Constructing Pareto Frontiers of Optimal Reasoning Termination Methods for Overthinking in Reasoning Models

Weixin Guan; Liang Li; Shiyu Xie; Jiapeng Liu; Bing Li; Peng Fu; Chengyang Fang; Xiaoshuai Hao

cs.AIOct 9, 2026

Constructing Pareto Frontiers of Optimal Reasoning Termination Methods for Overthinking in Reasoning Models

Authors: Weixin Guan, Liang Li, Shiyu Xie, Jiapeng Liu, Bing Li, Peng Fu, Chengyang Fang, Xiaoshuai Hao,

Organizations: Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China · School of Cyberspace Security, University of Chinese Academy of Sciences, Beijing, China · University of Florida, Gainesville, FL, USA · School of Computer and Artificial Intelligence, Jiangxi University of Finance and Economics ·

Abstract

Reasoning models can benefit from test-time scaling, but continued reasoning may become ineffective or harmful, a phenomenon termed overthinking. Evaluations against full thinking compare accuracy and token usage but lack references for overthinking severity and strategies' theoretical mitigation potential. To characterize overthinking at the model-task level, we first introduce Step-wise Truncation Probing (STP), repeatedly generating answers from multiple retained prefixes along each fixed sampled reasoning trajectory. Using each trajectory's earliest measured position attaining maximum empirical accuracy as a reference, we define Overthinking Ratio and Accuracy Degradation as the fraction of thinking tokens generated afterward and the accuracy decrease from this reference to full thinking, respectively. Secondly, we then formulate dynamic routing, fixed budgets, and dynamic early exit within a unified framework to quantify the theoretical mitigation potential of different termination strategies. Based on this unified framework, we use the complete STP measurements to construct a token-accuracy Pareto frontier for each strategy under a common normalized thinking-token budget. We further develop OTBench, a reusable benchmark built from the STP process, which produced 70.5B reasoning tokens and the corresponding probing measurements across six models and four benchmark groups.

Figures & tables

Figure 1: Step-wise truncation probing and overthinking metrics. (a) STP measures the corresponding accuracy by terminating reasoning at different points along the same reasoning trajectory and repeatedly generating answers from each retained prefix. (b) OR denotes the proportion of reasoning length after accuracy first reaches its maximum. AD denotes the decrease in accuracy under full reasoning relative to the maximum accuracy.

Model	AIME		MATH		GPQA		LCB		Avg.
Model	AD	OR	AD	OR	AD	OR	AD	OR	AD	OR
M1	3.02	34.4	1.66	45.4	16.15	35.4	9.89	49.1	7.68	41.1
M2	2.52	63.4	1.24	89.3	14.23	71.6	18.28	57.6	9.07	70.5
M3	1.53	63.5	1.73	92.0	10.69	73.9	8.63	68.2	5.64	74.4
M4	9.76	62.9	2.82	82.4	25.64	58.8	15.37	62.8	13.40	66.7
M5	7.52	59.0	1.80	79.3	18.73	65.2	9.95	55.9	9.50	64.8

Table 1: STP-based overthinking measurements. AD is reported in percentage points (pp) and OR in %. Avg. uses equal benchmark and model weights. Models: M1: GPT-OSS-20B; M2: Qwen3-4B-Thinking-2507; M3: Qwen3-30B-A3B-Thinking-2507; M4: DeepSeek-R1-Distill-Qwen-7B; M5: DeepSeek-R1-Distill-Qwen-14B; M6: DeepSeek-R1-Distill-Qwen-32B.

Figure 2: Local measured accuracy changes between adjacent STP measurements.

\Delta P(k)=P(k)-P(k-1)

. Left: equal-weight macro-averaged proportions of positive, negative, and flat changes. Right: the ratio of negative to positive changes. Both panels use the absolute number of retained thinking tokens

L(k)

on the horizontal axis. Later positions include only trajectories long enough to reach them. The signs reflect finite-probe accuracy differences, not the logical correctness or causal contribution of individual reasoning steps.

Strategy	Decision unit	Action and stopping position
Dynamic routing (DR)	Question $q$	Endpoint $a\in\{0,1\}$ (zero/full thinking): $k_{qs}(a)=an_{qs}$
Fixed budgets (FB)	Question $q$	Token cap $\tau_{q}$ : $k_{qs}(\tau_{q})=\max\{k:L_{qs}(k)\leq\tau_{q}\}$
Dynamic early exit (DEE)	Trajectory $(q,s)$	Position $k\in\{0,\ldots,n_{qs}\}$

Table 2: Termination strategies and corresponding actions of oracle methods in the unified framework. Here

q

indexes questions,

s

indexes sampled trajectories, and

n_{qs}

is the number of steps in a trajectory. Question-level actions apply to all sampled trajectories of the same question.

