SABER: Stability-Aware Early Exit for LLM Reasoning via Adversarial Branch Probing

Wanli Cheng; Haiya Xiang; Juntao Li; Hongling Wang; Wenliang Chen

cs.AIAug 28, 2026

SABER: Stability-Aware Early Exit for LLM Reasoning via Adversarial Branch Probing

Authors: Wanli Cheng, Haiya Xiang, Juntao Li, Hongling Wang, Wenliang Chen

Organizations: Soochow University, China

Abstract

Large Reasoning Models (LRMs) achieve strong reasoning capabilities, yet long-chain reasoning becomes inefficient once the intermediate answer stabilizes across reasoning steps: additional reasoning yields little marginal benefit while incurring substantial inference cost. Existing early-exit methods based on confidence or entropy poorly capture reasoning stability, while consistency-based approaches rely on multi-step trajectory agreement, requiring sequential evaluations that delay exit. To better balance efficiency and reliability, we propose SABER, a training-free framework for stability-aware early exit via adversarial branch probing. SABER constructs simple yet effective semantic perturbations around intermediate reasoning states to form adversarial branches, and applies lightweight probing to estimate their likely final outcomes without full trajectory rollouts. When the probed outcomes remain consistent across branches, SABER exits early; otherwise, it continues reasoning. Experiments across multiple reasoning benchmarks and model architectures show that SABER reduces reasoning token consumption by 30.2%--39.8% on average while maintaining competitive accuracy with full-length reasoning.

Figures & tables

Figure 1: Dynamics of reasoning behavior under adversarial perturbations across reasoning steps. Left: Answer consistency. Trajectories leading to correct solutions progressively become more stable and consistent under perturbation, whereas trajectories leading to incorrect solutions remain unstable. Right: Confidence variation. Trajectories leading to correct solutions exhibit progressively reduced confidence variation under perturbation, while incorrect trajectories remain highly volatile.

Figure 2: Overview of SABER. The framework performs adversarial probing by constructing neutral and adversarial branches at intermediate reasoning steps to estimate reasoning stability under perturbations. Semantic consistency and confidence stability are jointly integrated into the RSS, which dynamically determines whether reasoning should continue or terminate early.

	MATH										SCIENCE
Method	GSM8K		MATH-500		AMC23		Olympiad		AIME24,25		GPQA-D		Overall
	Acc $\uparrow$	Tok $\downarrow$	Acc $\uparrow$	Tok $\downarrow$	Acc $\uparrow$	Tok $\downarrow$	Acc $\uparrow$	Tok $\downarrow$	Acc $\uparrow$	Tok $\downarrow$	Acc $\uparrow$	Tok $\downarrow$	Acc $\uparrow$	CR $\downarrow$
DeepSeek-R1-Distill-Qwen-7B
Vanilla	91.2	1,164	90.4	3,797	90.6	6,032	56.3	7,461	46.3	10,683	31.8	7,437	67.8	100%
NoThinking	84.6	231	79.4	970	73.1	1,807	41.0	1,998	22.5	5,551	28.8	638	54.9	30.6%
Dynasor	89.8	773	89.4	2,987	86.7	4,689	54.8	6,477	42.5	9,726	31.3	1,471	65.8	71.4%

Table 1: Experimental results across multiple reasoning benchmarks and model scales. “Acc” denotes accuracy, “Tok” denotes reasoning token count, and “CR” denotes compression ratio.

\uparrow

(

\downarrow

) indicates higher (lower) values are better.The best results are highlighted in bold .

Figure 3: Accuracy of RSS early-exit on mathematical reasoning benchmarks: component ablation of semantic consistency (SC) and confidence stability (CS). Results are shown for RSS (our full method) compared with SC-only and CS-only variants on two representative models.

