{"id":"970c2500-31da-43da-8571-6c294efc93c4","arxiv_id":"2602.13935","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Uncertainty keyword arrivals in LLM reasoning are modeled as a renewal process and via conformal max-scores to create early stopping rules with controlled false-positive rates under exchangeability.","lead":"This paper introduces two early-stopping rules that watch for uncertainty words in an AI model's reasoning and stop it early when it appears to be overthinking. They work with black-box models and show large token savings on unanswerable math questions while rarely stopping correct answers.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Prop. 2.1's finite-sample FPR guarantee holds only under exchangeability, which the paper's headline evaluation deliberately violates; reported FPRs are therefore empirical, not guaranteed, and lack error bars.","rationale":"The reader identified the violation of exchangeability as the weakest assumption, and I agree that this is the most load-bearing concern. The finite-sample guarantee is the primary theoretical contribution, but the paper's main empirical evaluation deliberately operates outside the assumptions of that guarantee. In good faith, the paper is transparent about this limitation, and the conformal proof itself is mathematically correct. However, the central claim—'provides finite-sample guarantees'—is easy to over-read as applying to the reported results, when in fact the reported FPRs are empirical robustness observations, not guaranteed bounds. The absence of error bars or repeated-seed analysis further weakens the empirical support, making it impossible to distinguish genuine robustness from sampling variability. The cold-start selection using ill-posed labels is a secondary concern (it contradicts the 'no negative examples' claim), but it does not directly undermine the theoretical guarantee. Because the paper acknowledges the exchangeability limitation and the methodology is otherwise sound, a CONDITIONAL verdict remains appropriate: the authors should provide in-distribution validation of the guarantee and uncertainty quantification for the out-of-distribution results. Thus I recommend no change to the reader's verdict.","tokens_in":24488,"tokens_out":8905,"duration_ms":82340,"concrete_test":"Run the Maxwise conformal rule in-distribution: randomly split GSM8K well-posed problems into calibration and test sets (no dataset shift), repeat 100 times with different seeds, and report the empirical FPR distribution. If the mean FPR substantially exceeds the target α=5% (beyond sampling variability), the conformal implementation is flawed; if FPR ≤ α, the finite-sample guarantee is validated in-distribution. Then, as a secondary check, run the same repeated-seed protocol with GSM8K calibration and each out-of-distribution test set, reporting FPR with confidence intervals, to assess whether the observed FPR control is statistically robust or within noise of the exchangeability-violating regime.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim of 'finite-sample guarantees' rests on Proposition 2.1, which assumes calibration and test traces are exchangeable (i.i.d. from the same distribution). The paper's own evaluation deliberately breaks this assumption: calibration is on GSM8K while test sets are UMWP, MiP, MMLU, GPQA, and HLE. The text explicitly states 'strictly satisfying this requirement is almost never possible in practice.' Consequently, the FPR values in Tables 1, 3, 11 are not covered by the conformal guarantee; they are empirical observations under distribution shift. Without repeated-seed or bootstrap error bars, one cannot determine whether Maxwise's FPR close to the 5% target is reliable or a result of chance. The renewal rule is similarly built on i.i.d. inter-arrival times, which the authors call a 'working approximation,' and the Šidák correction is acknowledged as approximate. These are load-bearing because the abstract's headline claim is precisely the finite-sample FPR control, and the evaluation does not test that guarantee in the regime where it is proven. The paper does disclose the limitation, but the gap between theory and the reported experiments is the main vulnerability of the central claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes two early-stopping rules for LLM reasoning traces, both driven by a lexicon of 102 uncertainty keywords mined semi-supervised from paired well-posed/ill-posed GSM8K traces. The first rule models keyword inter-arrival times as a renewal process and performs sequential testing with a Šidák-corrected threshold. The second rule applies conformal prediction to the maximum prefix uncertainty density, claiming finite-sample control of the false-positive rate (FPR) on well-posed queries under exchangeability. The evaluation calibrates on GSM8K and tests on GSM-MC, UMWP, MiP, MMLU, GPQA, and HLE, deliberately breaking exchangeability to probe robustness. The paper reports that the uncertainty-based rules achieve lower FPR than length-, logit-, and probe-based baselines while stopping a large