Figure 3: Pareto frontiers for oracle reasoning termination. Left: averages over six models and four benchmark groups; right: per-model benchmark averages, with equal weights throughout. The x-axis shows budget caps normalized by full-thinking cost, not realized costs. Dashed lines mark the macro-average STP full-thinking endpoint accuracy

P(n)

. Diamonds and circles mark the first budgets reaching

P(n)

(

\beta_{C}^{\mathrm{match}}

) and the frontier maximum (

\beta_{C}^{\mathrm{sat}}

), respectively.

Figure 4: Adapted public methods versus strategy-specific oracle frontiers. Solid curves show oracle frontiers; same-color dashed curves show the corresponding adapted methods. The x-axis shows oracle allowed budget caps or public-method realized mean thinking-token costs, each normalized by the corresponding full-thinking token count. Horizontal dashed lines mark the macro-average STP full-thinking endpoint accuracy

P(n)

Appendix figures & tables11 assets

Supplementary material from the paper’s appendix.

Appendix

Model	AIME		MATH		GPQA		LCB		Avg.
Model	Acc.	Tokens	Acc.	Tokens	Acc.	Tokens	Acc.	Tokens	Acc.	Tokens
M1	75.07	8,210	93.64	1,400	65.37	3,167	72.36	7,075	76.61	4,963
M2	75.62	19,064	95.89	5,793	67.08	7,203	57.43	11,819	74.00	10,970
M3	85.28	15,649	96.04	4,716	72.66	6,756	78.04	13,004	83.00	10,031
M4	48.33	12,902	93.09	3,652	51.77	6,280	42.29	11,359	58.87	8,548
M5	55.83	11,849	94.33	3,362	58.78	5,196	59.71	9,898	67.16	7,576

Appendix

Table 3: Original full-thinking baselines. Acc. is the original full-thinking answer accuracy (%); Tokens is the mean number of thinking tokens retained by the original full-thinking generations. These accuracies use the original final answers, not the repeated answer probes used to estimate the STP endpoint

P(n)

. Avg. uses equal benchmark and model weights. Benchmarks: AIME combines AIME2024, AIME2025, and AIME2026; MATH: MATH500; GPQA: GPQA-Diamond; LCB: LiveCodeBench. Models: M1: GPT-OSS-20B; M2: Qwen3-4B-Thinking-2507; M3: Qwen3-30B-A3B-Thinking-2507; M4: DeepSeek-R1-Distill-Qwen-7B; M5: DeepSeek-R1-Distill-Qwen-14B; M6: DeepSeek-R1-Distill-Qwen-32B.

Model	AIME	MATH500	GPQA-Diamond	LiveCodeBench	Avg.
GPT-OSS-20B	[30.06, 38.96]	[42.81, 47.91]	[31.65, 39.21]	[45.66, 52.58]	[39.24, 42.87]
Qwen3-4B-Thinking-2507	[58.85, 68.10]	[88.03, 90.49]	[68.58, 74.56]	[54.01, 61.17]	[68.81, 72.17]
Qwen3-30B-A3B-Thinking-2507	[58.98, 68.32]	[90.89, 93.03]	[70.64, 77.09]	[64.49, 71.77]	[72.69, 76.12]
DeepSeek-R1-Distill-Qwen-7B	[58.17, 67.59]	[80.42, 84.20]	[56.01, 61.54]	[59.30, 66.24]	[65.05, 68.38]
DeepSeek-R1-Distill-Qwen-14B	[53.88, 64.05]	[77.37, 81.07]	[62.37, 68.06]	[52.15, 59.89]	[63.03, 66.67]
DeepSeek-R1-Distill-Qwen-32B	[54.78, 65.00]	[82.77, 86.25]	[60.63, 66.56]	[62.75, 69.65]	[66.78, 70.38]

Appendix

Table 4: Confidence intervals for OR (%) reported in Table 1 . Cells report 95% percentile intervals from 10,000 paired bootstrap replicates of questions and trajectories, with probe labels fixed.

