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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, Can Ma, Weiping Wang

arXiv:2610.13570v1cs.AI

TL;DR

Evaluations against full thinking do not provide references for overthinking severity or termination strategies’ theoretical mitigation potential. The paper uses STP to measure overthinking, constructs strategy-specific Pareto frontiers, and develops OTBench; it reports substantial overthinking and room between selected methods and their frontiers.

  • Problem

    Comparisons with full thinking lack references for overthinking severity and the best token–accuracy trade-offs theoretically available to each termination strategy.

    Source: §1 · pp. 1–2

  • Method

    STP probes multiple retained prefixes along fixed sampled trajectories, and a unified framework uses complete STP measurements to construct a token–accuracy Pareto frontier for each termination strategy.

    Source: §1 · p. 2

  • Results

    64.3% of thinking tokens follow the measured accuracy maximum and full thinking loses 9.03 percentage points against that reference on average; the strategy frontiers are ordered routing, fixed budgets, then early exit, with selected baselines below them.

    Source: §1 · pp. 2–3

  • Takeaways & Limitations

    The strategy-specific frontiers provide idealized references for assessing termination methods against the theoretical potential of their respective strategies.

    Source: §1 · pp. 2–3

    The offline frontiers optimize measured stopping actions and do not specify online policies with access to the same information before a trajectory is complete.

    Source: E LIMITATIONS AND FURTHER DIRECTIONS · p. 24

Abstract

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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.

1 INTRODUCTION

The paper addresses the lack of references for measuring overthinking severity and the theoretical mitigation potential of termination strategies. It introduces STP, strategy-specific token–accuracy frontiers, and OTBench, then reports substantial overthinking and unrealized potential for selected methods.

1 INTRODUCTION

  • Existing comparisons with full thinking lack references for overthinking severity and the best token–accuracy trade-offs theoretically available to each termination strategy.This leaves two questions unanswered: how severe overthinking is for a model and task, and how much each strategy could theoretically mitigate it.Source: §1 · pp. 1–2
  • STP probes multiple retained prefixes on each fixed sampled reasoning trajectory, using its earliest measured accuracy maximum to define OR and AD.OR is the fraction of thinking tokens after that reference; AD is the accuracy decrease from it to full thinking.Source: §1 · p. 2
  • Under a common normalized thinking-token budget, the paper formulates three termination strategies in one framework and constructs a token–accuracy Pareto frontier for each.The frontiers are idealized references for strategy potential; OTBench compares practical methods against their corresponding frontiers.Source: §1 · p. 2
  • 64.3% of thinking tokens follow the measured accuracy maximum, and full thinking loses 9.03 percentage points against that reference on average.The strategy frontiers are ordered dynamic routing, fixed budgets, then dynamic early exit; selected public baselines lie below their corresponding frontiers.Source: §1 · pp. 2–3
  • The paper contributes model–task overthinking measurements, idealized strategy-specific frontiers, and OTBench, a public reusable benchmark built from STP.OTBench evaluates termination methods against their corresponding frontiers.Source: §1 · p. 3

2 RELATED WORKS

Prior work describes overthinking-related inefficiency and performance degradation, while mitigation research includes both changes to reasoning generation and decisions about when to stop. The paper organizes termination methods by when their decision is made.

2 RELATED WORKS

3 CHARACTERIZING OVERTHINKING AT THE MODEL–TASK LEVEL

The section measures overthinking by probing retained prefixes along fixed trajectories and comparing each trajectory’s measured accuracy maximum with full thinking. Across six models and four benchmark groups, it finds substantial redundancy and accuracy loss, with differences across tasks and sampled trajectories.

3.1 MEASURING OVERTHINKING WITH STEP-WISE TRUNCATION PROBING

  • STP measures accuracy at multiple retained-token positions along the same trajectory, then uses the earliest measured position attaining maximum accuracy as its empirical reference.OR measures the fraction of tokens beyond the reference; AD measures the accuracy difference between it and the full-thinking endpoint.Source: §3.1 · p. 4

