ThinkFuse: Trajectory-Aware Test-Time Fusion for Small Reasoning Models

Myunghoon Kang; Jungseob Lee; Jaehyung Seo; Heuiseok Lim

cs.AIOct 6, 2026

ThinkFuse: Trajectory-Aware Test-Time Fusion for Small Reasoning Models

Authors: Myunghoon Kang, Jungseob Lee, Jaehyung Seo, Heuiseok Lim

Organizations: Department of Computer Science and Engineering, Korea University · Department of Computer Science and Engineering, Konkuk University · Human-inspired AI Research

Abstract

Small reasoning models (SRMs) have shown strong performance on complex reasoning tasks by generating extended chain-of-thought trajectories, but they often fail to recover once their reasoning enters an erroneous path. Existing test-time fusion methods rely on local fusion signals to determine when to trigger fusion, which can be misled by transient uncertainty fluctuations and may reinforce unstable reasoning trajectories. We propose ThinkFuse, a training-free test-time fusion framework that selectively intervenes in unreliable reasoning segments. ThinkFuse compares segment-level uncertainty shifts with trajectory-level uncertainty trends to identify unstable reasoning points and fuse auxiliary reasoning paths into the primary model's trajectory. Extensive experiments demonstrate that ThinkFuse outperforms baselines on mathematical and knowledge-intensive reasoning benchmarks, with consistent gains across model-family combinations, and remains robust with a smaller primary model. Our analysis shows that ThinkFuse requires fewer fusion triggers and generates fewer tokens, highlighting the efficiency of selective triggering. Our code is available at https://github.com/js-lee-AI/ThinkFuse.

Figures & tables

Figure 1: Overview of ThinkFuse framework. ThinkFuse monitors the segment-level uncertainty of the primary model $M_{p}$ using an adaptive threshold $\theta$ . Upon detecting uncertainty spikes, it invokes an auxiliary model $M_{a}$ to generate alternative reasoning steps. Both trajectory candidates are then evaluated for compatibility by $M_{p}$ via perplexity ( PPL ), fusing the most compatible segment into the context. This procedure iterates until the reasoning reaches a terminal state.

Method	Intervention unit	Selective trigger	Multi-model fusion	Trajectory-aware	Decision basis
Self-consistency ( Wang et al., 2023 )	answer	$\times$	$\times$	$\times$	post-hoc majority voting
Cool-Fusion ( Liu et al., 2025 )	segment	$\times$	$\checkmark$	$\times$	fuses at every segment
AdaFuse ( Cui et al., 2026 )	word / span	$\checkmark$	$\checkmark$	$\times$	local token confidence
MUR ( Yan et al., 2026 )	step	$\checkmark$	$\times$	$\checkmark$	single-model momentum uncertainty
SpecReason ( Pan et al., 2025 )	step	$\times$	$\checkmark$	$\times$	verifies every drafted step
ThinkFuse (ours)	segment	$\checkmark$	$\checkmark$	$\checkmark$	trajectory-calibrated segment uncertainty

Table 1: Triggering policies of test-time methods. Intervention unit denotes the granularity at which each method acts on the reasoning process, Selective trigger denotes whether auxiliary computation is invoked only at selected points, Multi-model fusion denotes whether a second model contributes to the trajectory, and Trajectory-aware denotes whether the decision is calibrated against the history of the ongoing trajectory.

Standalone models
Method	MATH-500	GSM8K	AIME24	GPQA	NQ-Open
Qwen3-4B	89.0	92.0	53.3	54.0	29.5
Qwen3-1.7B ‡	83.0	90.0	33.3	39.4	28.0
Ministral	32.5	67.0	0.0 †	25.8	24.0
EXAONE-4.0	57.0	85.0	3.3 †	38.9	22.0
Test-time compute baseline: Qwen3-4B

Table 2: Main benchmark results. Accuracy (%) for standalone models, test-time baselines, and ThinkFuse across five benchmarks under a 16K-token budget. Values in parentheses indicate the signed accuracy difference, in percentage points, relative to the standalone performance of the primary model, with green indicating gains and red indicating degradation. The

\dagger

symbol marks AIME24 results affected by length-limit or final-answer truncation. The

{\ddagger}

symbol marks the standalone Qwen3-1.7B evaluated with the Qwen3 recommended top-

k

of 20, whereas all other rows use the shared decoding setting. Additional experimental details, including the decoding settings and remaining cross-family and same-family configurations, are presented in Appendix A and C .