Model	AIME	MATH500	GPQA-Diamond	LiveCodeBench	Avg.
GPT-OSS-20B	[2.15, 3.96]	[1.28, 2.08]	[13.44, 18.88]	[8.34, 11.54]	[6.86, 8.51]
Qwen3-4B-Thinking-2507	[1.46, 3.76]	[0.68, 1.89]	[11.53, 17.09]	[15.66, 21.09]	[8.05, 10.11]
Qwen3-30B-A3B-Thinking-2507	[0.78, 2.42]	[0.98, 2.59]	[8.23, 13.38]	[6.64, 10.80]	[4.81, 6.54]
DeepSeek-R1-Distill-Qwen-7B	[7.53, 12.14]	[2.15, 3.54]	[22.57, 28.76]	[12.86, 17.97]	[12.24, 14.59]
DeepSeek-R1-Distill-Qwen-14B	[5.76, 9.35]	[1.26, 2.41]	[15.79, 21.81]	[8.09, 11.98]	[8.51, 10.53]
DeepSeek-R1-Distill-Qwen-32B	[3.60, 6.42]	[1.15, 2.43]	[13.71, 19.23]	[10.14, 14.83]	[7.92, 9.89]

Appendix

Table 5: Confidence intervals for AD (percentage points) reported in Table 1 . Cells report 95% percentile intervals from 10,000 paired bootstrap replicates of questions and trajectories, with probe labels fixed.

Model	AIME	MATH500	GPQA-Diamond	LiveCodeBench	Avg.
GPT-OSS-20B	[68.40, 81.39]	[91.89, 95.24]	[60.01, 70.74]	[67.50, 77.00]	[74.17, 79.05]
Qwen3-4B-Thinking-2507	[67.78, 82.92]	[94.25, 97.35]	[61.43, 72.66]	[52.25, 62.54]	[71.21, 76.68]
Qwen3-30B-A3B-Thinking-2507	[78.89, 91.25]	[94.42, 97.50]	[67.11, 78.03]	[73.32, 82.68]	[80.55, 85.37]
DeepSeek-R1-Distill-Qwen-7B	[40.14, 56.53]	[91.21, 94.80]	[46.69, 57.01]	[36.43, 48.43]	[55.97, 61.73]
DeepSeek-R1-Distill-Qwen-14B	[47.43, 64.10]	[92.53, 95.91]	[53.19, 64.46]	[53.82, 65.68]	[64.20, 70.10]
DeepSeek-R1-Distill-Qwen-32B	[54.24, 71.11]	[93.12, 96.36]	[57.92, 68.94]	[57.18, 68.68]	[68.07, 73.94]

Appendix

Table 6: Confidence intervals for original full-thinking answer accuracy (%) in Table 3 . These intervals refer to the original final answers, not STP

P(n)

. Cells contain only ordinary 95% percentile confidence intervals from 10,000 paired question-and-trajectory bootstrap replicates; probe labels are fixed. AIME pools 2024–2026. The Avg. column weights the four benchmark groups equally; the Avg. row weights models equally. Aggregate intervals use replicate-level macro-averages, not averages of interval endpoints.

Figure 5: Exact deterministic oracle frontiers with pointwise 95% two-stage bootstrap intervals. The analysis uses all six models and four reporting benchmark groups, including the combined AIME set, with equal model and benchmark weights. The horizontal axis is the allowed budget cap relative to full-thinking cost; shaded regions summarize 10,000 reoptimized bootstrap frontiers at 101 reporting budgets. The horizontal reference is the macro-average STP full-thinking endpoint accuracy

P(n)

. Shading does not provide simultaneous coverage of the whole frontier or interpolate new stopping actions.

Figure 6: Conditional sensitivity to probe and trajectory counts in the frozen experiment. Left: OR and AD after reducing the number of probes at each measured position, with the earliest maximum recomputed. Right: deviations from the full-16 OR and AD means under reduced trajectory pools per model–question, with conditional percentile ranges from 2,000 draws. Left-panel OR is in percent and AD in percentage points; right-panel deviations are in percentage points. These conditional analyses keep the observed questions fixed and are distinct from the bootstrap in Appendix A.5 .

(a) Zero-step
Model	AIME	MATH500	GPQA	LCB	Avg.
M1	9.95	67.02	37.27	40.67	38.73
M2	0.60	51.74	20.08	13.88	21.57
M3	1.78	59.21	32.26	22.14	28.85
M4	21.45	81.56	39.29	23.85	41.54
M5	20.42	74.98	46.63	28.36	42.60

Appendix

Table 7: Zero-step and direct-answer accuracies (%). Zero-step retains no thinking prefix and uses the frozen STP answer-probe protocol at

k=0

. Direct-answer uses a separately reported prompt that requests an answer without a reasoning trace. Zero-step values are reported to two decimals from the frozen

P(0)

records; direct-answer values are the returned two-decimal aggregate results. Models M1–M6 follow Table 1 . The Avg. column averages the four benchmark groups equally, and the Avg. row averages the six models equally.

