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REVIEW 1 major objections 2 minor 41 references

Celeus constructs anytime-valid confidence intervals for LLM evaluation by proving that uncertainty-guided sampling signals combined with surrogate approximations remain unbiased conditional on past observations.

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CELEUS applies e-processes to LLM evaluation to produce anytime-valid CIs that reach target precision with 54-62% fewer samples than baselines while preserving coverage guarantees.

T0 review reviewed 2026-06-29 challenge →

load-bearing objection Celeus applies e-processes to LLM eval for anytime-valid CIs by proving conditional unbiasedness under uncertainty sampling plus surrogates, with reported 54-62% sample cuts. the 1 major comments →

arxiv 2606.20820 v2 pith:SNLIWIGD submitted 2026-06-18 cs.LG

CELEUS: Certifiable and Efficient LLM Evaluation via E-Processes

Zhijian Zhou , Zesheng Ye , Zhaorun Chen , Bo Li , Feng Liu This is my paper
classification cs.LG
keywords LLM evaluatione-processesanytime-valid CIsuncertainty samplingsurrogate approximationcertifiable evaluationsequential sampling
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper aims to close the gap between theoretical guarantees and practical use in LLM evaluation by developing methods that provide valid confidence intervals even when the evaluation process adapts based on intermediate results. Existing approaches can lose their coverage guarantees if intervals are updated repeatedly to decide when to stop sampling more examples. Celeus addresses this by introducing signals that merge uncertainty-guided selection of samples with approximations for unevaluated ones, proving these signals are unbiased given the history. This unbiasedness supports the use of e-processes to form intervals that are valid at any stopping time. If correct, evaluators can confidently halt testing once a desired precision is achieved, knowing the reported interval truly covers the model's performance with the stated probability.

Core claim

The central discovery is that signals combining uncertainty-guided sampling to select informative samples for evaluation and surrogate-assisted approximations for unevaluated samples remain unbiased for the evaluation score conditional on the past. This property enables the construction of statistically-grounded and anytime-valid e-process confidence intervals. The approach also reduces estimation variance, allowing the target precision to be reached with fewer evaluated samples, and the intervals shrink at a near-parametric rate up to logarithmic factors.

What carries the argument

Unbiased signals from uncertainty-guided sampling and surrogate-assisted approximations that enable e-process based anytime-valid confidence intervals.

Load-bearing premise

The signals combining uncertainty-guided sampling to select informative samples and surrogate-assisted approximations for unevaluated samples remain unbiased for the evaluation score conditional on the past.

What would settle it

Observing that the empirical coverage of the constructed confidence intervals falls below the nominal level, such as 95%, in repeated experiments where stopping decisions are made adaptively based on the intervals.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • The CIs remain valid regardless of when the evaluation stops based on the intervals themselves.
  • Target precision is reached with 54-62% fewer evaluated samples than baselines.
  • Confidence intervals shrink at near-parametric rates up to logarithmic factors.
  • An oracle variance-optimal sampling rule exists that motivates the empirical uncertainty-guided approach.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar unbiased signal constructions might apply to sequential testing in other machine learning tasks like model selection or hyperparameter tuning.
  • The efficiency gains could make large-scale LLM benchmarking more feasible under resource constraints.
  • If extended, this might provide a template for certifiable evaluation in non-LLM settings where adaptive sampling is used.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

1 major / 2 minor

Summary. The paper proposes CELEUS, a framework for certifiable LLM evaluation that uses e-processes to construct anytime-valid confidence intervals. It introduces composite signals that combine uncertainty-guided sampling of informative examples with surrogate-assisted approximations for unevaluated items, proves that these signals are conditionally unbiased for the evaluation score given the past, establishes near-parametric shrinkage rates (up to log factors) for the resulting CIs, and reports that the method reaches target precision with 54-62% fewer evaluated samples than baselines while preserving coverage guarantees.

