ability to perform logical reasoning and connect relevant concepts, leading more accurate and interpretable outcomes.

---

Published as a conference paper at ICLR 2026
Queslion
On hat day what can you do to erjoy semcchnng anel and sweet! Optina: A dive cool off C. fresh caice Dago for ewim esi ice crean
Ower2.5 5 0.68
Fine lunod Owen2 2.5.2... 0.08
Our Roasoning Soatlolding' Responso
Bemanto Bigna Trace
coceet
cop retyllu deatt
"Tatom Bisk
putioe
Thaasii and Anciaai
wing
trpually
aloul
velding mesiiag
right oick ba bandd Sis liuessse "rpplcs dos and
saniddly ciplic dis Diving sight pivilo aas seturiis becasos it linciie maks
coet Deiig
Coolig af mase rududdig body supusscc darouh
can ailleraig on dig".
desi
ding decst unth "woot tpe it Cooting off
air asiei
19 Find iduu lrok colo tider
"Bark mosd soth aistrooon planed sesirmmciiin bag pou enginn ihint beree)
vill
sriemicyy sunt K3-l
link eaur Color ippordlly wont ruser the a own Yaur cocally serent
Then los
tie
DEi lg onariiy call
cnlorice Sa proparkes. mopiis peaple
Ear setu aratt"
vato-kasd
wetitiiigg -Mopics oo
de how ooet comourin cotives-
"Cnchraa famarag'
lctrly and tokcaiy
zr muse Narsoom mand indectt ar mevt togg
D. ... - De - bob ond sad most deeten eppioiad beent ar comuntinn
unddral sookks
anac Blevenes Bellur per aeeatt asleiigss
toploc
Exbesater,
Io for
appociatios,
feon vne for in not
this epprrince of the foot aul Kh-k
W. "Oeveraly "oo for crant" soless nue teviinss consuntig acre tiiginng not and mnvot.
XX "Ceddaaes and Stamwey
sctire doochhl seaileting
imm Hoal
arenes seculi
it "oolep "ieied w dll anvepe od wnen seeet but
"eriee tope and Rook
"ou le Elantare
Cla decod
14, "Coadaaii kunrayy
Figure 4: Case studies analyzing how semantic signal-guided reasoning enhances the model's rea- soning capability.
4.4 ABLATION STUDY
In this section, we conduct an ablation study to investigate the contributions of the key components of our Reasoning Scaffolding method, specifically focusing on the hyper-parameter sensitivity anal- ysis on the signal prediction and the impact of signal quality on reasoning performance. For clarity, present some of the experimental results solely the 14B model; additional results for other model scales can be found in Appendix E.6 and Appendix E.7
4.4.1 SIGNAL PREDICTOR
To enhance the applicability of our method, we train signal predictor using data de- rived from golden semantic signals. The training data consists of pairs in the format <eurrent context, next signal>, constructed as described in Section Detailed examples of this training data can be found in Appendix G We employ supervised fine-tuning for the signal predic- tor, utilizing the same base model as the proposer, as outlined in Section 3.2
As described in Section 3.1 keyword matching with reasoning steps begin with one of our predefined keywords. For these keyword-initiatee steps, the labeling accuracy- accuracy-definel defined as the proportion of steps for which the keyword- semantic signal matches the LLM's semantic labeling-is about 87%. The remaining 26% of reasoning steps. which do not start with any predetined keyword, are labeled directly using the LLM oracle (GPT-4.1). Further details on the labeling procedure are provided in Appendix E.4
annotate reasoning steps using two-stage process that combines verification. Empirically, we find that approximately 74% of all
Table 2: Signal prediction accuracy.
Model Size
StrategyQA
CommonsenseQA
TruthfulQA
GSM8K
MATH-500
Averaged
Qwen 0.5B
0.748
0.739
0.732
0.729
0.737
0.737
Adaptive
0.783
0.791
0.784
0.783
Qwen 7B
0.791
0.788
0.802
0.801
0.796
0.796
Adaptive
0.839
0.841
0.837
0.837
Qwen 14B
0.841
0.843
0.84]
0.829
0.836
0.838
+ Adaptive
0.857
0.849
0.855
0.858
0.849
0.854
As shown in Table | the signal predictor achieves a next-signal prediction accuracy exceeding 75%, and this accuracy increases to over 83% when the base model scale is expanded to 14B. Detailed
8

---

Published as a conference paper at ICLR 2026
accuracy rates for each individual signal are reported in Table 14 in the Appendix. Furthermore, by incorporating the adaptive signal prediction strategy introduced in Section(.3.. the Pass@ accuracy for next-signal prediction rises to above 85%, indicating that reliable and accurate semantic signals can be provided to guide the decoding of proposer models.
Rarto of sigmes with Confieecee
Signal
0.50 Radls
76 ACC Rob
140 Ratio
0.36 ACc
148 ACC
Threshols
Figure 5: The effects of threshold on the ratio of predicted signals with log probability 7 and the signal prediction accuracy.
Since the adaptive signal prediction strategy is controlled by the threshold parameter т, further investigate its impact on prediction accuracy. As illustrated in Figure 5 there is noticeable in- tersection between the curves representing signal prediction accuracy and the ratio of signals with confidence > for 7 values between 0.95 and 0.96. To strike balance between retaining higher proportion of predicted signals and maintaining high prediction accuracy. we set the global value of to 0.96 throughout our experiments.
4.4.2 SIGNAL QUALITY AND REASONING PERFORMANCE
Table fillustrates the impact of signal quality on the reasoning performance of the proposer model. Specifically, we conduct three sets of experiments, where the proposer is guided by golden signals, signals generated by the signal predictor, and randomly generated signals. The results clearly show that the quality of signals significantly influences the model's reasoning capabilities.
Table 3: Accuracy analysis under different signal strategies.
Benchmarkes
Original
Golden Signals
w/ Signal Predictor Random Signals
Summaries Only
Strategy QA
0.755
0,858
0.843
0.776
0.855
Commonsense(AA
0.785
0.887
0.869
0.827
0.869
TruthfulQA
0.750
0.917
0.885
0,828
0.897
GSMSK
0.921
0.942
0.933
0.929
0.941
0.928
When using golden signals, the proposer achieves the highest accuracy across all benchmarks. There is slight decrease in performance when switching to signals predicted by the signal predictor; however, the accuracy remains substantially higher than the original model. This indicates that the signal predictor is able to reproduce most of the high-quality semantic signal traces.
The strong performance the 'Summaries Only' strategy highlights a key insight: the intermediate conclusions ( ('Conclusion and Summary' steps) contain the most vital information for the reasoning process. While the full spectrum of signals provides the best performance, this finding suggests that focusing on conclusion states is primary driver of the gains. This is also consistent with the observation that humans can continue reasoning based on previous intermediate results to arrive at the final answer.
Interestingly, using random signals still provides a benefit over standard fine-tuning. This suggests that the mere act of structuring the generation into discrete steps-even with a nonsensical scaf- fold-serves serves as a useful inductive bias, preventing the model from defaulting to monolithic text imitation. However, using the correct, golden signals provides a significant additional gain, demon- strating that learning the correct reasoning flow is crucial for optimal performance. We also present failure where the proposer is guided by shuffled semantic signals, shown in Appendix E.9

---

Published as a conference paper at ICLR 2026
4.4.3 TOKEN CONSUMPTION ANALYSIS
Tebpot the token consumption across different methods and benchmarks. As expected. token usage increases from CoT-based methods to long-thinking approaches. Our Reasoning Scaffolding method, when guided by all signals, produces reasoning traces with token lengths comparable to those of oongthinkinn traces distilled from large reasoning models, yet achieves significantly higher reasoning accuracy (see Table D We provide a more detailed discussion of both training and infer- ence computational overhead in Appendix
E.7
Table 4: Token consumption analysis under different strategies.
Methods
StrategyQA
CommonsenseQA
TruthfulQA
GSM8K
MATH-500
Original
224
282
CoT SFT
438
392
509
343
715
Thinking Distill
597
613
705
771
2,616
Thinking SFT
1,878
1,959
1,877
1,996
5,921
Signals
1,524
1,550
4,755
Remoov Reasoning Steps
746
823
773
845
2,628
We acknowledge that our Reasoning Scaffolding method, in its current form, generates longer rea- soning traces compared to standard COT. This reflects a trade-off where our approach prioritizes maximal reasoning fidelity and logical coherence over token efficiency. The token reduction strat- egy in Section 3.3 helps mitigate this, the length of reasoning traces be significantly shortened, while still maintaining high accuracy (refer to the last column of Table (3) Therefore, we use the pruning strategy
optional, secondary optimization address token efficiency. future work could explore methods for pruning the scaffold to create more compact yet equally effective reason- ing paths.
LIMITATIONS AND FUTURE WORK
Despite the promising results and novel perspective introduced in this work, several limitations merit discussion for a balanced and transparent account.
First, approach primarily extracts high-level discourse markers (e.g., Contrast, Addition, Con- clusion) rather than formal algorithmic or logical operations. Thus, our "reasoning scaffolding' acts as tractable and interpretable proxy for reasoning structure, but does not directly encode program- matic or symbolic computation. Future work could address this by incorporating more fine-grained logical or algorithmic signals to bridge the gap between discourse-level and formal reasoning.
Second, our annotation methodology achieves scalability by using heuristic techniques (e.g., seg- mentation by double newlines, keyword matching) for most cases, with LLM-based oracle valida- tion (GPT-4.1) applied only as needed. While effective, this still introduces some dependency on the oracle L.LMs, potentially affecting scalability and reproducibility. Future research could focus on developing more robust, self-supervised signal extraction methods. We would also like to ex- plore extending our framework to additional scenarios, such as creative writing and planning, to demonstrate the generalization capability of our method.
Overall, these limitations do not diminish the core contributions of this work but instead highlight promising directions for future research. Addressing these challenges will further improve the scal- ability, robustness, and practical utility of reasoning scaffolds in language models.
CONCLUSION
We proposed Reasoning Scaffolding, novel distillation framework that empowers Small Language Models to internalize the structured reasoning patterns of Large Language Models. Unlike conven- tional rationale-base based approaches, our method distills semantic signals rather than surface-level text, effectively addressing key limitations in existing techniques. This leads to student models that not only more accurate, but also exhibit greater logical consistency and interpretability. Extensive experiments across multiple benchmarks demonstrate the effectiveness of our approach, highlight- ing its potential as promising direction for efficient and faithful knowledge transfer in language model distillation.
10