Figure 7: Representative measured accuracy curves, shown separately rather than overlaid. Each panel identifies its model and benchmark and reports token-based OR and AD; markers locate

k^{\star}

. The horizontal coordinate is the retained fraction of the trajectory’s full thinking-token count, and the vertical coordinate is

P(k)

. Line segments connect measured positions for readability and are not additional probe measurements. The examples illustrate possible shapes and do not estimate their prevalence.

Figure 8: Trajectory diversity for one fixed model–question pair. Each panel shows one of its 16 sampled trajectories, with the same accuracy and relative thinking-token axes and a marker at its earliest measured maximum. All trajectories of the selected question are displayed, including any flat curves; no subset is chosen to enlarge the visual contrast. The displayed model is GPT-OSS-20B and the question is GPQA-Diamond question recIj8lR4tuDgrHou .

Model	$\|B\|$	Seen	Events
GPT-OSS-20B	671	176	789,761
Qwen3-4B-Thinking-2507	565	182	3,393,687
Qwen3-30B-A3B-Thinking-2507	565	189	2,304,662
DeepSeek-R1-Distill-Qwen-7B	565	167	3,449,932
DeepSeek-R1-Distill-Qwen-14B	565	155	3,078,850
DeepSeek-R1-Distill-Qwen-32B	565	155	3,103,862

Appendix

Table 8: Token-boundary audit and decoded forms. Vocabulary construction decodes each ID; runtime splitting tests ID membership in

B

only. Seen counts observed boundary IDs; Events counts their occurrences. Cross counts overlapping literal LF–LF pairs crossing token payloads; Unmarked counts those whose right token is outside

B

. An asterisk denotes incomplete byte/decode verification; unavailable entries are not zeros. Below, P/W/S/I are vocabulary counts: pure double LF, other whitespace-only, compound double-LF suffix, and compound infix. The top three observed literal forms are escaped, with occurrence counts; complete forms and reconstruction checks remain in the accompanying CSV/protocol.

Figure 9: Empirical distributions of step-token lengths after repartitioning the same trajectories with

b=128

256

, and

512

. Panels separate the six models, and

b=256

denotes the main measurement setting. The horizontal axis counts tokens per resulting step. The analysis changes only the partition and does not generate answers at the alternative positions.

Overthinking in Language Models

Overthinking in language models studies when extra reasoning becomes redundant or harmful, and how to control it without losing accuracy.

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Thinking Past the Answer: Evaluating Harmful Overthinking in Large Reasoning Models

Simone Caldarella, Davide Talon, Rahaf Aljundi, Elisa Ricci+1

University of Trento · 3Fondazione Bruno Kessler · 2Toyota Motor Europe

LLM Evaluation Overthinking in Language Models Reasoning Evaluation LLM Reliability Large Reasoning Models Reasoning Trace Analysis

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Large Reasoning Models (LRMs) improve performance by generating explicit intermediate reasoning traces through increased test-time compute, yet the assumption that longer reasoning is consistently beneficial remains under-examined. While recent evidence shows that additional reasoning can lead models to overthink, we ask: "Once a model has reached the correct answer, does further reasoning refine the solution, or deviate from it?" To study the dynamics after correctness, we introduce a prefix-level trajectory evaluation protocol grounded in reasoning sufficiency, defining the minimum reasoning budget required for a model to first generate the correct answer. This allows us to disentangle verbose overthinking, where additional reasoning is redundant but harmless, from harmful overthinking, where continued reasoning destabilizes an already-correct trajectory. Starting from multimodal benchmarks, we find that many instances considered reasoning-intensive require surprisingly little reasoning. Moreover, stopping at the first correct prefix improves accuracy over standard reasoning up to 21%, revealing that current models are limited not only by their ability to reason, but also by their inability to stop at the right time. Furthermore, while common efficiency strategies like early stopping substantially reduce verbose overthinking (up to 50%), they fail to mitigate harmful overthinking. Failure analysis reveals that correctness deviations are mainly driven by logical drift and visual reinterpretation. Finally, we show that our findings generalize to language-only reasoning benchmarks, highlighting harmful overthinking as a broader reliability risk. Code available at https://simonecaldarella.github.io/thinking-past-the-answer.

Abstract

Overthinking in Language Models

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