Figure 2: Thinking-stage token statistics. Top: Average fused auxiliary tokens in log scale. Bottom: Average total thinking-stage tokens. All fusion configurations use Qwen3-4B as primary model and Ministral-3B-Reasoning as auxiliary model.

Method	Wall-clock (s)	TFLOPs	Acc.	Acc. / TFLOPs
Cool-Fusion	39.4	86	21.8	0.25
AdaFuse	33.9	74	43.7	0.60
ThinkFuse	68.7	77	72.9	0.95

Table 3: Efficiency comparison of ThinkFuse and comparable test-time fusion methods. Wall-clock time and TFLOPs are averaged per example, and accuracy is averaged over the five benchmarks, with the Qwen3-4B

\times

Ministral pair.

Auxiliary	MATH-500	GPQA
Llama-3.2-3B-IT	89.5 (+0.5)	50.5 ( $-$ 3.5)
Gemma-2-2B-it	87.5 ( $-$ 1.5)	51.0 ( $-$ 3.0)
Mistral-7B-Inst-v0.3	84.5 ( $-$ 4.5)	44.9 ( $-$ 9.1)
Qwen2.5-3B-Inst	88.0 ( $-$ 1.0)	52.5 ( $-$ 1.5)
Qwen3-1.7B (no-think)	89.5 (+0.5)	50.0 ( $-$ 4.0)

Table 4: Experimental results of pairing Qwen3-4B as a primary model with instruction-tuned or non-thinking auxiliaries. The general performance drop indicates that ThinkFuse strictly requires reasoning-specialized models to ensure trajectory compatibility. Values in parentheses show the difference from the standalone baseline.

Fusion budget penalty
Setting	MATH-500	GSM8K
Soft budget (ours, $\lambda{=}50$ )	90.0 (+1.0)	96.9 (+4.9)
No budget penalty ( $\lambda{=}0$ )	88.5 ( $-$ 0.5)	90.5 ( $-$ 1.5)
Segment length $T$
$T{=}4$	87.0 ( $-$ 2.0)	93.5 (+1.5)
$T{=}8$ (ours)	90.0 (+1.0)	96.9 (+4.9)

Table 5: Impact of individual ThinkFuse components on downstream performance. Values in parentheses denote the accuracy delta relative to the standalone baseline. All experiments are conducted with Qwen3-4B as the primary model and Ministral-3B-Reasoning as the auxiliary model.

Shared prefix. For AIME-2022 II #11, both traces begin with the same coordinate setup: $A=(0,0)$ , $B=(2,0)$ , $D=(p,q)$ , $C=(r,s)$ , and $M=((2+r)/2,s/2)$ is the midpoint of $BC$ . Both traces then try to use the two angle-bisector conditions at $M$ .
Standalone	ThinkFuse
Generated trace near the divergence. $\cdots$ I place the quadrilateral in coordinates and write the distance equations. Since $M$ is the midpoint of $BC$ , it should lie on the two angle bisectors. $\cdots$ the valid solution is b = -7/sqrt(2), a = 7/sqrt(2) So, D is at ((7sqrt(2))/2, -7sqrt(2)/2). $\cdots$ I plug this coordinate for $D$ back into the remaining constraints and solve for $C$ . $\cdots$ (2+sqrt(2))yˆ2 + 9(sqrt(2)+1)y + (22+7sqrt(2)) = 0 // Comment: this fixes D as if $\angle DAB=45^{\circ}$ . The second angle-bisector condition has not been used, so the trace enters a dead-end quadratic.	Generated trace near the fusion point. $\cdots$ I keep $D=(p,q)$ and $C=(r,s)$ symbolic, then express the two angle-bisector conditions as distance-to-line equations. $\cdots$ [Two angle-bisector distance equations from M = (B+C)/2] -8 - 2p + 3r = 0 => r = (8 + 2p)/3 => s = 2q/3 Substituting these relations keeps both angle-bisector constraints active while the remaining equations are solved. // Comment: the auxiliary segment keeps $D=(p,q)$ symbolic. It uses both angle-bisector conditions before solving.
Answer: $\boxed{0}\ \boldsymbol{\times}$	Answer: $\boxed{180}\ \checkmark$