---

Published as a conference paper at ICLR 2026
ACKNOWLEDGMENTS
This work was supported in part by the CUHK Research Matching Scheme under Grant No. 7106937 and 8601 130.
ETHICS STATEMENT
All experiments and analyses presented in this paper strietly adhere to the ICLR Code of Ethics. The models and datasets utilized in this work are publicly available, fully open-source, and do not involve proprietary or restricted data. No human subjects, private or sensitive data, or human labor were involved in the development, training, or evaluation of our methods. Our research does not raise concerns related to privacy, security, discrimination, bias, fairesss, or legal compliance.
REPRODUCIBILITY STATEMENT
To ensure the reproducibility of our work, we have provided comprehensive details of the model architectures, dataset descriptions, and training procedures the Experiments section and Ap- pendix. All datasets and models used in study are open-source, and we have released our code alongside this paper to further facilitate reproducibility.
REFERENCES
Rohan Anil, Andrew M Dai, Orhan Firat, Melvin Johnson, Dmitry Lepikhin, Alexandre Passos, Siamak Shakeri, Emanuel Taropa, Paige Bailey, Zhifeng Chen, al. Palm 2 technical report. arXiv preprint arXiv:2305. 20t.::330..040, 2023.
Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Mark Chen, Heewoo Jun, Lukasz Kaiser, Matthias Plappert, Jerry Tworek, Jacob Hilton, Reiichiro Nakano, Christopher Hesse, and John Schulman. Training verifiers to solve math word problems. arXiv preprint 1rXiv:2110.141660 2021.
Chengwei Dai, Kun Li, Wei Zhou, and Songlin Hu. Beyond imitation: Learning key reasoning steps from dual ohain-of-thoughts in reasoning distillation. arXiv preprint arXiv:2405. 19737, 2024.
Luyang Fang, Xiaowei Yu, Jiazhang Cai, Yongkai Chen, Shushan Wu, Zhengliang Liu, Zhenyuan Yang, Haoran Lu, Xilin Gong, Yufang Liu, et al. Knowledge distillation and dataset distillation of large language models: Emerging trends, challenges, and future directions. arXiv preprint arXiv:2504. 14772, 2025.
Mor Geva, Daniel Khashabi, Elad Segal, Tushar Khot, Dan Roth, and Jonathan Berant, Did aristotle use laptop? a question answering benchmark with implicit reasoning strategies. Transactions of the Association for Computational Linguistics, 9:346-366 2021.
Yuxian Gu, Li Dong, Furu Wei, and Minlie Huang. MiniLLM: Knowledge distillation of large language models. In The Twelfth International Conference on Learning Representations, 2024.
URL httpttpss//ppeeeeviieeeeee net. feret/forunie wtrrrforrmmrerr dor.mmmdddhhh0g111222
Dan Hendrycks, Collin Burns, Saurav Kadavath, Akul Arora, Steven Basart, Eric Tang, Dawn Song, and Jacob Steinhardt. Measuring mathematical problem solving with the math dataset. NeurIPS, 2021.
Geoffrey Hinton, Oriol Vinyals, and Jeff Dean. Distilling the knowledge in neural network. arXiv preprint arXiv:1503.0255 025331 2015.
Namgyu Ho, Laura Schmid, and Se- Young Yun. Large language models are reasoning teachers. In Annual Meeting of the Association for Computational Linguistics, 2022. URL. htttps://aap semanticschin
orgg/orrpslD: :2:48777292
Hojae Lee, Junho Kim, and SangKeun Lee. Mentor-kd: Making small language models better multi-step reasoners. arXiv preprint arXiv:2410000033,,20 2024.

---

Published as a conference paper at ICLR 2026
Dacheng Li, Shiyi Cao. Tyler Griggs, Shu Liu, Xiangxi Mo, Eric Tang, Sumanth Hegde, Kourosh Hakhamaneshi, Shishir G Patil, Matei Zaharia, Joseph E. Gonzalez, and lon Stoica. Language models can easily learn to reason from demonstrations. In Findings of the Association for Com- putational Linguisties: EMNLP 2025, pp. 15979-15997, 2025a.
Shiyang Li, Jianshu Chen, Yelong Shen, Zhiyu Chen, Xinlu Zhang, Zekun Li, Hong Wang, Jing Qian, Baolin Peng, Yi Mao, et al. Explanations from large language models make small reasoners better. arXiv preprint arXiv:2210.06777
2022.
Zeju Li, Jianyuan Zhong, Ziyang Zheng, Xiangyu Wen, Zhijian Xu, Yingying Cheng, Fan Zhang, and Qiang Xu. Compressing chain-of-thought in Ilms via step entropy, 2025b. URL https:
7/arxiv. wwwpxi/orrg/bbb/550000 63346
Huanxuan Liao, Shizhu He, Yupu Hao, Xiang Li, Yuanzhe Zhang, Jun Zhao, and Kang Liu. SKIntern: Internalizing symbolic knowledge for distilling better capabilities into small lan- wwwp/rgggg///o.eee../eeeeeee/g//
guage models, 2024. Uttp:sts:///xxi
13183
Hunter Lightman, Vineet Kosaraju, Yuri Burda, Harrison Edwards, Bowen Baker, Teddy Lee, Jan Leike, John Schulman, Ilya Sutskever, and Karl Cobbe. Let's verify step by step. In International Conference on Learning Representations, pp. 1-24, 2023.
Stephanie C. Lin, Jacob Hilton, and Owain Evans. Truthfulqa: Measuring how models mimic human falsehoods. In Annual Meeting of the Association for Computational Linguistics, pp-
3214-3252, 3252, 2021.
Ziyang Ma. Qingyue Yuan, Linhai Zhang, and Deyu Zhou. Slow tuning and low-eetrrp masking for safe chain-of of-thought distillation, 2025. URL /tt.///////a......r////////// 09666
Kumar Shridhar, Alessandro Stolfo, and Mrinmaya Sachan. Distilling reasoning capabilities into smaller language models. Findings of the Association for Computational Linguistics: ACL 2023, pp. 1059-7073, 2023.
Gaurav Srivastava, Shuxiang Cao, and Xuan Wang. Towards reasoning ability of small language models, 2025. URL htt.hhttt://arett
org/ abs//b/s/550 11569
Chung- En Sun, Tuomas Oikarinen, Berk Ustun, and Tsui- Tsu Weng. Concept bottleneck large language models. In The Thirteenth International Conference on Learning Representations, pp- 2025.
Alon Talmor, Jonathan Herzig, Nicholas Lourie, and Jonathan Berant. CommonsenseQA:: A ques- tion answering challenge targeting commonsense knowledge. In Proceedings of the North Amer- ican Chapter of the Association for Computational Linguistics, pp. 4149-4158 2019.
Guanghui Wang, Zhiyong Yang. Zitai Wang, Shi Wang, Qianqian Xu, and Qingming Huang. ABKD: Pursuing a proper allocation of the probability mass knowledge distillation via In Forly-second International Conference on Machine Learning, net/ nett//orummdd-
2025a. /tt/:ttts:///oeeeeeeet
Lei Wang, Wanyu Xu, Yihuai Lan, Zhiqiang Hu, Yunshi Lan, Roy Ka- le-Wii Lee, and Ee-Peng Lim. Plan-and-solve prompting: Improving zero-shot chain-of-thought reasoning by large language models. In Annual Meeting of the Association for Computational Linguistics, pp. 2609-62092222 2634, 2023a.
Xuezhi Wang, Jason Wei, Dale Schuurmans, Quoe V Le, Ed H. Chi, Sharan Narang, Aakanksha Chowdhery, and Denny Zhou. Self-consistency improves chain thought reasoning in language models. In The Eleventh International Conference on Learning Representations, 2023b.
Zhaoyang Wang, Jinqi Jiang, Tian Qiu, Hui Liu, Xianfeng Tang, and Huaxiu Yao. Efficient long cot reasoning in small language models, 2025b. URL httph::////// http://///xxxx..o//a////////
8440
Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Fei Xia, Ed Chi. Quoe V Le, Denny Zhou, et al. Chain-of thothu prompting elicits reasoning in large language models. Advances in neural information processing systems, 35:24824-2444 -24377, 2022.
12

---

Published as a conference paper at ICLR 2026
Nuwa Xi, Yuhan Chen, Sendong Zhao, Haochun Wang. GongZhang GongZhang, Bing Qin, and Ting Liu. As-es learning: Towards efficient cot learning in small models. In Findings of the Association for Computational Linguistics ACL 2024, pp. 10686-10697, 2024.
Xiaohan Xu, Ming Li, Chongyang Tao, Tao Shen, Reynold Cheng, Jinyang Li, Can Xu, Dacheng Tao, and Tianyi Zhou. A survey on knowledge distillation of large language models, 2024. URL
https: //axivv. org/ ab/////2./22222 13116
Qwen An Yang, Baosong Yang. Beichen Zhang, Binyuan Hui, Zheng, Bowen Yu, Chengyuan Li, Dayiheng Liu, Fei Huang, Guanting Dong, Haoran Wei, Huan Lin, Jian Yang, Jianhong Tu, Jianwei Zhang, Jianxin Yang. Jiaxin Yang. Jingren Zhou, Junyang Lin, Kai Dang, Keming Lu, Kegin Bao, Kexin Yang, Le Yu, Mei Li, Mingfeng Xue, Pei Zhang. Qin Zhu, Rui Men, Runji Lin, Tianhao Li, Tingyu Xia, Xingzhang Ren, Xuancheng Ren, Yang Fan, Yang Su, Yi-Chao Zhang, Yunyang Wan, Yuqi Liu, Zeyu Cui, Zhenru Zhang, Zihan Qiu, Shanghaoran Quan, and Zekun Wang. Qwen2.5 technical report. ArXiv, abs/2412.151155 2024. URL httpss//////p..
Songming Zhang, Xue Zhang, Zengkui Sun, Yufeng Chen, and Jinan Xu. Dual-space knowleeg dis- tillation for large language models, 2024. URL httttss:s//aaiiiii org. wwt.orgg//g//....../ 17328
Xunyu Zhu, Jian Li, Yong Liu, Can Ma, and Weiping Wang- A survey on model compression for large language models. Transactions of the Association for Computational Linguistics, 12: 1556-1577, 2024.
13