Significance. If the conditional-unbiasedness claim holds, the work supplies a statistically rigorous, anytime-valid alternative to existing sequential LLM evaluation procedures. The combination of e-process theory with practical variance-reduction techniques (uncertainty sampling plus surrogates) and the reported sample savings would be a meaningful contribution to efficient, certifiable evaluation, especially given the high cost of human or model-based scoring of large test sets.

major comments (1)
  1. [§3 (proof of unbiasedness)] The central load-bearing claim is the proof that the uncertainty-guided sampling plus surrogate signals remain conditionally unbiased for the evaluation score given the past (abstract and §3). Because this property is what licenses the e-process construction and the anytime-valid coverage, the derivation must be checked in full for any dependence introduced by the sampling rule or the surrogate training that could violate the martingale property.
minor comments (2)
  1. [Experiments] The experimental section should report the precise definition of the target precision (e.g., CI width) and the stopping rule used in the anytime-valid setting so that the 54-62% reduction claim can be reproduced.
  2. [§2-3] Notation for the surrogate model and the uncertainty measure should be introduced once and used consistently; several symbols appear to be overloaded between the sampling rule and the e-process construction.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment and recommendation for minor revision. We address the sole major comment below.

read point-by-point responses

  1. Referee: [§3 (proof of unbiasedness)] The central load-bearing claim is the proof that the uncertainty-guided sampling plus surrogate signals remain conditionally unbiased for the evaluation score given the past (abstract and §3). Because this property is what licenses the e-process construction and the anytime-valid coverage, the derivation must be checked in full for any dependence introduced by the sampling rule or the surrogate training that could violate the martingale property.

    Authors: We appreciate the referee underscoring the centrality of this property. In §3 the proof proceeds by verifying that the composite signal S_t satisfies E[S_t | ℱ_{t-1}] = heta (the target score) for the filtration ℱ_{t-1} generated by all prior evaluations and the surrogate parameters fitted on them. The uncertainty-guided sampling probabilities are ℱ_{t-1}-measurable by construction, and the surrogate approximation is likewise a deterministic function of ℱ_{t-1}. Consequently the product of the sampling indicator and the (surrogate or true) score remains a martingale difference; no extra dependence is introduced that would break the conditional unbiasedness. We have re-examined every step of the derivation and confirm it holds. In a minor revision we will insert a short paragraph after the main proof explicitly stating the measurability of each component with respect to ℱ_{t-1}. revision: partial

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper claims to prove that the proposed signals (uncertainty-guided sampling plus surrogate approximations) remain conditionally unbiased for the evaluation score given the past; this is presented as an independent derivation that enables the e-process CIs. No equation or step in the abstract reduces the unbiasedness claim, the variance reduction, or the near-parametric rate to a fitted parameter or self-referential definition. The method is explicitly built on external e-process theory, and the reported sample-efficiency gains are experimental. The derivation chain is therefore self-contained against the listed circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the property that the constructed signals are unbiased conditional on the past; this is treated as a domain assumption whose proof is asserted but not inspectable from the abstract. No free parameters or invented entities are introduced in the abstract description.

axioms (1)
  • domain assumption Signals combining uncertainty-guided sampling and surrogate-assisted approximations remain unbiased for the evaluation score conditional on the past
    This property is required for the e-process CIs to be anytime-valid; it is stated as proven in the abstract.

reviewed 2026-06-29 · how reviews work

0 comments
Cite this review

Pith. "Pith review of CELEUS: Certifiable and Efficient LLM Evaluation via E-Processes." pith.science (2026). https://pith.science/paper/SNLIWIGD

@misc{pith2026260620820,
  author       = {Pith},
  title        = {Pith review of: CELEUS: Certifiable and Efficient LLM Evaluation via E-Processes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SNLIWIGD}},
  note         = {Machine review of arXiv:2606.20820}
}
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abstract

Can we trust evaluation scores to capture an LLM's true real-world performance? Certifiable evaluation answers this question by providing guarantee for LLM evaluation. In particular, existing methods sequentially curate evaluation samples and keep updating confidence intervals (CIs) that cover the true performance with high probability (e.g., 95%) until some conditions are satisfied, e.g., the CI width reaches a target precision. However, existing methods are not generally anytime-valid: the claimed coverage (e.g., 95%) may fail when CIs are repeatedly updated and used to decide when to stop, leaving a gap between theoretical rigor and practice. This paper bridges this gap by proposing Celeus, a Certifiable framework for Efficient LLM evaluation, which leverages E-processes to build anytime-valid CIs. Concretely, we propose signals that combine two ingredients: (i) Uncertainty-guided sampling to select informative samples for evaluation, and (ii) Surrogate-assisted approximations for unevaluated samples. We prove that such signals remain unbiased for the evaluation score conditional on the past, enabling statistically-grounded and anytime-valid $e$-process CIs. More importantly, the two ingredients reduce estimation variance and help reach the target precision with fewer evaluated samples. We also prove that CIs obtained by Celeus can shrink at a near-parametric rate up to logarithmic factors and analyze the oracle variance-optimal sampling rule that motivates the empirical uncertainty-guided one. Experiments show that Celeus reaches the target precision using 54-62% fewer evaluated samples than baselines, while preserving anytime-valid coverage.