Table 6: Qualitative comparison on AIME 2022. Standalone denotes Qwen3-4B. ThinkFuse uses Qwen3-4B as the primary model and Ministral-3B-Reasoning as the auxiliary model. Both traces start from the same coordinate formulation; the highlighted text marks the standalone step that enters a dead-end quadratic and the auxiliary symbolic step selected by ThinkFuse .

Scope	Setting	Implementation details
Shared	Engine / hardware	All generation and PPL computation use vLLM v0.8.5 with bfloat16 precision. Each model pair is served on two NVIDIA A100-80GB GPUs.
	Generation budget / sampling	Standard decoding uses max_model_len =16384, max_new_tokens =16384, temperature=0.6, top- $p$ =0.95, top- $k$ =-1, and min- $p$ =0.0. The standalone Qwen3-1.7B alone uses top- $k$ =20 following the Qwen3 recommendation. Within this budget, explicit thinking-stage generation uses an additional 2K-token cap. Self-consistency uses separate sampling settings.
ThinkFuse	Trigger signal	Every time the primary model generates $T=8$ tokens, we compute top-5 token entropy and aggregate token-level uncertainty into segment-level uncertainty using EWCA with $(\alpha,\beta)=(0.1,0.5)$ .
	Adaptive threshold	The EMA update rate is $\eta=0.05$ , the uncertainty tolerance is $\tau=1.0$ , and the initial statistics are $(\mu_{0},\sigma_{0})=(0.5,0.1)$ . The soft-budget coefficient is $\lambda=50$ ; the trigger uses both recent uncertainty history and the cumulative fusion ratio.
	Segment selection	When fusion is triggered, primary and auxiliary candidate segments are compared under the current context using primary-model PPL. Segment boundaries from different tokenizers are aligned by the shared prefix that decodes identically under both tokenizers, and each segment is restored to the reasoning-tag format of the model used for PPL scoring.
Baselines	Cool-Fusion	Each participating LLM generates a candidate segment; all generated candidates are scored by the PPL of all participating LLMs, and the candidate with the lowest average PPL is selected.

Table 7: Implementation hyperparameters. Shared implementation settings and method-specific settings used in the main and appendix experiments.

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Auxiliary	MATH-500	GSM8K	AIME24	GPQA	NQ-Open
Ministral	+0.5 [ $-$ 1.5, +2.5]	+3.1 [+1.0, +5.6]*	+20.0 [+6.7, +36.7]*	+10.6 [+1.0, +20.2]*	+10.0 [+5.5, +15.0]*
EXAONE-Deep	+2.0 [+0.5, +4.0]*	+3.1 [+1.0, +5.8]*	+20.0 [+6.7, +33.3]*	+1.0 [ $-$ 8.1, +10.1]	+9.0 [+4.5, +14.0]*
DeepSeek-R1	+1.5 [ $-$ 0.5, +4.0]	+3.0 [+0.0, +6.5]	+3.3 [ $-$ 10.0, +16.7]	+8.7 [ $-$ 0.5, +17.9]	+8.0 [+3.5, +13.1]*
Qwen3-1.7B	+2.0 [+0.5, +4.0]*	+2.0 [ $-$ 0.5, +5.0]	+16.7 [ $-$ 3.3, +36.7]	+1.0 [ $-$ 8.6, +10.1]	+7.5 [+3.5, +12.0]*

Appendix

Table 8: 95% bootstrap confidence intervals for the accuracy delta of ThinkFuse over the standalone Qwen3-4B with each auxiliary. * marks intervals excluding zero. Deltas are from re-executed runs and may differ slightly from Table 2 .