fraction of ill-posed queries, with modest token savings.","tokens_in":24814,"tokens_out":8560,"duration_ms":76749,"significance":"If the claims hold, the work offers a practical, interpretable, black-box-compatible stopping mechanism for reasoning models, with a rigorous conformal guarantee in the exchangeable regime and promising robustness under distribution shift. The empirical breadth (12 models, 6 benchmarks) and the inclusion of an oracle upper bound are strengths. However, the significance is tempered by three issues: the main-text method description omits the cold-start tuning step that is actually used in all experiments; the headline finite-sample guarantee does not apply to the shifted evaluation, yet the abstract does not qualify this; and the empirical FPRs are reported without uncertainty quantification, making it difficult to assess how reliably the 5% target is met under shift.","major_comments":[{"comment":"Algorithm 1 and the main-text description of Maxwise stopping monitor all bin boundaries with no cold-start offset. Appendix A.6, however, introduces a cold-start index s* selected on paired well-posed/ill-posed GSM8K training traces and states that this procedure is applied uniformly to keyword-, DEER-, and entropy-based signals. The experiments therefore evaluate a different rule from the one for which the conformal guarantee is stated. This also conflicts with the claim that calibration 'requires no negative examples' (Section 1, Section 2.2): selecting s* uses ill-posed traces. Please integrate the cold-start step into the formal method, state its data requirements, and qualify the 'no negative examples' claim accordingly.","section":"§2.2 / Algorithm 1 vs Appendix A.6"},{"comment":"The abstract states that the second approach 'provides finite-sample guarantees on the probability of halting too early on well-posed queries.' Proposition 2.1 provides this guarantee only under exchangeability between calibration and test traces, which the evaluation deliberately breaks. The paper acknowledges the limitation in Section 3.3, but the abstract is unqualified. Moreover, the FPRs in Tables 1 and 13 are empirical, not guaranteed, and no confidence intervals or repeated-seed analyses are given. Some per-model FPRs are high (e.g., Table 13, MiMo-7B on UMWP: 14.04%; Table 12, DeepSeek-7B on GSM-MC: 0.00%), which may or may not be within sampling noise. Please add uncertainty estimates (e.g., binomial CIs or bootstrap) and qualify the abstract.","section":"Abstract and Section 3.3, Table 1/Table 13"},{"comment":"The renewal-process rule relies on the CLT for renewal processes with i.i.d. inter-arrival times, which the authors call a 'working approximation' for LM traces, and the Šidák correction requires independence that is acknowledged not to hold. These caveats appear in footnotes/appendix text but not in the main narrative. Since the Renewal rule is presented as statistically principled and its FPRs are central to the evaluation, the manuscript should clearly state in the main text that the Renewal rule is heuristic and has no finite-sample guarantee, distinguishing it more sharply from the conformal rule.","section":"Section 2.2, Renewal stopping and Section C"}],"minor_comments":[{"comment":"For the prompting baselines, FPR is measured as accuracy drop and power as abstention rate, while for the other methods FPR and power are early-stopping rates. This makes the rows not directly comparable. The table caption should state this explicitly (it is mentioned only in the text).","section":"Table 1 / Section 3.2"},{"comment":"L_max is set to the median calibration trace length, which is not a true maximum and may lead to an incorrect number of tests in the Šidák correction. Please clarify how this choice affects the correction and whether a sensitivity analysis was performed.","section":"Section 2.2, footnote 4"},{"comment":"The GSM-MC row says 'GSM8K problems with one key variable deliberately removed' but then says 'We remove questions in the other GSM8K set to avoid data leakage.' Please clarify the relationship between the well-posed and ill-posed versions and which split is used for the FPR evaluation.","section":"Table 7"},{"comment":"The keyword extraction procedure uses random-forest importance and manual categorization; the final 102-keyword list is not printed. Since the method depends on this lexicon, including the full list (or a stable URL to it) in the paper would improve reproducibility.","section":"Appendix A.1.1"}],"recommendation":"major_revision","confidential_remarks":"The central conformal proof is correct, but the manuscript oversells the finite-sample guarantee by presenting an unqualified abstract while the evaluation deliberately violates exchangeability. The cold-start mismatch between the algorithm and the implementation is the most serious technical gap and is fixable. I would be willing to re-review after the authors integrate the cold-start step into the main method, add uncertainty quantification to the empirical FPRs, and qualify the theoretical claims."