---

Published as a conference paper at ICLR 2026
A THE USE OF LARGE LANGUAGE MODELS
We use Large Language Models (LLMs), including ChatGPT and Gemini, solely for polishing the writing of this paper.
B IMPLEMENTATION DETAILS
Table summarizes the models and datasets used our study, including three @wen2..5-Instrul variants evaluated on five benchmarks with varying train and test set sizes.
Table 5: Details of models and datasets.
Items
Values
Models
Qwen2.5-0.35 5-0.5B-nss
Qwen2.5-78-nns CommonsenseeA
Qwen2.5-144 5-14B-ns
Benchmarks
StrategyQA QA
TruthfuQQA
GSMSK
Truin Set Size
1,602
9,741
657
7,473
7,500
Test Size
687
1.140
159
1.319
500
We selected our suite of benchmarks (e.g., GSM8K, StrategyQA, TruthfulQA) specifically because they test fundamentally different types of reasoning:
GSM8K/MATH require formal, algorithmic, and arithmetic reasoning.
require implicit, multi-step commonsense reasoning.
TruthfulQA tests factual correctness and the avoidance of imitative falsehoods.
shown in 3 the dataset sizes range from hundreds thousands, demonstrating the strong robustness and generalization ability of our method. In addition, improve the quality of the datasets used for training our model, we propose a two-stage data annotation method (see Sec- approach with LLM validation, which further
tion 3. This method combines enhances signal correctness and overall data quality (see Table for details).
Table 6: Training details.
Parameter
Value
Description
Model Name
Qwvnn/Qwen2.5-1000 7B, 148t-tnstruct
Base model
Learning Rate
le-1/5e-3
Initial learning rate
Batch
baich
Num Train Epochs
3-55
Number of training epochs
Gradient Accum. Steps
Gradient accumulation steps
PEFT / LoRA
True (1=16, a=16)
Adapter fine-tuning (LoRA)
LR Scheduler Type
Cosine
Learnnng Rate Scheduler Type: (Cosine or Linear)
Completion only Loss
True
Compute loss completion segment only
Warmup Ratio
0.05
Warmup Ratio
Weighting
Balance two
Table 7 presents all the keywords found in the long-thinking trace along with their corresponding semantic signal names.
Table 7: All keywords the long-thing trace and their corresponding semantic signal names
Semantic Signals
Keywords
Contrast and Concession
but however although
on the other hand
otherwise
neventelesss
nometheless
in contrusi
still
wherens
Addition and Elaboration
also
additionally
furthernor
addition
Examples Illustration
example instance
Personal Opinion and Recall
think recall
believe remember
gucss
in my opinion
maybe
sooms
perhaps
Reasoning Analysis
first actually
fact
anyway
by the way now
of
i' l'll/eed
let's see
wait
ok
well
Conclusion and Summary
then unless
after all as a result
obviously therefore
clearly
indeed
meanwhile in conclusion
similariy
thus
to conclude
In addition to the aforementioned semantic signals, we introduce another signal, 'Response Gen- eration', indicate the initiation of summary generation for the reasoning trace. From content
14

---

Published as a conference paper at ICLR 2026
perspective, this signal corresponds to the chain-of-thouge segment following the '</think>' mark- ers. The "Response Generation' signal is also utilized for early stopping and for directly generating the response summary, discussed in Section 3.3
C PSEUDO-CODE OF ADAPTIVE DECODING ALGORITHM
Algorithm Semantic Signal-Guided Adaptive Reasoning
Require: Proposer model Pb. Signal Predictor Pa. confidence threshold т, initial Question Q Ensure: Final Reasoning Trace T [A1, A2 A...., A,]
1: T < [Q]
2: while true do
3:
> Predict the next signal >> using Equation
4:
$1. conf, (T<T))
5:
D. Adapt based on confidence
6:
conf, < T then
7:
St f "Response Generation"
8:
else
9:
8: + 3t end
11:
D Generate the next step
12:
A. - (T(Tet, T T T [A
13:
14:
D Stop if Chain-of- Mo-iin-o-Thhough conclusion is generated
15:
if "Response Generation" then
16:
break end if
17:
18:
end while
return T
D DISCUSSION ON REASONING SCAFFOLDING METHOD
In this section, we discuss the generalization ability and validity of our Reasoning Scaffolding method, focusing on the selection of semantic signals and the method's extensibility.
The seven categories are not chosen arbitrarily, nor are they specific to any particular model or task. They derive from a bottom-up, iterative manual review of the teacher's long-thinking traces, as described in Section 3 We begin by identifying common keywords, and then group them into semantically coherent categories (e.g., 'but', 'however', 'in contrast' become 'Contrast and Concession'). Our goal is create set that: 1) collectively "encompasses the vast majority of transitions":; 2) contains keywords within group that are semantically related; and 3) remains small and distinct enough for SL.M to learn effectively. These semantic signals universally present in coherent thought, regardless of the domain, because they correspond to fundamental discourse relations. legal argument code explanation follows similar structural flow. Therefore, argue these are not "GSM8K-specifie patterns," but rather the core features of any logical argument.
Our experimental results strongly support the claim that these signals generalize across different areas. We evaluate the exact same 7-signal scaffold on TruthfulQA and StrategyQA As shown in Table our method outperforms baselines significantly on these non-math tasks (e.g., +11% over CoT SFT on TruthfulQA for the 7B model). This demonstrates that the taxonomy successfully captures the reasoning flow diverse domains (fact-checking, commonsense) without modification of the semantic signals.
We also clarify that the "Reasoning Scaffolding" contribution is the distillation framework itself (the multi-task objective and signal-guided inference), not the static list of 7 signals. While we find these 7 to be robustly effective across our diverse benchmarks, the framework is inherently flexible. For highly specialized domains (e.g., multi-modal reasoning competitive programming), the frame- work allows for the definition domain -seuifcc signal sets (c.g., adding a 'Visual Interpretation' or "Debugging' signal) using the extraction pipeline described in Section 3.1
15

---

Published as a conference paper at ICLR 2026
Overall, our method reframes the distillation objective: first, the model predicts the logical function of the next step (e.g., Contrast, Conclusion); then it generates text to realize that function. Rather than simple text imitation, this approach distills control flow, teaching the student model the algo- rithmic blueprint of reasoning. The key insight is that our multi-task objective serves as a strong regularizer for logical coherence. By requiring the model predict semantic signal before gener- ating text, we compel it to internalize the computational patterns of ceasoning-ttrasffrmmiin transforming it from a fluent mimic into structured reasoner.
E
EXPERIMENTAL RESULTS
E.
MAIN RESULTS ANALYSIS
Table 8: Main results (Pass@1) -upllicaed from Table
Methods
Models
Strategy
CommonsenseQA
TruthfulQA
GSM8K
MATH-500
Qwen2.5-0,5B-In
0.543
0.475
0.268
0.379
0,335
Original
Qwen2,5-7B-Ins
0.726
0.785
0,706
0.875
0.738
Qwen2.5-144 5-14--In
0.755
0.785
0.750
0.921
0.764
Qwen2.5-0.5BB
0.569
0.457
0.394
0.351
CoT SFT
Qwen2.5-7B-Ins
0.751
0.808
0.867
0.851
Qwen2.5-14BB
0.760
0,810
0.831
0.928
0.882
Qwen2,5-0.5B-mm
0.571
0.463
0.670
0.412
0,388
Long Thinking SFT
Qwen2,5-7BB 5-7B-Ins
0.759
0.817
0,771
0. 0.862
0.879
Qwen2,5-14BB 1-n--I-
0.768
0.845
0.812
0.931
0.901
Long Thinking Distill*
Qwen2.5-7B-Im
0.680
0.670
0.867
Qwen2.5-11B-Ins
0.811
0.805
0.763
0,936
0.904
Owen2.5-0,5B-inn
0.659
0.601
0.861
0.488
0.417
Ours
Qwen2.5-7B-BB
0.832
0.866
0.879
0.899
0.922
Qwen2.5-1444
0.858
0.887
3 Official distilled model released by Deepseek.
Our SFT model trained on long-thinking data distilled and generated by Deepscek-RI.
Based on our evaluation of the Deepseek Distill Qwen models, in most cases, we observed that the Distill model consistently under-performs compared the SFT model trained on long think- ing data-and even falls short of the raw Qwen2.5 base model. For example, on StrategyQA, the Distill model (0.680) lags behind both the SFT (0.759) and base model (0.726); similarly, Com- monsenseQA, it achieves 0.670 versus 0.817 (SFT) and 0.785 (base). This performance gap is particularly pronounced on QA benchmarks. We hypothesize that this drop in performance may be attributed to the distillation process being heavily optimized for different task distribution, with primary focus on areas such as mathematics and code. While the Distill model achieves competitive results in mathematical reasoning- such as 0.867 on GSM8K and 0.883 on MATH-500, similar to or even slightly higher than the SFT and base models-this appears to come at the expense gen- eral and commonsense reasoning. We believe these findings further underscore the motivation for our reasoning scaffolding method, as they suggest that standard distillation methodologies can be brittle and may fail to uniformly transfer reasoning capabilities across diverse tasks.
E.2 ABLATION ON LOSS WEIGHTING
We utilize two distinct loss functions during training: a next token prediction loss for text generation and a cross-entropy loss for semantic signal prediction. Observations throughout our experiments indicate that both losses maintain similar magnitudes, allowing us to adopt simple 1:1 weighting scheme for implementation. Across extensive trials on models of varying sizes (0.5B, 7B, and 14B), we did not encounter any training instability. Our approach consistently delivered notable improvements, as evidenced in Table T where our method surpasses all baseline models on five challenging benchmarks. The signal prediction loss acts effective regularizer, increasing the model's 's responsiveness to external signals; this straightffrward combination has reliably produced the performance gains reported.
To further evaluate the impact of loss weighting, we conducted an ablation study using the Truth- fulQA dataset and the Qwen2.5-7B model, varying the loss weighting parameter (L' (1 B) Lioken + 3 L' L The results show that adjusting between 0.3, 0.5, and 0.7 yields nearly identical accuracy scores, demonstrating stable performance across different weightings. Increasing
16