3.2 QUANTIFYING OVERTHINKING FOR SIX MODELS ACROSS FOUR BENCHMARK GROUPS

  • The evaluation samples 16 trajectories per model–question pair across six models and four benchmark groups, with 16 answer probes per position and b = 256.The original full-thinking baseline uses original final answers, unlike the STP full-thinking endpoint estimated from repeated probes.Source: §3.2 · p. 4
  • 64.3% is the mean Overthinking Ratio, and the STP full-thinking endpoint is 9.03 percentage points less accurate than the trajectory-level reference on average.Across six models, OR ranges from 41.1% to 74.4%, while AD ranges from 5.64 to 13.40 percentage points.Source: §3.2 · pp. 4–5
  • Higher length redundancy does not imply greater accuracy degradation: MATH has the highest mean OR (78.8%) and lowest AD (1.83 percentage points), while GPQA has lower OR (61.4%) and highest AD (16.98 percentage points).Across 24 model–benchmark means, OR and AD have a weak negative Spearman correlation of −0.330.Source: §3.2 · p. 5
  • At later measured positions, flat accuracy changes become more prevalent and the negative-to-positive ratio generally rises, while the overall negative-change fraction does not grow.Among non-flat changes, decreases become more common relative to improvements.Source: §3.2 · p. 5
  • For the same model and question, sampled trajectories differ by an average pairwise absolute difference of 20.23 percentage points in OR and 10.06 percentage points in AD.Both measured token redundancy and endpoint accuracy difference vary substantially across trajectories.Source: §3.2 · p. 5

4 PARETO FRONTIERS OF ORACLE REASONING-TERMINATION METHODS

The section constructs offline token–accuracy Pareto frontiers for three oracle termination strategies using a shared budget-constrained framework. The frontiers show how their measured trade-offs and budget requirements differ as decision-making becomes more flexible.

4 PARETO FRONTIERS OF ORACLE REASONING-TERMINATION METHODS

  • The offline frontiers select the best measured accuracy–cost actions at each budget and serve as theoretical references, not deployable stopping algorithms.Macro-averaging gives each model–benchmark combination the same fraction of its own full-thinking budget before equal-weight accuracy averaging.Source: §4 · p. 5, §4.1 · p. 7

4.1 A UNIFIED FRAMEWORK FOR ORACLE TERMINATION METHODS

  • The unified framework treats termination as maximizing selected-action accuracy subject to an average thinking-token budget.Changing decision units and allowed actions instantiates the strategies while preserving the objective.Source: §4.1 · p. 6
  • Dynamic routing chooses a question-level zero-or-full endpoint, fixed budgets use a shared question-level cap, and dynamic early exit chooses separately for each trajectory.Fixed-budget candidate caps come from the measured token counts for that question.Source: §4.1 · p. 6

4.2 FRONTIER HIERARCHY ACROSS TERMINATION STRATEGIES

  • Dynamic routing’s frontier is no higher than fixed budgets’, which is no higher than dynamic early exit’s under the same budget.The gaps reflect the potential of question-level intermediate caps and trajectory-specific stopping choices.Source: §4.2 · p. 7, Figure 3 · p. 8
  • 71.4%, 35.0%, and 14.2% are the relative budget caps needed for dynamic routing, fixed budgets, and dynamic early exit to match the STP endpoint reference.The reference is the macro-average STP endpoint accuracy, distinct from the original-answer baseline.Source: §4.2 · p. 7, Figure 3 · p. 8
  • Approximately 73%, 76%, and 81% are the measured accuracy ceilings for dynamic routing, fixed budgets, and dynamic early exit, reached at respective caps of 94.2%, 87.2%, and 58.6%.These are macro-averaged ceilings within the measured action space.Source: §4.2 · pp. 7–8, Figure 3 · p. 8

5 EVALUATING REASONING-TERMINATION METHODS WITH OTBENCH

OTBench evaluates practical termination methods against strategy-specific Pareto frontiers through a shared action interface and evaluator. Its protocol compares measured token–accuracy curves with offline references using common measurements and normalized costs.

5 EVALUATING REASONING-TERMINATION METHODS WITH OTBENCH

  • OTBench compares each practical method’s measured token–accuracy curve with the frontier for its termination strategy.The benchmark provides a shared action interface and dedicated evaluator.Source: §5 · p. 8

5.1 A COMMON EVALUATION PROTOCOL FOR TERMINATION METHODS

  • The evaluator derives retained thinking-token cost and answer accuracy from STP measurements for selected stopping actions.It represents method actions for decision units using retained token costs and probe accuracies.Source: §5.1 · p. 8
  • OTBench reserves test measurements for final evaluation and compares methods with corresponding oracle frontiers on the same questions and normalized costs.Training supervises learned components, while validation supports model selection and calibration; token cost excludes feature-extraction and signal-computation overhead.Source: §5.1 · p. 9

5.2 COMPARING PUBLIC METHODS WITH STRATEGY-SPECIFIC PARETO FRONTIERS

  • The evaluation adapts one public method per strategy and sweeps its control parameter to form nondominated operating-point curves.Figure 4 places adapted-method curves against corresponding oracle frontiers in normalized token–accuracy coordinates.Source: §5.2 · p. 9, Figure 4 · p. 9

6 CONCLUSION

The paper introduces STP to characterize overthinking, constructs strategy-specific Pareto frontiers as idealized references, and develops OTBench from measurements across six models and four benchmark groups.