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. First, this is a real new combination: modeling uncertainty-keyword arrivals in reasoning traces as a renewal process and calibrating a maxwise conformal threshold on keyword density. It works from text only, so it is compatible with proprietary APIs, and the keywords are interpretable. Second, the paper's central advertised guarantee does not cover its own main experiments. Proposition 2.1 is correct as a conformal statement under exchangeable calibration and test traces, but the evaluation calibrates on GSM8K and tests on other benchmarks, and the paper admits exchangeability is almost never satisfied in practice. The FPR numbers in Tables 1, 3, and 11 are empirical robustness results, not instances of the finite-sample guarantee. That distinction matters, but it is not fatal; the paper is honest about it.\n\nWhat is genuinely good: the maxwise conformal argument is clean; the comparison across 12 models and multiple out-of-distribution math and science benchmarks is unusually broad; the oracle upper bound gives a useful yardstick; and the source code is linked. The keyword lexicon construction is described in enough detail to reproduce, and the ablations around keyword categories and bin size are the right checks. The empirical wins over prompting and length baselines look real, especially on math. This is a solid engineering-plus-statistics paper, not a toy.\n\nSoft spots, in proportion. Missing error bars is the most concrete: FPRs like 5.42% and 5.52% are close to the 5% target, but without repeated-seed or bootstrap intervals you cannot tell whether the method is calibrated or lucky. The cold-start index s* is selected on the GSM8K ill-posed training traces, so the \"no negative examples\" claim is true for calibration but not for the entire pipeline; the paper discloses this in the appendix, but the main method description should too. The renewal rule depends on i.i.d. inter-arrival times, which the authors call a working approximation, and the Sidak correction is acknowledged as approximate; that rule should be read as heuristic with asymptotic motivation, not as a formal guarantee. The oracle upper bound reuses the test sets to train a classifier, so it is soft in both directions; the regression slopes of 0.82-0.85 are a rough yardstick, not a tight bound. Minor: on scientific datasets the ill-posed queries are often still answerable, and the authors admit this.\n\nBottom line: the central idea is sound, the guarantees are correctly stated, and the gap between theory and deployment is disclosed. Who benefits: people building black-box early stopping or abstention for reasoning models, and anyone wanting a clean conformal stopping template. I would send it to a serious referee. Ask for variance estimates, a main-text disclosure of the cold-start tuning, and a sharper statement of when the finite-sample guarantee does and does not apply.","headline":"A genuinely new black-box early-stopping method with a clean conformal core; the headline finite-sample guarantee is real only under exchangeability, which the paper's own experiments deliberately break, so treat the empirical FPRs as suggestive, not proven.","tokens_in":25310,"tokens_out":2177,"would_cite":true,"duration_ms":21107,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["60K05","62L10"],"pacs":[],"model":"deepseek-v4-flash","headline":"Reasoning models can be stopped early on ill-posed prompts by watching for uncertainty keywords, with a finite-sample guarantee that well-posed reasoning is rarely cut short.","keywords":["early stopping","reasoning models","uncertainty keywords","renewal process","conformal prediction","false-positive control","ill-posed queries","token efficiency"],"falsifier":"Calibrate the conformal rule on short, direct math word problems and deploy it on well-posed questions from a domain where models habitually hedge, such as medical case analyses with verbose differential diagnosis; if the empirical rate of premature halts on those well-posed questions substantially exceeds the target α, the exchangeability assumption is the load-bearing failure point.","tokens_in":24381,"feed_emoji":"🤔","tokens_out":6476,"duration_ms":57745,"temperature":0.7,"pith_summary":"The paper argues that reasoning models often verbalize their confusion as they generate—through phrases like 'cannot determine' or 'insufficient information'—and that this text signal is enough to stop them early on ill-posed queries. It proposes two stopping rules: a parametric one that models the timing of these uncertainty phrases as a renewal process, and a nonparametric conformal rule that bounds the probability of halting a well-posed query. The conformal rule is the keystone: it gives a finite-sample guarantee that premature stopping stays below a user-chosen level, provided calibration and test traces are exchangeable. Across math and science benchmarks with twelve models, the rules cut wasted tokens on ambiguous questions while keeping false-positive rates near the target, and they outperform length-, logit-, and activation-based alternatives. If