Figure 4: Sampling number ablation on MATH-500 using Qwen3-8B. Left: Accuracy improvement with increasing

k

. Right: Probe overhead growth and its proportion of total generated tokens as a function of

k

GSM8K
Model	$\alpha=0.3$	$\alpha=0.5$	$\alpha=0.7$
R1-Distill-Qwen-7B	90.4/739	90.1/652	91.0 /662
Qwen3-4B	94.3/1,635	94.5/1,503	94.8 /1,389
Qwen3-8B	95.3/1,604	95.1/1,394	96.0 /1,258
OlympiadBench
R1-Distill-Qwen-7B	56.1 /5,560	54.4/5,462	53.8/5,122

Table 2: Sensitivity analysis of weight

\alpha

on GSM8K and OlympiadBench. Each cell shows accuracy (%) and average token count.

Figure 5: Accuracy (left y-axis) and average token count (right y-axis) on OlympiadBench under different stopping thresholds

\tau

with

\alpha=0.3

. Results are shown for three reasoning models.

Model	Probe	Total	Ratio (%)
R1-Distill-Qwen-7B	221	4,477	4.9%
Qwen3-4B	147	5,221	2.8%
Qwen3-8B	181	4,815	3.8%
Average	183	4,838	3.8%

Table 3: Probe overhead under the default configuration. Probe tokens account for only a small fraction of total generated tokens.

Model	Vanilla	SABER	Reduction
R1-Distill-Qwen-7B	149.4	92.9	37.8%
Qwen3-4B	190.1	107.0	43.7%
Qwen3-8B	243.0	98.5	59.5%
Average	194.2	99.5	48.8%

Table 4: Average inference latency (in seconds) of SABER across GSM8K, AIME24, and GPQA-D.

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 6: Comparison between SABER and a confidence-only early-exit strategy on MATH-500. SABER consistently achieves a better efficiency–accuracy trade-off and remains closer to the oracle upper bound across different stopping thresholds.

Scoring Function	GSM8K		MATH-500		Olympiad		AIME24,25		GPQA-D		Overall
Scoring Function	Acc $\uparrow$	Tok $\downarrow$	Acc $\uparrow$	Tok $\downarrow$	Acc $\uparrow$	Tok $\downarrow$	Acc $\uparrow$	Tok $\downarrow$	Acc $\uparrow$	Tok $\downarrow$	Acc $\uparrow$	CR $\downarrow$
Vanilla	91.2	1,164	90.4	3,797	56.3	7,461	46.3	10,683	31.8	7,437	63.2	100%
RSS (Ours)	91.0	662	91.2	2,401	56.1	5,560	50.9	9,333	34.8	3,326	64.8	69.7%
SC $\cdot$ CS	91.1	659	91.4	2,509	56.1	5,505	48.4	9,697	31.8	4,576	63.8	75.1%
Branch-UQ Diff	90.1	864	90.6	2,826	55.0	5,639	47.1	8,788	31.3	2,998	62.8	69.1%

Appendix

Table 5: Ablation of different scoring functions under the same neutral/adversarial probing framework on DeepSeek-R1-Distill-Qwen-7B.

Category	Perturbation Prompt
Self-Correction	“Wait, I might have made a mistake. Let me reconsider, the answer is \boxed{ ”
Reflection	“Wait, let me reconsider the reasoning, the answer is \boxed{ ”
Alternative Path	“Wait, let me try a different approach, the answer is \boxed{ ”
Verification	“Wait, let me verify the reasoning once more, the answer is \boxed{ ”

Appendix

Table 6: Example perturbation probes. Each category represents a family of possible prompts; only one example is shown per category. SABER defaults to the Self-Correction style (not separately marked).