Figures

Figures reproduced from arXiv: 2606.20820 by Bo Li, Feng Liu, Zesheng Ye, Zhaorun Chen, Zhijian Zhou.

Figure 1
Figure 1. Figure 1: CI width versus the number of evaluated samples. Each trajectory is averaged over 50 seeds and surrogate–target pairs, with shaded bands showing ±1 standard deviation. The dashed line marks ϵ = 0.05. At the budget where ORACLE reaches ϵ, CELEUS reduces the CI-width gap between EVALUE and ORACLE by 90%/93%/84% on SST-2/MMLU/AG News, compared with 53%/60%/60% for CELEUS (W/O SURR). generation), DeepSeek-67B,… view at source ↗
Figure 2
Figure 2. Figure 2: Mechanism analysis for CELEUS, pooled across the six surrogate-target pairs. Left: empirical bias of the final estimator Rˆt in Eqn. (4) versus the unweighted estimator that removes um,t. Middle: MSE of the proposed signal Sˆt in Eqn. (1) versus the naive single-step observed risk of the newly evaluated sample. Right: Var(Sˆt | Ft−1) under uniform sampling, CELEUS’s uncertainty-guided sampling, and the ora… view at source ↗
Figure 3
Figure 3. Figure 3: Confidence interval width versus number of evaluated samples under cross-entropy loss on SST-2, MMLU, and AG News. Each curve is the mean width at each label budget, aggregated over 50 seeds and the four surrogate-target pairs of App. D.2; the shaded band is ±1σ across the per-pair means. The dashed line marks the target precision ϵ = 0.05, and triangles mark the median samples-to-ϵ for CELEUS, which reach… view at source ↗
Figure 4
Figure 4. Figure 4: Sample-selection strategy comparison under 0-1 risk. We compare the sample-selection strategies in Rem. 1 by plotting CI width versus the number of evaluated samples on SST-2, MMLU, and AG News. Each curve is averaged over 50 seeds, and the dashed line marks the target precision ϵ = 0.05. 0-1 loss family. The strategies in Rem. 1 differ in how they approximate the oracle residual |ℓ(f(xj ), yj ) − ˜ℓf (xj … view at source ↗
Figure 5
Figure 5. Figure 5: Sample-selection strategy comparison under cross-entropy risk. We compare the sample-selection strategies in Rem. 2 by plotting CI width versus the number of evaluated samples on SST-2, MMLU, and AG News. Each curve is averaged over 50 seeds, and the dashed line marks the target precision ϵ = 0.05. same sample-selection ranking as Strategy A but a different correction term in Eqn. (4). Strategy C is the on… view at source ↗
Figure 6
Figure 6. Figure 6: Sensitivity of median samples-to-ϵ to the betting-magnitude floor β, on three benchmarks (SST-2, MMLU, AG News) and two surrogate-target pairs per benchmark. Each curve is the median number of evaluate samples used, over 50 seeds at ϵ = 0.05 under 0-1 loss. The vertical dashed line marks the deployed value β = 0.4. Curves are L-shaped on the left and either flat or mildly increasing on the right; the deplo… view at source ↗
Figure 7
Figure 7. Figure 7: Confidence interval width versus evaluated samples on each (dataset, surrogate, target) experimental configuration. Rows index the six surrogate-target pairs of App. D.2, and columns index the three benchmarks. Each curve is the mean width over 50 seeds. The dashed line marks the target precision ϵ = 0.05, and triangles mark the median samples-to-ϵ. The ordering CELEUS ≤ CELEUS (W/O SURR) ≤ EVALUE holds on… view at source ↗

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Reference graph

Works this paper leans on

41 extracted references

  1. [1]

    Measuring massive multitask language under- standing

    Dan Hendrycks, Collin Burns, Steven Basart, Andy Zou, Mantas Mazeika, Dawn Song, and Jacob Stein- hardt. Measuring massive multitask language under- standing. InICLR, 2021

    2021

  2. [2]

    Truth- fulQA: Measuring how models mimic human false- hoods

    Stephanie Lin, Jacob Hilton, and Owain Evans. Truth- fulQA: Measuring how models mimic human false- hoods. InACL, 2022