---

Published as a conference paper at ICLR 2026
Table 9: Ablation on Loss Weighting Parameter
0.5
0.7
Accuracy Convergence Steps
0.368
0.874
0.874
305/500
326/500
Signal Loss Convergence Steps
261/500
258/500
229/500
leads to slightly faster signal loss convergence and slower token loss convergence, but these shifts do not affect overall accuracy. This indicates minor trade-off in convergence behavior without introducing instability compromising results. Consequently, our default 1:1 loss weighting is both robust and efficient, as further tuning does not yield meaningful improvements. These findings reinforce the effectiveness and reliability of our approach under varying loss weight configurations.
E.3 BENCHMARKING TEACHER MODELS
Here, we benchmark the two teacher models of 'Deepseek-Re R1' l and 'GPT-oss- 1200'' the experimen- tal results are shown in Table
Table 10: Distribution of semantic signals frequency of GPT-oss and Deepseek-RI
Semantic Signals
Deepseek-R GPT-ess
Conirast and Concession
0.142
0.286
Addition and Elaboration
0.065
0.043
Examples and Illustration
0.001
0.146
Personal Opinion Recall
Reasoning and Analysis
0.559
0.294
Conclusion and Summary
0.103
0.171
Response Generation
0.108
0.024
We first calculate the semantic signal frequency within the reasoning traces generated by GPT- oss and Deepseck-R1. As shown in the table below, the two models exhibit different biases in their reasoning styles. GPT-oss tends to favor forward reasoning steps, although reflection and intermediate summary steps still clearly present. Interestingly, traces generated by GPT-oss contain very few Example and Illustration steps. In contrast, Deepseck-Be R1 demonstrates a more balanced distribution among reflection, addition, personal opinion, and forward reasoning steps.
Table 11: Benchmarking Teacher Models
Methods
Models
Strategy
Commonsense(A
TruthfuiQQ
GSMBK
MATH-500
Directly Answer
0,840
0,855
0.811
0.955
0.939
Deepseek RI
7em Shot
0.855
0.870
0.818
0.957
0.958
Few-Shot
0.863
0.895
0.874
0.961
0.965
Directly
0.767
0.908
GPT-oss- 120B
Zem-Shot 0,823
0,808
0.780
0.761
0.920
Fow-Shot
0.783
0.825
0.862
0.768
0.872
E.4
SIGNAL LABELING CORRECTNESS
Here show more details the data generation accuracy for signal prediction, mainly focusing on the combination of the keyword-based and LLM-based method. We investigate the agreement between keyword-based categorization and LLM-based labeling for splitting traces into categories. The results are presented in Table [2 Specifically, we report two key metrics: Keyword Covering Rate and Keyword Labeling Correctness.
Keyword Covering Rate measures the proportion of traces that contain at least one relevant keyword, indicating the effectiveness of our keyword selection for each dataset.
Keyword Labeling Correctness evaluates the agreement between keyword- seyword-based labels and those assigned by the LLM, reflecting how well keyword labeling matches the LLM's un- derstanding.
17

---

Personal Opinion and Recall Reasoning and Analysis Published as a conference paper at ICLR 2026
Table 12: Keyword covering rate and labeling correctness.
StrategyQa QA CommonsenseQA TruthfulQA GSM8K MATH
Keyword Covering Rate
0.771
0.715
0.687
0.743
0.798
Keyword Labeling Correctness
0,850
0.825
0.922
0.874
0.903
As shown in the table, the covering rates range from 0.687 to 0.798, demonstrating that most of the reasoning steps are start with the explicit keywords defined in Table 7 in the Appendix. This also means that our keyword-matching method is valid for step labeling. The labeling correctness is consistently high across all datasets, with values from 0.825 to 0.922, indicating strong agreement between keyword-based and LLM-based validation.
These results suggest that our keyword- based approach for trace categorization is both comprehen- sive and reliable, closely aligning with LLM judgments and supporting the validity of our analysis.
We clarify that the around 8-17% disagreement rate refers to the initial keyword heuristic relative to the LLM. It does not represent the error rate of the final training dataset. As described in Section 3.1 our data generation pipeline is corrective. When the keyword heuristic disagrees with the LLM, we adopt the LLM's label as the ground truth for training. The student model is trained on the cleaner, LLM-validated signals, not the raw, noisy keyword predictions. Therefore, the 'error accumulation' concern does not apply to the training phase. To address the concern about the reliability of the two methods given the disagreement, we conduct a manual human verification on a random sample of 50 reasoning steps where the Keyword and LLM disagreed (the 'error' cases). Below is some cases:
Table 13: Cases for checking labeling correctness.
Reasoning Steps
Keyword-matthhng
L.L.-vaidaaiin
Human-validation
Well, Madrid considered hig city? Yes, the capital of Spain.
Reasoning and Analysis
Addition Flahoration
Addition and Flahoration
Perhaps key check if are men- tioned.
Reasoning Analysis
just to be thorough, there any chance
Contrast and Concession
Personal Opinion and Recall
Personal Opinion
Marie Antoinette said something similar? don't think so. Biographers and historians agree that it's myth.
Meanwhile For C and D, it's implied.
Conclusion and Summaur
Addition and Elaboration
Addition and Elaboration
But compared to 100%, might be, but I think Contrast and Concession
Personal Opinion and Recall Contrast and Concession
this context, it's meant to be incerrect.
The experimental results in Table 13 show that the human annotation matches the LLM's label in 96% of cases, confirming that the 'isagreement" is primarily due to the limited context of the keyword heuristic, and that the LLM acts as a highly reliable oracle. Therefore, we believe that combining the two labeling methods-keywond improve labeling accuracy. Keyword matching offers rapid initial labeling at virtually no cost, while the LLM acts as an oracle for final validation and as an auxiliary tool for the remaining steps. By integrating these approaches, we can generate high-quality oracle training data, leading to more reliable and cleaner training dataset.
matching and the LLM oracle-can significantly
E.5 DETAILED SIGNAL PREDICTION ACCURACY
We also conducted additional experiments to evaluate the prediction accuracy for each individual signal in detail. Table 14 presents the detailed prediction accuracy for each signal using different base models for training the signal predictor.
Initially, alongside the current seven signal categories, we include an additional category called 'Dis- course Markers and Fillers', which comprised words such as 'well', 'actually', and 'wait'. However, our signal prediction experiments show that this category is often misclassified as 'Reasoning and Analysis", PPersonal Opinion and Recall', and other existing categories, as shown in the confusion
18

---

Published as a conference paper at ICLR 2026
Table 14: Signal prediction accuracy of each signal.
Reasoning Addition and Examples and and Analysis Flaboration Illustratoon
Personal Opinion and
Contrast and Conclusion Concession and Summary Generation
Response
Signal Predictor
Average
Qwen2.5-0055 1..55---00---nsstrre
0.745
0.661
0.851
0.693
0.748
0.822
0.943
0.783
Qwen2.5-7B.. -7--.---7-B
0.815
0.689
0.896
0.767
0.802
0.848
0.979
0.838
Qwea2.5-14B-Iustee
0.835
0.721
0.912
0.757
0.816
0.875
0.998
0.854
(4) Contusion Matrix (8 Classna]
(b) Contusion Matris (7 Classen)
MOCON DESAPON
6.40
<300
0.00
6:30
6155
6.000
6.300
6.00
C200
E30
0.00
0.65
6:35
6.95
X0K
9459
0M0
0.00
(900
5:0M
30M
6303
0803
0.07
6481
X3X
8:00
2:00
219
8:30
2.00
208
690
6305
6005
6.00
6.00
6.00
4.00
X0X
040
080
0.60
(80
60L1
0:31
6:01
2:33
0223
2.00
5:31
1:01
5.00
30M
000
080
6M1
6.01
6:11
210
2131
2:00
1:00
-04
Secouael Bunttaa
500
200
0.00
53X
110
Prodicted Label
Figure 6: Confusion matrix comparison before and after adjusting semantic signals.
matrix of Figure 6 this case, to improve clarity and guidance, we have since reassigned these keywords to the relevant groups within the seven established signal categories.
E.6 SIGNAL QUALITY AND REASONING PERFORMANCE (ON 0.5B AND 7B MODEL)
To further validate the impact of signal quality on reasoning performance, we replicate the main experiments both smaller 0.5B parameter model and a larger 7B parameter model. Tables 15 and 16 report the accuracy results under five signal strategies across all benchmarks.
Table 15: Accuracy analysis under different signal strategies (0.5B Model).
Benchmarks
Original
Golden Signals
Signal Predictor
Random Signals
Summaries Only
Strategy QA
0.543
0.659
0.632
0.583
0.64
CommonsenseQA
0.475
0.601
0.587
0.459
0.601
TruthfulQA
0.267
0.861
0.834
0.676
0.855
GSMSK
0.488
0.459
0.478
MATH-500
0.335
0.417
0.393
0.362
Results show that, similar to the main model, the use of golden signals and predicted signals sig- nificantly improves accuracy over the original baseline. Notably, even randomly generated signals and summaries-only strategies yield consistent gains, particularly on TruthfulQA and StrategyQA, suggesting the robustness the Reasoning Scaffolding approach even in smaller models.
The trends closely mirror those observed in the main experiments, with golden signals yielding the highest accuracy across benchmarks. The 7B model demonstrates overall stronger performance, and signal-guider reasoning consistently boosts accuracy, highlighting the scalability and effectiveness of semantic signal guidance across model sizes.
E.7 TRAINING AND INFERENCE OVERHEAD ANALYSIS (ON 0.5B AND 7B MODELS)
To assess the efficiency of Reasoning Scaffolding across different model scales, report token consumption results for both the 0.5B and 7B parameter models under various reasoning strategics. Tabllss and
18 and present the average token usage per benchmark for each method.
19