Standalone models
Method	MATH-500	GSM8K	AIME24	GPQA	NQ-Open
Qwen3-4B	89.0	92.0	53.3	54.0	29.5
EXAONE-Deep	83.5	90.5	43.3	57.1	17.5
DeepSeek-R1	13.0	30.5	0.0 †	21.2	14.5
ThinkFuse cross-family pairs
Qwen3-4B $\times$ EXAONE-Deep	91.0 (+2.0)	99.0 (+7.0)	73.3 (+20.0)	55.1 (+1.1)	38.5 (+9.0)

Appendix

Table 9: Additional ThinkFuse model pairs. Accuracy (%) for the cross-family pairs with EXAONE-Deep and DeepSeek-R1 as auxiliary models under the same 16K-token budget and evaluation protocol as Table 2 . Values in parentheses indicate the signed accuracy difference relative to the standalone Qwen3-4B. The

\dagger

symbol marks AIME24 results affected by length-limit or final-answer truncation.

Benchmark	Qwen3-4B pass@5
MATH-500	90.5 (+1.5)
GSM8K	95.5 (+3.5)
AIME24	70.0 (+16.7)
GPQA	71.2 (+17.2)
NQ-Open	48.5 (+19.0)

Appendix

Table 10: Qwen3-4B pass@5 oracle sampling upper bound. pass@5 counts an instance as correct if at least one of five independently sampled Qwen3-4B responses contains the correct answer. Values are accuracy (%); colored values in parentheses denote the difference from Qwen3-4B standalone accuracy. This table reports only the sampling upper-bound diagnostic, which is not included in the main results table.

Figure 3: ThinkFuse fusion-position distribution. Normalized positions of thinking-stage segments where fusion is triggered, separated by final-answer correctness. The primary model is Qwen3-4B and the auxiliary model is Ministral-3B-Reasoning.

Benchmark	ThinkFuse	Post-hoc critique
MATH-500	91.0 (+2.0)	86.3 ( $-$ 2.7)
GSM8K	99.0 (+7.0)	92.0 (+0.0)
AIME24	73.3 (+20.0)	30.0 ( $-$ 23.3)
GPQA	55.1 (+1.1)	27.8 ( $-$ 26.2)
NQ-Open	38.5 (+9.0)	40.0 (+10.5)

Appendix

Table 11: ThinkFuse vs. post-hoc critique. Accuracy (%) with the same Qwen3-4B

\times

EXAONE-Deep-2.4B model pair and the same evaluation protocol as the main experiments. Colored values in parentheses denote the difference from Qwen3-4B standalone accuracy.

Method	AIME24	GPQA
Qwen3-4B standalone	53.3	54.0
MUR ( $\phi$ -decoding)	16.7 ( $-$ 36.6)	37.9 ( $-$ 16.1)
MUR (Ministral critic)	53.3 (+0.0)	48.0 ( $-$ 6.0)
ThinkFuse	73.3 (+20.0)	64.6 (+10.6)

Appendix

Table 12: Comparison with MUR. Accuracy (%) with Qwen3-4B as the reasoning model under the 16K-token budget and the same evaluation protocol as the main experiments. ThinkFuse pairs Qwen3-4B with Ministral-3B-R. Values in parentheses denote the difference from Qwen3-4B standalone accuracy.