6 CONCLUSION

  • STP measures overthinking at the model–task level and finds it substantial and variable across sampled trajectories.The conclusion describes STP as a measurement procedure for characterizing overthinking.Source: §6 · p. 10
  • The paper formulates dynamic routing, fixed budgets, and dynamic early exit in a unified budget-constrained framework with strategy-specific token–accuracy frontiers.The frontiers are idealized references for termination potential.Source: §6 · p. 10
  • OTBench contains 70.5B reasoning tokens and STP measurements from six models across four benchmark groups.The benchmark provides a common protocol for evaluating practical methods against corresponding strategy-specific frontiers.Source: §6 · p. 10

A EXPERIMENTAL PROTOCOL AND ANALYSIS PROCEDURES

The appendix outlines the procedures underlying the paper’s analyses, from trajectory generation and STP to frontier construction, public-method adaptations, and uncertainty estimation.

A EXPERIMENTAL PROTOCOL AND ANALYSIS PROCEDURES

A.1 MODELS, TASKS, AND GENERATION

The experimental setup uses six fixed model checkpoints and four benchmark groups, with sampled trajectories partitioned by question and specified generation and probing procedures.

A.1 MODELS, TASKS, AND GENERATION

  • The study evaluates six fixed checkpoints spanning GPT-OSS, Qwen, and DeepSeek-R1-Distill-Qwen models.The set includes dense models and two models with stated total and active parameter counts.Source: §A.1 · p. 13
  • The evaluation covers 963 questions across four benchmark groups and samples 16 trajectories per question for each model.All sampled trajectories from a question remain in the same train, validation, or test partition.Source: §A.1 · p. 13
  • Generation uses a 32,768-token thinking limit, while each answer probe generates at most 4,096 tokens with 16 samples per position.The context limit is 65,536 tokens, and model-specific sampling configurations are used.Source: §A.1 · p. 13
  • Prompts request step-by-step reasoning, with answer formats adapted to the benchmark and model family.Seeds are derived deterministically from model, benchmark, question, trajectory, and generation phase; STP seeds also include probe position.Source: §A.1 · p. 13
  • Table 3’s full-thinking accuracies use original final answers, not the repeated probes used to estimate the STP endpoint P(n).The corresponding confidence intervals are reported in Table 6.Source: §A.1 · p. 13

A.2 PROBING AND ANSWER EVALUATION

The appendix specifies how STP measurements are constructed and evaluated, how strategy-specific frontiers are optimized, and how uncertainty and public-method comparisons are reported. Its intervals quantify resampling variation within the fixed evaluated models and benchmarks.

A.2 PROBING AND ANSWER EVALUATION

  • STP reuses fixed reasoning prefixes for answer probes, and OR and AD compare each trajectory with its earliest measured accuracy maximum.The appendix distinguishes the original full-thinking answer accuracy from the STP full-thinking endpoint P(n).Source: §A.2 · pp. 13–14

A.3 EXACT CONSTRUCTION OF STRATEGY-SPECIFIC ORACLE FRONTIERS

  • Question-level actions define dynamic routing and fixed budgets, while dynamic early exit selects measured stopping positions separately for each trajectory.The exact Pareto frontier removes dominated actions and combines decision units by dynamic programming, reporting the best attainable accuracy under each budget.Source: §A.3 · pp. 14–15

A.4 PUBLIC METHODS AND THEIR ADAPTATIONS

  • Public-method curves use adapted decision interfaces and measured accuracy–cost points, without interpolating new operating points.The reported token cost excludes predictor training, feature extraction, and signal-computation overhead.Source: §A.4 · p. 15

A.5 RESAMPLING AND UNCERTAINTY ESTIMATION

  • 10,000 paired two-stage bootstrap replicates resample questions and trajectories, while holding the 16-probe curves fixed.Frontiers are reoptimized in each replicate; their percentile intervals are pointwise, and the fixed model identities and benchmarks do not represent broader populations.Source: §A.5 · pp. 15–16

B UNCERTAINTY AND MEASUREMENT ROBUSTNESS

B.1 INTERVAL MATRICES AND ORACLE FRONTIERS

  • Tables 4–6 report intervals for OR, AD, and original full-thinking accuracy; Figure 5 gives pointwise uncertainty for strategy frontiers.The frontier’s full-thinking reference is the STP endpoint P(n), not original-answer accuracy.Source: §B.1 · p. 16, Table 4 · p. 16, Table 5 · p. 16

B.2 SENSITIVITY TO PROBE AND TRAJECTORY COUNTS

The appendix examines how probe and trajectory counts affect measured overthinking, then presents zero-step comparisons and examples of accuracy curves and within-question trajectory diversity. It also frames step construction as a measurement-resolution choice.