    2022

  3. [3]

    Evaluating large language models trained on code.arXiv, 2021

    Mark Chen, Jerry Tworek, Heewoo Jun, Qiming Yuan, Jared Kaplan, Harri Edwards, Yuri Burda, Nicholas Joseph, Greg Brockman, Alex Ray, et al. Evaluating large language models trained on code.arXiv, 2021

    2021

  4. [4]

    Training language models to follow instructions with human feedback

    Long Ouyang, Jeffrey Wu, Xu Jiang, Diogo Almeida, Carroll Wainwright, Pamela Mishkin, Chong Zhang, Sandhini Agarwal, Katarina Slama, Alex Ray, et al. Training language models to follow instructions with human feedback. InNeurIPS, 2022

    2022

  5. [5]

    Judging llm-as-a-judge with mt-bench and chatbot arena

    Lianmin Zheng, Wei-Lin Chiang, Ying Sheng, Siyuan Zhuang, Zhanghao Wu, Yonghao Zhuang, Zi Lin, Zhuohan Li, Dacheng Li, Eric Xing, et al. Judging llm-as-a-judge with mt-bench and chatbot arena. In NeurIPS, 2023

    2023

  6. [6]

    Yupeng Chang, Xu Wang, Jindong Wang, Yuan Wu, Linyi Yang, Kaijie Zhu, Hao Chen, Xiaoyuan Yi, Cunxiang Wang, Yidong Wang, et al. A survey on eval- 9 CELEUS: Certifiable and Efficient LLM Evaluation via E-Processes uation of large language models.ACM transactions on intelligent systems and technology, 15(3):1–45, 2024

    2024

  7. [7]

    Beyond the imitation game: Quantifying and extrap- olating the capabilities of language models.Transac- tions on Machine Learning Research, 2023

    Aarohi Srivastava, Abhinav Rastogi, Abhay Rao, Abu Awal Md Shoeb, Abubakar Abid, Adam Fisch, et al. Beyond the imitation game: Quantifying and extrap- olating the capabilities of language models.Transac- tions on Machine Learning Research, 2023

    2023

  8. [8]

    Holis- tic evaluation of language models.Annals of the New York Academy of Sciences, 1525(1):140–146, 2023

    Rishi Bommasani, Percy Liang, and Tony Lee. Holis- tic evaluation of language models.Annals of the New York Academy of Sciences, 1525(1):140–146, 2023

    2023

  9. [9]

    Cer-eval: Certifiable and cost-efficient evaluation framework for llms.arXiv, 2025

    Ganghua Wang, Zhaorun Chen, Bo Li, and Haifeng Xu. Cer-eval: Certifiable and cost-efficient evaluation framework for llms.arXiv, 2025

    2025

  10. [10]

    Angelopoulos, Stephen Bates, Clara Fannjiang, Michael I

    Anastasios N. Angelopoulos, Stephen Bates, Clara Fannjiang, Michael I. Jordan, and Tijana Zrnic. Prediction-powered inference.Science, 2023

    2023

  11. [11]

    Angelopoulos, John C

    Anastasios N. Angelopoulos, John C. Duchi, and Ti- jana Zrnic. Ppi++: Efficient prediction-powered infer- ence.arXiv, 2023

    2023

  12. [12]

    Estimating means of bounded random variables by betting.Jour- nal of the Royal Statistical Society Series B: Statistical Methodology, 86(1):1–27, 2024

    Ian Waudby-Smith and Aaditya Ramdas. Estimating means of bounded random variables by betting.Jour- nal of the Royal Statistical Society Series B: Statistical Methodology, 86(1):1–27, 2024

    2024

  13. [13]

    Hashimoto

    Xuechen Li, Tianyi Zhang, Yann Dubois, Rohan Taori, Ishaan Gulrajani, Carlos Guestrin, Percy Liang, and Tatsunori B. Hashimoto. Alpacaeval: An automatic evaluator of instruction-following models.GitHub repository, 2023

    2023

  14. [14]

    Can large lan- guage models be an alternative to human evaluations? InACL, 2023

    Cheng-Han Chiang and Hung-yi Lee. Can large lan- guage models be an alternative to human evaluations? InACL, 2023

    2023

  15. [15]

    Scaling up active testing to large language mod- els

    Gabrielle Berrada, Jannik Kossen, Freddie Bickford Smith, Muhammed Razzak, Yarin Gal, and Tom Rain- forth. Scaling up active testing to large language mod- els. InNeurIPS, 2025