Explore similar work

Apr 16, 2026cs.AI

TrigReason: Trigger-Based Collaboration between Small and Large Reasoning Models

Large Reasoning Models (LRMs) achieve strong performance on complex tasks through extended chains of thought but suffer from high inference latency due to autoregressive reasoning. Recent work explores using Small Reasoning Models (SRMs) to accelerate LRM inference. In this paper, we systematically characterize the capability boundaries of SRMs and identify three common types of reasoning risks: (1) path divergence, where SRMs lack the strategic ability to construct an initial plan, causing reasoning to deviate from the most probable path; (2) cognitive overload, where SRMs fail to solve particularly difficult steps; and (3) recovery inability, where SRMs lack robust self-reflection and error correction mechanisms. To address these challenges, we propose TrigReason, a trigger-based collaborative reasoning framework that replaces continuous polling with selective intervention. TrigReason delegates most reasoning to the SRM and activates LRM intervention only when necessary-during initial strategic planning (strategic priming trigger), upon detecting extraordinary overconfidence (cognitive offload trigger), or when reasoning falls into unproductive loops (intervention request trigger). The evaluation results on AIME24, AIME25, and GPQA-D indicate that TrigReason matches the accuracy of full LRMs and SpecReason, while offloading 1.70x - 4.79x more reasoning steps to SRMs. Under edge-cloud conditions, TrigReason reduces latency by 43.9% and API cost by 73.3%. Our code is available at https://github.com/QQQ-yi/TrigReason

Yi Zhao, Yajuan Peng, Cam-Tu Nguyen +4

AGI Institute, School of Computer Science, Shanghai Jiao Tong University, Shanghai, China · Shanghai Key Laboratory for Intelligent Information Processing, Fudan University · State Key Laboratory for Novel Software Technology, Nanjing University +2

Large Reasoning Models Inference Latency Collaboration Offloading

Ask PDF

Aug 11, 2026cs.AI

ThinkRetrieve: Retrieval-Augmented Reasoning Traces for Test-Time Scaling

Large Reasoning Models (LRMs) improve performance by allocating additional inference-time compute to generate extended chain-of-thought reasoning. However, recent studies reveal that sequential test-time scaling often yields diminishing or even negative returns, as longer traces exhibit increased uncertainty, error compounding, and drift from the original problem. We propose ThinkRetrieve, a test-time scaling framework that augments the reasoning traces of LRMs with dynamically retrieved solved examples at each reasoning step. Given an external corpus of problems paired with step-by-step solutions, ThinkRetrieve retrieves relevant exemplars at each intermediate step and injects them directly into the thinking trace, providing the model with guidance on how to reason rather than merely what facts are relevant. Experiments across five reasoning models (1.5B--8B parameters) on GSM-8K, MATH-500, AIME 2025, and SciQ demonstrate that ThinkRetrieve consistently improves accuracy over standard test-time scaling, with relative gains of up to

60\%

on AIME 2025.

Vaibhav Singh, Soumya Suvra Ghosal, Sarvesh Gharat +3

IIT Bombay · University of Maryland, College Park · Adobe Research

Test-Time Scaling Large Reasoning Models Reasoning Traces Progressive Reasoning Inference-Time

Ask PDF

Sep 28, 2026cs.AI

Knowing When Thinking Is Not Enough: Teaching Small Reasoning Models to Reason Beyond Their Parametric Knowledge

Scaling test-time computation is a powerful way to improve language-model reasoning, and is particularly appealing for small reasoning models (sRMs) that are cheap to serve. However, is additional thinking always the right operation? By intervening at intermediate reasoning states across two model families and multiple scales, we find that self-refinement largely consolidates probability mass onto solutions already reachable from the current state, rather than making new ones reachable. These interventions reveal two failure regimes: execution bottlenecks, where the correct path is reachable and reflection can recover it, and knowledge bottlenecks, where relevant external information makes it reachable. Motivated by this distinction, we introduce FlyBy, a selective querying framework, and train 4B and 8B variants to reason first, diagnose what remains unresolved, and, at a knowledge bottleneck, query stronger models whose parametric knowledge extends beyond its own. Supervised fine-tuning bootstraps a multi-depth query action, and cost-aware reinforcement learning calibrates whether to query, what to ask, and how much to spend. On 1,158 hard problems across six benchmarks, FlyBy-4B achieves 45.96% pass@8, surpassing Qwen3-14B (41.64%) at 2.7 times lower serving cost, while also exceeding Qwen3-8B in pass@1 (16.85% vs. 15.31%). Scaling to FlyBy-8B further improves pass@8 to 51.81%.

Chanuk Lee, Minki Kang, Sangwoo Park +3

KAIST

Small Reasoning Model Test Time Bottlenecks Aeroact

Ask PDF