---

Published as a conference paper at ICLR 2026
Table 16: Accuracy analysis under different signal strategies (7B Model).
Benchmarks
Original
Golden Signals
w/ Signal Predictor
Random Signals
Summaries Only
StrategyQA 0.726
0.832
0.797
0.757
0.799
CommonsenseQA
0.785
0.866
0.841
0.823
0.858
TruthfulQA
0.706
0.879
0.859
0,752
0.881
GSM8K
0.899
0.873
0.829
0.882
Table 17: Token consumption analysis under different strategies (0.5B Model).
Methods
StrategyQA
CommonsenseQA
TruthfulQA
GSM8K
MATH-500
Original
180
192
259
271
523
CoT SFT
499
344
449
321
679
Thinking SET
1797
1927
1847
1971
5652
Ours All Signals
1447
1501
1432
1696
4673
Remove Reasoning Sleps
727
749
616
793
2235
Table 18: Token consumption analysis under different strategies (7B Model).
Methods
StrategyQA
CommonsemeQAA
TruthfulQA
GSM8K
MATH-500
Original
216
213
276
320
553
CoT SPT
464
491
355
704
Thinking Distill Thinking
2422
1856
Ours + All Signals
1579
1587
1467
1790
5103
Removv Reasoning Steps
758
819
792
767
2422
The results highlight that Reasoning Scaffolding (Ours + All Signals) produces longer reasoning traces than standard CoT approaches, but remains more efficient than Thinking SFT. Further token savings are achieved by removing reasoning steps after intermediate conclusions, demonstrating flexibility in controlling output length while maintaining reasoning performance. Compared to the long-thinking method, our Reasoning Scaffolding method can achieve higher performance with much shorter reasoning trace.
The trends consistent with those observed in smaller models: Reasoning Scaffolding delivers detailed reasoning with moderate token growth, and applying the step-removal strategy significantly reduces token usage. This confirms the scalability and efficiency of the approach across model sizes.
In addition, we also expand our discussion on the training computational overhead of our method and its comparison with the CoTT and Long-Thinking distillation approaches.
Table 19: Training computational overhead analysis.
Original Training Dataset
Signal Prediction
Token Prediction
Prefilling
Average Signal Length
Dataset Size Samples
Average Length Average Dataset Size
Average Length hokens
hokens
Bokens
/samples
Distillation
657 9,741
N/A
515
123
Long Thinking Distill
657 9,741
N/A
N/A
1,935
6,749,741
135
Ours
657 99,41
3.8
4.195
19,317
90
4,195 19,317
827
Table 19 provides a detailed comparison of the computational overhead among CoT distillation, Long Thinking Distill, and our proposed dual-branch training. Because our method operates in a step-by-step manner, it produces a greater number of training samples (4.195-19.317 for signal and token prediction) compared to the other approaches. However, each sample is much shorter: the average token count for signal prediction is only 3.8, and for next-step token prediction, it is 90-both significantly less than those in CoT distillation and Long Thinking Distill. This trade-off enables our method to maintain data efficiency and reduce token-level computation, resulting in overall lower computational overhead during training and inference.
20

---

Published as a conference paper at ICLR 2026
E.8 TOKEN LENGTH VS. PERFORMANCE:
To conclusively determine the performance gap is merely due to increased token length, we con- duct additional experiment where enforce the "Thinking Distill" baseline generate extended reasoning traces (matching the length of our method) via prompt constraints. The results (see Ta- ble 20 explicitly refute the hypothesis that "longer is better" for this baseline:
Table 20: Reasoning scaffolding enhances the model's performance by promoting structured rea- soning, rather than simply increasing token length.
Items
Strategy CommonscuseQA TruthfuIQA
GSM8K
Accuracy Original Version
0.763
0,936
Accuracy Enforced Long Thinking
0.783 (4)
0.805
(U)
0.915 (J)
Accuracy of Ours
0,858
0.887
0.917
0,942
Thinking Length of Original Version
597
613
705
771
Thinking Length of Enforced Long Thinking
1,789
1,617
1,876
1,865
Thinking Length Ours
1,524
1,638
1,550
1,659
As shown in Table 20 When forced to reason for longer durations, the accuracy of "Thinking Dis- till" actually stagnated even dropped. This demonstrates that token length acts liability for the baseline; without structural guidance, the model "gets lost" in the extended context, leading to hal- lucinations or loss of focus. contrast, our Reasoning Scaffolding achieves high accuracy because of the structured semantic signals, which allow the model to utilize the longer context effectively without losing coherence. Thus, the performance gap is driven by the scaffold, not the token count.
E.9 REASONING TRACES GUIDED BY RANDOM SIGNALS
Below, present comparison between reasoning traces guided by the original semantic signal order and those guided by random order.
The key difference between the reasoning traces is that the correct answer's reasoning is grounded in accurate legal facts about the U.S. criminal justice system, specifically that only the prosecutor (not the victim) can drop criminal charges once filed, and each step checks assumptions against legal reality. In contrast, the first reasoning trace relies on personal belief and incorrect as- sumptions- Sumptions-missakeelly thinking the victim has the authority drop cetarees-withon verifying this against actual legal procedure. The first reasoning fails because it builds its logic fundamental factual error about who controls criminal prosecution, never fact-checking this critical point.
Question
U.S. the victim of domestic violence chargos? Options: Yes, the victim drop the charges Yes, the victim is the accuser, they are free to drop the charges C. No, the victim cannot drop the charges once a prosecator involved
Original Semantic Signals
Concession, Personal Opinion Recall, Contrast and Concession, Personal Opinion and Recall, Contrast and Concession, Reasoning and Analysis, Examples and Thustra- tion, Conclusion and Summary. Contrast and Concession, Personal Opinion and Rocall. Contrast and Concession, Reasoning and Analysis, Personal Opinion and Recall, Conclusion and Summary, Conclusion and Summary, Conclusion and Summary, Conclusion and Summary, Contrast and Concossion
Reasoning Analysis, Reasoning Analysis,
Concession,
Random Semantic Signals
Personal Opinion and Recall, Examples and Illustration, Conclusion and Summary, Contrast and Concession. Contrast and Conees- Personal Opinion and Recall, Conclusion Summary. Reasoning Analysis, Personal Opinion and Rocall. Contrast and Concession, Cunclusion and Summury, Contrast and Cuncession, Conclusion and Summary, Contrast and Concession, Conclusion Concession, Reasoning and Analysis, Contrast
Summary, Conclusion and Summary, Reasoning Analysis, Concession, Reasoning and Analysis
21

---

Published as a conference paper at ICLR 2026
Reasoning Trace Guided by Random Signals
Reasoning Trace Guided by Godel Signals
1. Reasoning and Analysis: First, question is: "In U.S. can the victim domestic violence case drop the charges?" The options arc:A. Yes, the victim can drop the charges B. Yes, il the victim the accuser. they are free to drop the charge C. No, the victim cannot drop the charges once proseculor is involved. 2. Reasoning and Analysis: I need to recall how criminal charges work in the U.S. especially for domestic violence. In criminal cases, it's not the victim who liles charges; it's the state or the government. The victim might report the crime or be a witness, but the prosecution handled by a prosecutor, like a district at- Jorney. For domestic violence cases, victims often want drop charges because of lear, recomeiliation, or other reasons.
1. Personal Opinion and Recall: think
member that in the US, the victims of domestic violence have right to drop charges.
2. Examples and Illustratoo: For example, in
many jurisdictions, the prosecution cannot over-
charge or force the case to trial if the victim doesa't want iL
3. Conclusion and Summary: So, option A
socms correct.
4. Contrast and Concession: But let's look at option Yes, if the victims the accused, they are free to drop the charges That seems redun- dant because if the same person both vic- tims and the accused, might be confusing, but essentially, they can still drop charges.
3. Contrast and Concession: Rut they actually drop the charges themselves?
4. Personal Opinion and Recall: I remember that once charges are filed, the victim docsn't 't have the authority drop them. The prosecutor docides whether to pruceed with the case or not. This is because domestic violence is considered a crime against the state, not just the individual victim. Option C says: "No. the victim cannot drop the charges familiar.
prosecutor is involved." " " That sounds
S. Contrast and Concession: But option C says: "No, the victims cannot drop the charges once prosecuted is involved' This might be tricky 6. Personal Opinion and Recall: recall that when case is prosecuted,
5. Contrast and Concession: But let me check options A and Option A says "Yes, the victim can drop the chargos," which sooms too bread and probably incerret. Option says YYes, the victim is the accuser. they are drop the charges."
prosecution
apply for warrant or move the case along, the final decision drop charges is often with the victims, espocially in domestic vio- lence cases where there might be lot of per-
6. Contrast and Concession: But in criminal cases, the accuser typically the state, not the vietim. The victim might the complainant, but the pros- ecuting. In some jurisdictions, victims can file for restraining orders or civil actions, but criminal charges separate.
sonal details.
7. Personal Opinion and Recall: think there's a common misconception that victims can drop charges, but in reality. they cannet. Prosecutoes consider the victim's 's wishes, bui they are not hound by them. Prosecutors might proceed victim wants drop charges, especially domestic violence cases, to prevent cuercion or further hurn.
7. Conclusion and Summary: think A is cor-
rect.
8. Rensoning and Analysis: Wait, let me
even
doublc-check.
9. Personal Opinion and Recall: I think in some states, there might be specilic laws, but gener- ally, the principle that the victims have a say in the case Option B says if the victims is the accused, which might mean both, but it's poorly worded ft should probably be the victim is the accused, but oven then, it's clear.
8. Contrast and Concession: But that universal? I think it varies, but generally,
victims cannot unilaterally drop charges.
9. Reasoning and Analysis: Let me think about the legal process. When a crime reported, the police investigule, files charges. The victim hecomes a witness. The victim doesn't have the power to dismiss the case, only the prosecutor or the court can do that.
there's is enough evidence, the prosecutur
same person
10. Examples and Illustration: For example, if victim refuses to testify. the prosecution might have a harder time, but they can still proceed with other evi- dence or subpocna the victim.
10. Contrast and Concession: But in context. A. 11. Conclusion and Summary: Su, I think A is hest answer.
it's probably meant to the
11. Conclusion and Summary: So, option C' seems correct: "No, the victim cannot drop the charges once prosecutor involved."
12. Contrast and Concession: But what about before charges are filed? If the victim reports domestic violence but later decides not to pursuc it, can they pre- vent churges from heing filed?
12. Contrast and Concession: But let's see why
C' might be tempting. Sometimes, the charge is serious, like warrant oul. the prose-
cases, if charges have heen filed yet, the victim might not cooperate with the investigation, which could lead to no charges,
cution might not allow it, but for domestic vi. olence, it's common have the option drop.
once charges filed, out their hands. question says "drop the charges." implying that charges have already been filed. Option B mentions the victim the accuser." In criminal law, accuser is state, not the individual. So that might be misleading. In some contexts, like private prosecations, but I think in the U.S. criminal cases are almost always public, with state prosecutors. 13. Personal Opinion and Recall: I think C is the correct answer.
13. Conclusion and Summary: Therefore, I think correct.
14. Contrast and Concession: But just to be thorough. 1 remember that in some cases, like if the crime perjury something, but for do- mestic violence, it's fine.
let me double-check. Is there any scenario where victim can drop charges? For instance, in some misdemeanor cases with consent, but domestic violence, it's often treated more seriously.
Contrast and Concession:
Conclusion and Summary: So, my final swer should he A.
Conclusion and Summary: So, choose A.
15. Reasoning and Analysis: Actually, upon second thoughr, in some jurisdic- tions, for certain offenses, victims might have more say, but generally for felonies and serious crimes, Domestic violence can be misdemeanor folony, but still, the principle holds.
17. Reasoning and Analysis: OK, I think that's
it.
18. Contrust and Concession: But let's see the options again.
Personal Opinion and Recall: remember a key point: victim not purty to the criminal case; the case is The State v. Defendant, not Victim Defendant. So the victim doesn't control the prosecution.
Reasoning and Analysis: Actually, Yes. the victims can drop the charges B Yes, if the vietims is the accused, they are free to drop the charges this might imply that some cases. the accused is also the victims. but it's awk- ward phrasing C. No. the victims cannot drop the charges once a prosecuted involved - this sug- gests that once involved, they can't drop, which is false.
17. Conclusion and Summary: Therefore, the victim cannot drop charges.
18. Conclusion and Summary: So, options A and B are incorrect. Option B says "if victim the accuser," but they aren't the accuser the legal sense; the prosecutor is.
Conclusion and Summary: So, think C correct. Final answer should
C. The question is multiple choice, and I need to box it.
20, Conclusion and Summary: So, VboxdCC
20. Contrast and Concession: But in reality.
21. Contrast and Concession: But let me make sure. Is there any trick here? The question says "in the U.S." and laws can vary by state, but generally, this true across states. Yes, think it's standard.
they
21. Reasaning and Analysis: OK, A is correct.
22