    2025

  16. [16]

    Confidence sequences for sampling without replacement

    Ian Waudby-Smith and Aaditya Ramdas. Confidence sequences for sampling without replacement. In NeurIPS, 2020

    2020

  17. [17]

    Concentra- tion inequalities for dependent random variables via the martingale method.Annals of Probability, 36(6): 2126–2158, 2008

    Leonid Kontorovich and Kavita Ramanan. Concentra- tion inequalities for dependent random variables via the martingale method.Annals of Probability, 36(6): 2126–2158, 2008

    2008

  18. [18]

    Stabil- ity bounds for stationary φ-mixing and β-mixing pro- cesses.Journal of Machine Learning Research, 11(2), 2010

    Mehryar Mohri and Afshin Rostamizadeh. Stabil- ity bounds for stationary φ-mixing and β-mixing pro- cesses.Journal of Machine Learning Research, 11(2), 2010

    2010

  19. [19]

    Active testing: Sample-efficient model evaluation

    Jannik Kossen, Sebastian Farquhar, Yarin Gal, and Tom Rainforth. Active testing: Sample-efficient model evaluation. InICML, 2021

    2021

  20. [20]

    Adaptive concentration inequalities for sequential decision problems

    Shengjia Zhao, Enze Zhou, Ashish Sabharwal, and Stefano Ermon. Adaptive concentration inequalities for sequential decision problems. InNeurIPS, 2016

    2016

  21. [21]

    Hypothesis testing with e-values.Foundations and Trends® in Statistics, 1(1-2):1–390, 2025

    Aaditya Ramdas and Ruodu Wang. Hypothesis testing with e-values.Foundations and Trends® in Statistics, 1(1-2):1–390, 2025

    2025

  22. [22]

    Probability inequalities for sums of bounded random variables.Journal of the American Statistical Association, 58(301):13–30, 1963

    Wassily Hoeffding. Probability inequalities for sums of bounded random variables.Journal of the American Statistical Association, 58(301):13–30, 1963

    1963

  23. [23]

    On statistical bias in active learning: How and when to fix it

    Sebastian Farquhar, Yarin Gal, and Tom Rainforth. On statistical bias in active learning: How and when to fix it. InICLR, 2021

    2021

  24. [24]

    Adaptive sub- modularity: Theory and applications in active learning and stochastic optimization.Journal of Artificial Intel- ligence Research, 42:427–486, 2011

    Daniel Golovin and Andreas Krause. Adaptive sub- modularity: Theory and applications in active learning and stochastic optimization.Journal of Artificial Intel- ligence Research, 42:427–486, 2011

    2011

  25. [25]

    Manning, Andrew Ng, and Christopher Potts

    Richard Socher, Alex Perelygin, Jean Wu, Jason Chuang, Christopher D. Manning, Andrew Ng, and Christopher Potts. Recursive deep models for seman- tic compositionality over a sentiment treebank. In EMNLP, pages 1631–1642, 2013

    2013

  26. [26]

    Character-level convolutional networks for text classi- fication

    Xiang Zhang, Junbo Zhao, and Yann LeCun. Character-level convolutional networks for text classi- fication. InNeurIPS, 2015

    2015

  27. [27]

    Instruction-following evaluation for large language models.arXiv, 2023

    Jeffrey Zhou, Tianjian Lu, Swaroop Mishra, Sid- dhartha Brahma, Sujoy Basu, Yi Luan, Denny Zhou, and Le Hou. Instruction-following evaluation for large language models.arXiv, 2023

    2023

  28. [28]

    Safetybench: Eval- uating the safety of large language models

    Zhexin Zhang, Leqi Lei, Lindong Wu, Rui Sun, Yongkang Huang, Chong Long, Xiao Liu, Xuanyu Lei, Jie Tang, and Minlie Huang. Safetybench: Eval- uating the safety of large language models. InACL, 2024

    2024

  29. [29]

    Adversarial glue: A multi-task bench- mark for robustness evaluation of language models

    Boxin Wang, Chejian Xu, Shuohang Wang, Zhe Gan, Yu Cheng, Jianfeng Gao, Ahmed Hassan Awadallah, and Bo Li. Adversarial glue: A multi-task bench- mark for robustness evaluation of language models. In NeurIPS Datasets and Benchmarks Track, 2021