Perturbation Strategy	GSM8K		MATH-500		Olympiad		GPQA-D		Overall
Perturbation Strategy	Acc $\uparrow$	Tok $\downarrow$	Acc $\uparrow$	Tok $\downarrow$	Acc $\uparrow$	Tok $\downarrow$	Acc $\uparrow$	Tok $\downarrow$	Acc $\uparrow$	Tok $\downarrow$
SABER (Ours)	94.4	1,349	92.0	2,744	60.0	5,918	57.6	6,502	76.0	4,128
Self-Correction	94.1	1,098	91.6	2,591	59.4	5,837	57.0	5,497	75.5	3,756
Reflection	94.2	1,085	90.8	2,647	58.5	5,600	57.6	5,279	75.3	3,653
Alternative Path	94.1	1,173	90.2	2,765	61.0	5,875	52.5	6,029	74.5	3,961
Verification	94.2	1,023	91.6	2,538	58.7	5,198	52.0	5,315	74.1	3,519

Appendix

Table 7: Comparison of different perturbation styles on four benchmarks using Qwen3-4B.

Trigger	GSM8K		MATH-500		AIME24		AIME25		Olympiad		GPQA-D		Overall
Trigger	Acc $\uparrow$	Tok $\downarrow$	Acc $\uparrow$	Tok $\downarrow$	Acc $\uparrow$	Tok $\downarrow$	Acc $\uparrow$	Tok $\downarrow$	Acc $\uparrow$	Tok $\downarrow$	Acc $\uparrow$	Tok $\downarrow$	Acc $\uparrow$	CR $\downarrow$
Vanilla	96.4	2,192	92.8	5,135	66.7	12,003	54.2	12,999	59.0	9,447	55.1	9,047	70.7	100%
‘‘Wait’’	96.0	1,258	92.4	2,303	65.0	9,645	52.5	10,592	61.5	4,892	57.6	5,056	70.8	66.4%
Newline ( \n\n )	95.7	1,312	92.8	3,387	65.0	9,115	55.0	10,797	59.7	6,190	56.1	5,726	70.7	71.9%

Appendix

Table 8: Trigger sensitivity analysis on Qwen3-8B. Replacing the lexical trigger “Wait” with a semantically neutral double newline ( \n\n ) yields comparable performance, suggesting limited sensitivity to the choice of trigger.

Figure 7: A case on GSM8K where SABER identifies unstable reasoning states.

Figure 8: Comparison of vanilla reasoning and SABER on a MATH-500 problem. SABER reduces token consumption from 5840 to 1626 while maintaining correctness.

Figure 9: A case on MATH-500 where vanilla reasoning exceeds the context limit due to endless reflection, while SABER exits early and produces the correct answer.

Figure 10: A GSM8K case where vanilla reasoning degrades the correct answer through over-reflection, while SABER preserves it by timely early exit.

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Large Reasoning Models (LRMs) achieve strong performance by generating long chains of thought (CoT), but often overthink, continuing to reason after a solution has already stabilized and thereby wasting tokens and increasing latency. Existing inference-time early-exit methods rely primarily on answer-level signals, such as confidence or trial-answer consistency, to decide when to stop. However, these signals mainly reflect answer readiness rather than reasoning convergence: they may trigger before the model has finished exploring or self-correcting, causing premature exits that can degrade final-answer accuracy and leave the retained reasoning chain semantically incomplete. We identify reasoning-level semantic redundancy as a complementary signal for semantic-preserving early exit: when successive steps no longer add novel progress and instead revisit established conclusions, the reasoning trajectory has likely converged. Building on this insight, we propose PUMA, a plug-and-play framework that combines a lightweight Redundancy Detector with answer-level verification. The detector flags semantically redundant candidate exits, while verification confirms whether stopping is safe, allowing PUMA to remove redundant continuation while preserving both answer accuracy and a coherent reasoning prefix. Across five LRMs and five challenging reasoning benchmarks, PUMA achieves 26.2% average token reduction while preserving accuracy and retained CoT quality. Additional experiments on code generation, zero-shot vision-language reasoning, and learned stopping-policy internalization further demonstrate that reasoning-level redundancy is a robust, transferable, and learnable signal for efficient reasoning. Our code is available at https://github.com/giovanni-vaccarino/PUMA.

Abstract

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