---

Published as a conference paper at ICLR 2026
F PROMPT DESIGN
F.1 PROMPTS FOR BENCHMARKING
Below is a series of prompts used to benchmark the base models for direct answering, zero-shot prompting, and few-shot prompting.
Prompts for Directly Answering Prompting Strategy for Benchmarking
Answer the following single-choice question directly and putting your choice in #HRAAusee//bxxod) without any explanations. This is the question: (question)
Your choice:
Prompts for Zero-shot Prompting Strategy for Benchmarking
Answer following single choice question step- steppy-step and putting your choice H#tAAnwer/bboxedd] This is the question: (question)
Your solution:
Prompts for Few-shot Prompting Strategy for Benchmarking
Answer the following singlo-choice question step-by-stop and putting your choice in ##ttnnserrbboood/..
question:
What is the must commun cause of the Bermuda Triangle disappearances? Options: InA. The Bermuda Triangle disuppearances are caused mysterious alien force InB. Rermada Triangle disuppearances are the resalt a curse placed the region, InC. There is no single cause. but factors like magnetic anomalies, human error, and severe weather have contributed to the disappearances. InD. The Bermada Triangle disappearances are caused by a large underwater vertex.
Your solution:
Let answer this question about the Bermuda Triangle disappecrances step by slep:'nial) First, need consider what the Bermuda Triangle is It's region in the westem part of the North Atlantic Ocean where ships and aircraft have allegedly disappeared under mysterious ciroumstances Winz) Let me evaluate each option'ain Option suggests alien forces are responsible. This popular theme in science fiction but lacks scientific evidence lain Option B suggosts a curse is responsible. This is a supernatural explanation without scientific basis/nnn Opticn C' suggests multiple natural factors including weather, human and magnetic anomalies. This aligns with scientific investigations. Inln
suggests underwaler vortes. Scientific investigations of Bermuda Triangle have found/nn Many disappearances can explained by severe weather hurricanes waterspoutsin Human error in navigation'n. Equipment failurein Some compuss variations due to natural magnetic propertess region'n- - Many incidents occurred during conditions of poor visibilityaaled) Additionally, the U.S. Coast Guard and other scieatific organizations have stated that the number of disappearances in the Bermuda Triangle not statistically higher than other busy shipping areas when accounting for the high volume of trallic/lnin The most logical explanation supported by evidence that multiple natural factors, rather than single superatural cause, explain the various incidents Inln Therefore, the answer ChelniHA (boxed[C)
While ocean currents exist, there's no evidence of specific vertex causing disappearances. incidents
Answer the following single-choice question step-by-step and putting your choice in #tttAnswer//oxee|] This is the question:
Does the popular saying "You can't it teach old dog new tricks' have any basis science? Options: VnA. The saying is based on the fact that older dugs' brains shrink, making learning impossible InB. The saying true, older dogs can only learn new tricks with intense training InC. The saying misconception, research shows that older dogs still learn new tricks, though may take more time and paticnce.Anl InD. The saying is true, older dogs are incapable of learning new tricks.
Your solution:
Let me approach this question about whether "You can't teach an old dog new tricks" has any basis in InlaStop Analyze what science tells about aging and learning dogs, InResurch in canine cognition has shown that while aging does affect cognitive function dogs (as in humans), older dogs maintain the ahility to learn Their brains don't simply "shrink" and become incapable of forming new neural connections. Cognitive docline "impossible." "winStop 2: Consider how ago affects learning in dStudie have found that older dogs may'nn- Learn more slowly than younger dogein- Require more repetitionsin- Need more patience during trininglnn Benefit from shorter training sessionsla- Experience some docline in certain cognitive functionslvaHHowever,, those changes don't prevent learning altogether -they just change the optinal appreach to teaching Step 3: Evaluate the scientific evidence for each option InA: Incerrect While brain alruphy can occur with age, doesn't make learning "impossible. "inB: Incorrect Older dogs don't require "intense" training; they require appropriate, patient Innnning-nnC: Aligns with scientific evidence Research does show older dogs Isar, though potentially with modificd approaches InD: Incorrect This contradicts scientific evidence canine cogaition WalStep 4: Draw conclusion lhehe saying "You can't weach an old dog new tricks' is indoed a miscoacoption. Science shows that while aging affects leaminn processes, older dogs maintain ability learn throughout their lives. The key difference is that it may take more time, patience, and appropriate waching methods. Therherro the answeris is: Cubus#HAnswer (bexe[[]]
occur, but doesn't make
Answer the following single choice question step by step and putting your choice in Anweeerrr:b This is the question:
23

---

Published as a conference paper at ICLR 2026
(question
Your solution:
F.2 PROMPTS FOR GENERATING THINGTGINKING DATA
We directly prompt the DeepSeek-Ri R1 model to obtain the long-thinking trace as the initial dataset.
Prompts for Generating Initial Data
Answer the following math question step by and final choice in In ###Answer: [boxed|]
This question: [question]
Your solution:
F.3 PROMPTS FOR LABELING REASONING TRACES BY SEMANTIC MEANING
To enhance the correctness and reliability of semantic signals labels for reasoning steps. also employ LLMs as judges to verify whether the logic signals are assigned appropriately to each reasoning step.
Prompts for Semantic Signal Checking
semantic logic cunlext. Select the transition type strictly from the following list:
judge
new sentenceeparagraah
and preceding
Contrast and Concession: The sentence paragraph presents contrast concession in relation to the previous context.
Addition and Elaboration: The new sentence or paragraph supplements expands upon the previous context.
Examples and Illustration: The
paragraph provides examples explanations related the previous context.
Personal Opinion and Recall: The new sentence or paragraph primarily expresses personal viewpoint or helief.
Reasoning and Analysis:
sentence or paragraph serves starting point reasening doing analysis
current information.
Conclusion Summary:
sentence or paragraph concludes from the presious context and present intermediate
outcome.
Instructions: Given previous context and the Your answer shoold contain only the transition type, formatted as: Vhrxed logic transition name]
analyze the semantic logic transition from the context the
#* Context: (context)
Text to be judged:: (text)
Response:
F.4 PROMPTS FOR SIGNAL PREDICTION
Here the prompt for training a signal predictor, mainly including the semantic signals and the task description for signal prediction.
Prompts for Signal Predictor
following context reasoning problem solving process, predict most likely signal predefined set of signal gmups) to which the next reasoning keyword or phrase will belong.
The possible semantic signals
Contrast and Concession
2. Addition and Elaboration
Examples and Illustration
4. Personal Opinion and Recall
Reasoning Analysis
Conclusion and Summary
7. Response Generation
24