    2021

  30. [30]

    Promptrobust: Towards evaluating the robustness of large language models on adversarial prompts

    Kaijie Zhu, Jindong Wang, Jiaheng Zhou, Zichen Wang, Hao Chen, Yidong Wang, Linyi Yang, Wei Ye, Yue Zhang, Neil Gong, et al. Promptrobust: Towards evaluating the robustness of large language models on adversarial prompts. InACM LAMPS, 2023. 10 CELEUS: Certifiable and Efficient LLM Evaluation via E-Processes

    2023

  31. [31]

    Active surrogate estimators: An active learning approach to label-efficient model eval- uation.NeurIPS, 2022

    Jannik Kossen, Sebastian Farquhar, Yarin Gal, and Thomas Rainforth. Active surrogate estimators: An active learning approach to label-efficient model eval- uation.NeurIPS, 2022

    2022

  32. [32]

    Ash, Chicheng Zhang, Akshay Krishna- murthy, John Langford, and Alekh Agarwal

    Jordan T. Ash, Chicheng Zhang, Akshay Krishna- murthy, John Langford, and Alekh Agarwal. Deep batch active learning by diverse, uncertain gradient lower bounds. InICLR, 2020

    2020

  33. [33]

    Howard, Aaditya Ramdas, Jon McAuliffe, and Jasjeet Sekhon

    Steven R. Howard, Aaditya Ramdas, Jon McAuliffe, and Jasjeet Sekhon. Time-uniform, nonparametric, nonasymptotic confidence sequences.The Annals of Statistics, 49(2):1055–1080, 2021

    2021

  34. [34]

    Howard, Aaditya Ramdas, Jon McAuliffe, and Jasjeet Sekhon

    Steven R. Howard, Aaditya Ramdas, Jon McAuliffe, and Jasjeet Sekhon. Time-uniform chernoff bounds via nonnegative supermartingales.Probability Surveys, 17:257–317, 2020

    2020

  35. [35]

    Active statisti- cal inference

    Tijana Zrnic and Emmanuel J Candès. Active statisti- cal inference. InICML, 2024

    2024

  36. [36]

    Adaptive prediction-powered autoeval with reliability and efficiency guarantees

    Sangwoo Park, Matteo Zecchin, and Osvaldo Simeone. Adaptive prediction-powered autoeval with reliability and efficiency guarantees. InNeurIPS, 2025

    2025

  37. [37]

    Active, anytime-valid risk controlling prediction sets

    Ziyu Xu, Nikos Karampatziakis, and Paul Mineiro. Active, anytime-valid risk controlling prediction sets. InNeurIPS, 2024

    2024

  38. [38]

    Revisiting active sequential prediction-powered mean estimation

    Maria-Eleni Sfyraki and Jun-Kun Wang. Revisiting active sequential prediction-powered mean estimation. InICLR, 2026

    2026

  39. [39]

    Levin, Yu- val Peres, Csaba Szepesvari, and Geoffrey Wolfer

    Daniel Hsu, Aryeh Kontorovich, David A. Levin, Yu- val Peres, Csaba Szepesvari, and Geoffrey Wolfer. Mixing time estimation in reversible markov chains from a single sample path.The Annals of Applied Probability, 29(4):2439–2480, 2019

    2019

  40. [40]

    1 N NX n=1 ˜ℓf (xn) # +E

    Jean Ville.Etude critique de la notion de collectif, volume 3. Gauthier-Villars Paris, 1939. 11 CELEUS: Certifiable and Efficient LLM Evaluation via E-Processes Appendix Contents A Additional discussions 13 A.1 Related work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 A.2 Remarks on practical choices...

    1939

  41. [41]

    This proves that(C t)1≤t≤N is(1−α)anytime-valid forR

    + Pr (Ec 2)≤α 1 +α 2 =α. This proves that(C t)1≤t≤N is(1−α)anytime-valid forR. For any setA⊂Rand anyr≥0, the Minkowski sum satisfies sup (A⊕[−r, r]) = supA+r,inf (A⊕[−r, r]) = infA−r, hence width (A⊕[−r, r]) = (supA+r)−(infA−r) = width (A) + 2r. Applying this withA=M ± t andr= ∆ N(α2)gives width M± t ⊕[−∆ N(α2),∆ N(α2)] = width M± t + 2∆N(α2). Since Ct = ...

    2000

This paper was first reviewed by grok-4.3 on June 29, 2026.