B.2 SENSITIVITY TO PROBE AND TRAJECTORY COUNTS

  • At 4, 8, 12, and 16 probes, expected macro-average OR is 74.69%, 69.09%, 66.22%, and 64.34%, while expected AD is 11.07, 9.87, 9.34, and 9.03 percentage points.The full-16 earliest maximizer is retained with probabilities 51.83%, 69.94%, 84.88%, and 100%, respectively; these are conditional results, not evidence of an infinite-probe optimum.Source: §B.2 · pp. 16, 18
  • With two trajectories per question, conditional ranges are [63.88, 64.82]% for OR and [8.68, 9.41] percentage points for AD; with eight, they narrow to [64.16, 64.52]% and [8.89, 9.17] percentage points.Uniform thinning leaves conditional expectations unchanged, while widening sampling variation.Source: §B.2 · p. 18, Figure 6 · p. 18

B.3 ZERO-STEP AND DIRECT-ANSWER COMPARISONS

  • Zero-step and direct-answer overall means are descriptively similar, but the comparison establishes neither question-level agreement nor statistical equivalence.Zero-step uses the frozen STP prompt and probe protocol; direct answer uses a separate no-thinking prompt.Source: §B.3 · pp. 18–19, Table 7 · p. 19

C.1 REPRESENTATIVE STP ACCURACY CURVES

C.2 TRAJECTORY DIVERSITY WITHIN A QUESTION

  • Figure 8 displays all 16 sampled trajectories for one GPT-OSS-20B and GPQA-Diamond question in separate panels with shared axes.The example illustrates within-question variation but does not establish its frequency or a universal pattern.Source: §C.2 · pp. 19, 21, Figure 8 · p. 21

D STEP CONSTRUCTION AND MEASUREMENT RESOLUTION

  • Step construction controls the resolution of the measurement used by the main-text local-change analysis.The section examines the boundary rule and resulting step-length distributions.Source: D STEP CONSTRUCTION AND MEASUREMENT… · p. 21

D.1 BOUNDARY IDENTIFICATION AND RESULTING STEP LENGTHS

The boundary audit checks token-level segmentation against decoded trajectories, while alternate target step lengths examine realized measurement resolution without generating new answers.

D.1 BOUNDARY IDENTIFICATION AND RESULTING STEP LENGTHS

  • Across 92,448 trajectories and 576,688,123 stored thinking tokens, the byte-level audit found no double-newline pair spanning token boundaries.Reconstructing the main b = 256 partition produced zero trajectory-level step-position mismatches.Source: §D.1 · pp. 21–22, Table 8 · p. 22
  • Mean realized step lengths were 128.18–129.92 tokens for b = 128, 255.16–256.84 for b = 256, and 499.80–513.01 for b = 512.The repartitioning changes no generated content and performs no new answer probing, so it makes no claim about OR, AD, or frontier changes.Source: §D.1 · p. 22, Figure 9 · p. 23

E LIMITATIONS AND FURTHER DIRECTIONS

The paper identifies limits in what its offline frontiers represent, how its measurements are obtained, and how broadly its empirical results generalize. It points to finer-grained and trajectory-aware termination as future work.

E LIMITATIONS AND FURTHER DIRECTIONS

  • Offline frontiers optimize measured stopping actions but are evaluation references, not deployable policies with access to the same information before trajectories finish.Source: E LIMITATIONS AND FURTHER DIRECTIONS · p. 24
  • STP measurements depend on step boundaries, target average step length, and repeated answer generation, while token-cost accounting excludes that probing overhead.These choices determine the resolution and measurement uncertainty of OR, AD, and the frontiers.Source: E LIMITATIONS AND FURTHER DIRECTIONS · p. 24
  • The evaluation covers six models, four benchmark groups, and one adapted public method per termination strategy, so extension to other settings is undetermined.Future work can examine richer prefix information, finer stopping decisions, broader model and task coverage, and deployment overhead.Source: E LIMITATIONS AND FURTHER DIRECTIONS · p. 24
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