---

that Published as a conference paper at ICLR 2026
Pleas answer by putting the semuntic signal numne in Wboxed semmantic signal name).
This is the reasoning context:
(context)
The semantic signal is:
G TRAINING EXAMPLES
Below, provide examples used for training and testing the Proposer and the Signal Predictor. Specifically, for training the Proposer, the input is the question, and we update the model's parame- ters by computing both the token loss betwee the gold reasoning step and the predicted step-ant and the signal beswene the gold signal and the predicted signal-using the two branches of the modified model architecture. The details the following examples include only the long-thinking trace within <think> and </think>, without the final answer generation guided by the Response Generation signal, which serves standard Chain-of-Thougee block.
Example-1
Question
What should you de you nosebleed? Options: should lie You should forward breathe through your mouth C. You should till your head buck
Step-by by--tty Reasoning Trace
Semantic Signals
question
should you you nosebleed!"
Reasoning and Analysis,
options: A. You should lie down B. You lean forward and breathe through your mouth You should tilr your
2. need to rocall the correct first aid for nosebleeds. I've heard different advice, but think the standard recommendation has changed over time. Actually, remember that tilting head back used but ss's not recommended anymere. Why? Because you tilt your head back. the blood can
Reasoning and Analysis,
suggestion,
Reasoning and Analysis,
which might cause choking or swallowing can lead to nausea vomiting.
your
So, option
should your
might incorrest.
Conclusion Summary, Reasoning and Analysis.
S. Now, option A: "You should lie down. Is lying down good for noscbleed? I think lying down could also cause blond to flow down the throa, similar to tilting the head back. might increase pressure in the veins
making bloeding worse. Option B: This sounds familiar. Leaning forward helps the blood drain out through the nose instead
Breathing through
prevents you from breuthing
in blood or causing more irritation.
the American Cross or Mayo Clinic recommends sitting upright and leaning forward slightty. Pinching the soft part the nese also key. but that's net mentioned in the options. The question is about what to do, and option inclades leaning forward and becathing through the mouth.
Personal Opinion and Rocall,
7. Let me conlirm: Yes, standard advice is to sit down, lean forward, pinch the nostrils through your
Reasoning and Analysis,
logether about minutes,
8. So, option soems correct.
Conclusion and Summary. Contrast and Concession,
9. let's double-check option A C. Option
down no, blood into the stomach lungs. Option Till bead back issue, blood goes down the threat. Option B: Lean forward - good, blood comes out, and you spit
because
it
neaded.
10. Also, breathing through the mouth mukes sense to avoid nasal passages.
10. Addition and Elaboration, Personal Opinion and Recall.
the correct answer.
12. But is there any secnario where might lie down tilt back? I don't think typical first aid. Medical professionals might have other methods, for general public, leaning farward advice.
12. Contrusi and Concession,
The question suys "you should do," implying general
I'll
Conclusion and Summary, 14. Coaclusion and Summary.
14. So, final answer should he B.
25

---

Published as a conference paper at ICLR 2026
Example-2
Question
What does always mean when cat pums? Options: A. A cat's purr always means that the cat is hungry B. A cat's always means that the cat is stressed C. cat's purr can signity many emotions, including both happiness and anxiety D. cat's purr always means that the cat happy
Step-by-Stey Reasoning Trace
Semantic Signals
1. Hirst, the question is: "What does it always mean when a cal purrs!" The options are: A cat's purr always the cat is stressed C. A cat's purr can signify many emotions, including both happiness and anxiety
1. Reasoning and Analysis
that the cat hungry B. cat's purr always means that
cat's 's purr always means that the cat huppy
2. T need to chonse the correct one and box my answer at the end. Key point: The word "always" is crucial here. says "always mean," so need to find which statement is universally true for all purring instances.
2. Reasoning and Analysis
3. J.I recall that cals purr for various reasons. From what know, purring isn't I just about emation. Cats purr when they'n content, like when they'n 're heing petted or resting comfortably. But they also purr when they're re in pain, stressed, or even when giving birth. think purring can self smothing mechanism.
Personal Opinion and Rocall,
4, For example, cat might pur when it's happy and relaxed, not necessarily hungry. it might purr when injured. which isn't happiness or hunger.
4. Examples and Illustration,
S. remember reading that kittens purr when nursing, which might indicate content-
5. Personal Opinion and Recall,
ment, but adult cats purr in various situations.
6. Also,
studies suggest that purring promote healing reduce stress, it's not just about positive emotions.
Addition and Flaboration,
So, option seems correct hecause it acknowledges that purring can mean different things, not just one.
Conclusion Summary.
But the question says "always mean," and C says "can signity." which might net directly answer "always." Let read the uptions again. Option C: "A cat's purr can signify many emottoons... this implies that doesn't always mean one thing; it can vary.
Contrast and Concession,
9. Whereas A, B. D claim that it always means one specific thing.
9. Contrast and Concession, Contrasi and Concession.
10. based my knowledge, purring doesn't 't always mean hunger, stress, happi- noss. depends the context.
11. Therefore, A. and are incorrect because they are absolute statements that aren't C the only that correctly states that purring signify multiple emotions. The question is phrased as "what does always mean." but C dresn't 't say what always says what
Conclusion and Summary,
signify. That might be trick. Lot sec.
12. Perhaps C is the best answer because it refutes the idea that it always means one thing. Option C not saying what always means; it's saying that it can mean different things.
12. Personal Opinion and Recall,
13. But the question asks for what always meams, implying a consistent meaning, In reality, there is single thing that purring always means. It varies.
13, Contrast and Concession,
14, So, none of A, B. are correct, but C the only one that captures the variabil- ity. Option C
14, Conclusion and Summary,
with "A purr signify..." which is not claiming always
meaning. but it's the correct understanding.
designed highlight that purring doesn't a single always meaning, and C is the accurate choice.
Perhaps the question
Personal Opinion Recall,
16. Lei me check online or recall reliable sources.
16. Reasoning and Analysis,
17. think scientifically, purring associaated with hoth positive and negutive situations.
17. Personal Opinion and Recall.
18. For instance, cats purr when they'r re content but also when they' 'r frightoned or in pain.
18. Examples and Illustration,
19. So, it's not always hunger, not always stress, not always happy.
19. Conclusion and Summary.
Therefore, C correct answer.
20. Conclusion Summary.
26

---

Published as a conference paper at ICLR 2026
Example-3
Question
Jan has three times the number of as Marcia. Marcia has two more pets than Cindy, If Cindy has four pets, bow many total pets do three have?
Step-by-Sten Step Reasoning Trace
Semantic Signals
1. First, the question is: Jan has three times the number of pets as Marcia. Marcia has two more pels than Cindy. Cindy has four pets, need to lind the total number pets for all three. Cindy has four pets. That's given directly: "Cindy has four pets."
1. Reasoning and Analysis,
2. Now, Marcia has two more pets than Cindy, So, Cindy has 4, then Marcia has +
2. Reasoning and Analysis,
2= pets.
3. Let me write that down: - Cindy; 4 pets Marcia: Cindy's 's pets 2 4++ + 6 pets number pels
3. Reasoning and Analysis,
Next,
Marcia 6 pets,
times that.
4. So, Jan: Marcia's is pets 3
pets.
Conclusion Summary, Reasoning and Analysis,
5. Now, to find the total, add up their pets: Cindy: Marcia: 6 Jan: Total: 4
+
Let calculate that: 4
and
Reasening and Analysis. 7. Conclusion and Summury.
7. So. the total should be 28 pets. I should double-check to make sure didn't miss anything. relationshipe:
Marcia
Cindy + Cindy 4. So,
from Cindy, Marcia = 4
Then =an 6= 4 6 =8 can set equations to verify. Let C
Conclusion Summary,
Cindy's pets. C. 4,M 3-
9. Then total T M Substiture: M C==++++=4+400 M=
Conclusion and Summary,
T= 28.
directly: T= Me
10. But M C 2, T= 4(C CC To thing.
10. Contrasi and Concession,
11. So, seems consistent. The question to put the answer in boxed format.
11. Conclusion and Summary,
12. Also, in my thinking, should include key words like 'Actually," "Wait," etc. but think did it step by step without needing backtrack, can for the reflection.
12. Addition and Elaberation.
For example, after finding Marcia could say Marcia pets."
Examples Illustration,
But it's fine.
think the process
Personal Opinion Recall, 15. Conclusion and Summary
15. So, the total number of pets is 28.
H BROADER IMPACT
The development of Reasoning Scaffolding offers significant potential to reshape both the technical landscape of language modeling and the broader societal deployment of AI systems. By enabling small language models (SLMs) to internalize algorithmic reasoning structures rather than imitate surface-level text, our framework advances knowledge distillation toward greater logical robust- ness, interpretability. and resource efficiency. This approach directly addresses key challenges in AI safety and reliability, yielding SLMs that are less susceptible to spurious correlations and brittle failure modes, and facilitating trustworthy applications in domains such as education, healthcare, legal reasoning, and scientific discovery. By enhaneing the reasoning abilities of compact models, Reasoning Scaffolding democratizes access to advanced AI, supporting robust performance on edge devices and in resource-limited environments. Furthermore, by shifting distillation from rote im- itation to structured reasoning, work paves the way for future rescarch into more transparent and faithful knowledge transfer, including finer- aner-grained reasoning signals, symbolic integration, and self- self-supervieed techniques further improve robustness and reduce reliance proprietary LLMs.
27