correct, this offers a lightweight, interpretable, black-box-compatible way to make reasoning models abstain instead of overthink.","feed_headline":"Halting reasoning on uncertainty preserves well-posed answers","feed_subtitle":"A conformal rule reads keyword density in the trace and provably caps how often decoding stops too early.","key_machinery":"The load-bearing object is the maxwise conformal stopping threshold τ*: an uncertainty density u(T;ℓ) = (number of keyword arrivals in prefix ℓ)/ℓ, evaluated at bin boundaries; its maximum per calibration trace M_i, and the quantile τ* = M_(⌈(n+1)(1−α)⌉). Exchangeability of the (M_i) makes the false-positive bound in Proposition 2.1 true. The renewal-process rule is a secondary mechanism that models the gaps between keyword arrivals as i.i.d. inter-arrival times and uses the asymptotic normality of renewal counting processes, Z_t = (N_t − t/μ̂)/sqrt(tσ̂²/μ̂³), to flag abnormally fast uncertainty rates.","core_discovery":"The paper's central discovery is that the rate at which uncertainty keywords appear in a reasoning trace can separate answerable from unanswerable queries, and that this rate can be monitored online to decide when to abort generation. The main mathematical object is a maxwise conformal threshold: over a calibration set of well-posed reasoning traces, compute the maximum keyword-density score over token bins for each trace, then take the (1−α)(1+1/n) quantile as the global threshold. A new trace is halted the first time its density exceeds that threshold, and Proposition 2.1 shows the probability of halting a well-posed trace is at most α when the calibration and test traces are exchangeable.","pith_inferences":["The finite-sample guarantee is likely the most fragile part: the paper's own evaluation breaks exchangeability by design, so real-world false-positive control will depend more on the robustness of the keyword signal than on Proposition 2.1.","A natural extension is to retrain or expand the keyword lexicon per domain; the 'insufficiency' category drives most of the power, suggesting that domain-specific missing-information cues could further close the gap to the oracle bound.","The conformal rule could be combined with learned text-based uncertainty scores that are not restricted to a fixed lexicon, potentially raising power on scientific queries where the current method reaches only 47–58% of the oracle.","One could test a fully online variant that updates the threshold as traces accumulate, replacing the static calibration set with a streaming calibration."],"forward_implications":["Practitioners can calibrate an early-stopping rule using only well-posed queries, with no need to enumerate the many ways a question can be ill-posed.","Because the signal is text-only, the method applies to proprietary models exposed through black-box APIs.","The rules shrink the token cost of ambiguous queries, reducing serving latency and computation.","The interpretable keyword categories (impossibility, speculation, insufficiency) allow developers to see exactly why a run was halted.","The same conformal framework works with any scalar uncertainty score, not just keyword density, as the paper shows by plugging in logit-based scores."],"fun_headline_variants":["Uncertainty density flags when LLMs should stop reasoning","Conformal rule stops overthinking in LLMs, preserving accuracy","Early stopping via keyword density keeps well-posed answers safe","Statistical early stop cuts needless steps in LLM reasoning","Monitor uncertainty to halt reasoning early, provably safe"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The rule that stops too early on well-posed queries no more than α times out of 100 depends on the calibration traces and the deployed traces being exchangeable—drawn from the same distribution of well-posed reasoning.","fun_headline_variants_meta":{"raw":{"variants":["Uncertainty density flags when LLMs should stop reasoning","Conformal rule stops overthinking in LLMs, preserving accuracy","Early stopping via keyword density keeps well-posed answers safe","Statistical early stop cuts needless steps in LLM reasoning","Monitor uncertainty to halt reasoning early, provably safe"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000129,"raw_usage":{"total_tokens":904,"prompt_tokens":639,"completion_tokens":265,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":383,"completion_tokens_details":{"reasoning_tokens":184}},"tokens_in":383,"tokens_out":265,"duration_ms":3034,"temperature":1.0,"reasoning_tokens":184,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-02T23:20:30.994941+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Calibrate the conformal rule on short, direct math word problems and deploy it on well-posed questions from a domain where models habitually hedge, such as medical case analyses with verbose differential diagnosis; if the empirical rate of premature halts on those well-posed questions substantially exceeds the target α, the exchangeability assumption is the load-bearing failure point.","supporting_citations":[],"review_version":1}