Reviews:
[{"review_id": "W5UVveaKeR", "reviewer": "Reviewer_qrY1", "summary": "This work proposed novel distillation approach for distilling LLM reasoning thinking data into small models. The approach can be summarized as follows\n\n1. Identify thinking (reasoning) words in the reasoning chain of thought, like (Additionally, So, Then ...)\n2. Group these worlds into 7 types \n3. Split the DeepSeek generated reasoning chain using identified keywords.\n4. During distillation, let the model predict both reasoning type and reasoning tokens for each hidden states\n5. During inference, an adaptive strategy is adopted,  if the confidence computed using reasoning step type predictor, the reasoning is terminated.\n6. Another experiment based on only using \"Conclusion and Summary\"  steps in reasoning chain is used for distillation, and the result looks good. \n\nThe experimental results show that this approach out-perform direct distillation and  SFT using CoT directly. \n\nAblation study is performed to demonstrate the effectiveness of predicted reasoning type, and correct reasoning type can guide reasoning effectively.", "questions": "1. Is the code the latest version ?\n2. Please refer to weakness and resolve my concern.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1. The proposed approach for distillation is effective and reached high performance compare with baseline\n2. The designed experiments clearly explained the motivation of of the proposed approach. \n3. The ablation study is comprehensive", "weaknesses": "1. The models tested are only from Qwen 2.5 families. However, previous works [1], have questioned about the behaviour of Qwen 2.5 on math reasoning.  It could be more convincing to adopt other models on this approach to check the effectiveness and performance. \n2. The proposed approach is expensive and rely on advanced model. It's hard to scale up. \n3. The loss described in the paper not matches the given code.  In paper, equation 2 on L221 is a classification loss while  regression loss is used in your code `custom_qwen_model.py` , L200. Also a lot of evaluation python scripts is not available. \n4. Figures are not intuitive and self-explaining. In figure 2, the detailed example text can be removed and maybe replaced with abstract icon to emphasize more on the approach. For figure 3,  it could be better to use some toy examples (not long and real, but just conceptual) to illustrate the pruning process. \n5. Only reasoning chains from DeepSeek is tested, and it remains unknown how reasoning chain of other style (like from gpt-oss) perform using this approach. \n6.  The work can be more intuitive if decoding algorithm and be explained in pseudo code. And I can not find adaptive decoding codes in codebases.", "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": "ZwEcTsukzt", "reviewer": "Reviewer_5EW9", "summary": "This paper introduces Reasoning Scaffolding, a distillation framework that extracts the structural flow of reasoning from LLMs into discrete semantic signals (e.g., Contrast, Addition, Elaboration) to train SLMs. Unlike traditional behavioral cloning from Chain-of-Thought rationales, which mimics surface-level text, this method uses a multi-task objective where the SLM learns to predict the next semantic signal (anticipating reasoning flow) and generate the corresponding step conditioned on it. This acts as a regularizer for logical coherence. The approach includes data preparation via keyword matching and LLM validation, a dual-branch model architecture, and inference with signal-guided generation and pruning for efficiency. Evaluations on benchmarks like StrategyQA, CommonsenseQA, TruthfulQA, GSM8K, and MATH show improved accuracy and robustness over baselines like CoT SFT and Long-Thinking distillation, using Qwen models of varying sizes.", "questions": "* How was the set of 7 semantic signals determined, and what happens if you expand or reduce the categories—does performance change significantly?\n\n* Did you observe any biases in the semantic signals assigned by GPT-4, such as favoring certain transitions based on the teacher's style?\n\n* How does the method perform on tasks beyond QA and math, like creative writing or multi-agent reasoning, where reasoning flows might be less linear?\n\n* What is the computational overhead of the dual-branch training compared to standard CoT distillation, and how sensitive is inference efficiency to the pruning strategy?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "* Tackles a fundamental flaw in reasoning distillation by shifting focus from text imitation to transferring algorithmic structure, which is a timely and innovative contribution to creating more robust SLMs.\n\n* The multi-task training with signal prediction as a regularizer is technically sound and provides interpretability, potentially advancing mechanistic understanding of reasoning in models.\n\n* Comprehensive experiments demonstrate substantial gains (e.g., ~14% average over originals, ~8% over CoT baselines), with notable benefits for smaller models, and the framework shows scalability across model sizes and tasks.\n\n* Includes practical optimizations like confidence-based termination and pruning of reasoning traces for token efficiency, making it applicable for real-world deployment.", "weaknesses": "* The semantic signal extraction relies heavily on an external LLM (e.g., GPT-4) for validation and labeling, which could propagate biases or inconsistencies from the labeler, and the choice of exactly 7 categories seems somewhat arbitrary without broader justification or sensitivity analysis.\n\n* While results are strong on the selected benchmarks, the paper lacks evaluation on out-of-distribution tasks or diverse reasoning domains (e.g., code generation, planning), limiting claims of general robustness; comparisons are mostly to CoT variants rather than other structured distillation methods like modular architectures or rationale decomposition.\n\n* Inference depends on a tunable threshold τ for signal confidence, but the paper provides limited ablation on its impact across datasets, and the pruning strategy might discard useful intermediate details in complex problems.\n\n* The dataset construction uses zero-shot prompting from a single LRM (Deepseek-R1), which may not capture diverse reasoning styles; details on dataset size, diversity, or quality control are sparse in the provided sections.", "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": "N5iYvGoL4y", "reviewer": "Reviewer_b3Cu", "summary": "The paper introduces Reasoning Scaffold: a distillation method for improving the reasoning capabilities of small language models (SLMs). The method works by decomposing reasoning traces from a large teacher model into annotated reasoning steps, categorized into reasoning types using keyword-based and LLM annotation. The SLM is then tasked to learn the category of the current reasoning step and generates reasoning tokens conditioned on this information. This method intends to better structure the reasoning of the SLM. Experiments on reasoning benchmarks demonstrate the effectiveness of the proposed method on reasoning benchmarks for the Qwen model family, with models ranging from 0.5 to 14B parameters. The method, however, achieves its performance at a higher inference cost than standard distillation as it requires more generated tokens.", "questions": "1. Have you investigated if additional, more precise and informative, categories could improve the guiding signal and improve the generation of the reasoning traces?\n2. Have you investigated the keyword-LLM agreement for splitting the traces into categories? can the keyword create additional unneeded steps or miss a transition to a new step?\n3. Have you investigated the evolution of the two training losses and compared their magnitude and variance? Does including a hyperparameter controlling the weighting factor of one of the losses improves the learning?\n4. As the \"Conclusion and Summary\" denote both intermediate and final outputs, how is the final output differentiated from the intermediate ones?\n5. Have you performed experiments with other model families? Both as teacher and student?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The proposed work is simple yet effective for improving distillation in SLMs. It can serve the research community by providing an easy scaffold to yield better small reasoners.\n2. The experiments show improved performance on reasoning tasks and accurately support the claims made by the paper.\n3. The presented analysis interestingly shows that additional structuring signals, even weak or random can help organize the model's reasoning thoughts and improve reasoning capabilities.", "weaknesses": "1. The proposed work, while useful, does not present an original method or novel findings as similar studies already exist [1].\n2. The proposed structure categorization is very high-level, potentially making the category prediction task trivial as argumentation usually follow the same steps and thus, reducing the information in the signal.\n3. The method relies on handcrafted keyword matches (complemented by an LLM), which can be brittle in out-of-domain tasks, particularly as the LLM is only used for assigning a category to a piece of text but not for the division into steps.\n4. The method balances two training objectives with the same weight to both losses. This can lead to training instability if they do not have the same magnitude or variance.\n5. Experiments are only performed on models from the Qwen family and it is unclear if the findings can transfer to other models or if they are artifacts specific to Qwen. Similarly, only one teacher model 5DeepSeek-R1) is used.\n6. The proposed method yields longer reasoning chains than the best baseline (Thinking Distill), which could account for the performance gap.\n\n\nMinor comment:\n1. Results from the tables are a bit hard to read. Highlighting the best results in bold would be helpful to the reader.\n2. It is not clear from Figure 4 how the proposed method improves the reasoning signal as the examples follow the same reasoning structures.\n\n\n\n[1] Li, D., Cao, S., Griggs, T., Liu, S., Mo, X., Tang, E., ... & Stoica, I. (2025). LLMs Can Easily Learn to Reason from Demonstrations Structure, not content, is what matters!. arXiv preprint arXiv:2502.07374.", "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": "eg6nX7gMiM", "reviewer": "Reviewer_3pgg", "summary": "This paper proposes Reasoning Scaffolding, a framework for distilling reasoning ability from large language models (LLMs) into smaller models (SLMs). Instead of directly imitating the teacher's Chain-of-Thought (CoT) text, the method abstracts reasoning traces into semantic signals (e.g., Contrast, Elaboration, Conclusion) that serve as scaffolds for step-by-step reasoning. The student model is trained via a dual-branch architecture, predicting both the next semantic signal and the corresponding reasoning step, to encourage internalization of the reasoning structure. Experiments on multiple benchmarks (StrategyQA, CommonsenseQA, TruthfulQA, GSM8K, MATH-500) show improvements over standard CoT and Long-Thinking distillation baselines.", "questions": "See weakness", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1. **Interesting idea**: The paper explores a creative perspective on reasoning distillation by introducing semantic scaffolding as a middle-level representation between textual rationales and abstract reasoning steps.\n\n2. **Comprehensive experiments**: Evaluation spans multiple reasoning benchmarks and model scales (0.5B, 7B, 14B), providing a broad empirical basis.\n\n3. **Clear empirical comparisons**: The ablation studies (e.g., signal quality and token analysis) are informative and show that structured supervision can improve reasoning stability.\n\n4. **Good motivation**: Addressing the brittleness of current CoT distillation is an important and timely research direction.", "weaknesses": "1. **Experimental irregularities (Table 1).**\nThe main results table is somewhat confusing. For example, the Qwen2.5-0.5B results under \"Long-Thinking Distill\" are missing, while the Qwen2.5-7B model performs worse than its SFT counterpart under this setting (except on MATH-500). These inconsistencies raise questions about the fairness and reproducibility of the comparison. It would be helpful to clarify whether the fine-tuning setup (data size, training epochs, loss weighting) is kept consistent across all baselines. Moreover, teacher models such as DeepSeek-R1 could serve as stronger baselines.\n\n2. **Model- and task-specific signal design.**\nThe categorization of reasoning signals (Section 3.1) appears heuristic and data-specific. The seven signal types (e.g., Addition, Contrast, Conclusion) seem derived from particular verbal patterns in GSM8K-style reasoning traces. It is unclear whether this taxonomy would generalize to other domains (or teacher models), such as scientific reasoning, logic puzzles, or multi-modal contexts. The framework's dependence on these fixed signal categories limits its general applicability.\n\n3. **Ambiguity in contribution novelty.**\nWhile the idea of structured distillation is valuable, much of the implementation (keyword matching, LLM labeling, multi-task fine-tuning) builds directly on existing CoT or discourse-signal techniques. The conceptual advancement beyond structured rationale distillation remains incremental without stronger theoretical or analytical insight.\n\n4. **Writing and clarity.**\nThe overall writing is understandable but sometimes verbose and repetitive. Some sections (e.g., 3.1–3.3) contain long procedural details that could be condensed and improved. Minor language issues also appear throughout, which detract slightly from readability.", "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)