{"id":"de11cb72-ed77-49b6-a738-09f79f902ca8","arxiv_id":"2504.14350","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Under strict output token budgets, LLM rankings change: smaller instruction-tuned models can beat larger or reasoning-specialized models, and mid-sized models are latency-optimal.","lead":"This paper tests 30 open-source LLMs on math problems under hard output-length limits, using an early-stopping trick that tells the model to wrap up before time runs out. It finds that the best model size and prompt style change with the budget, and that mid-sized models offer the best accuracy per second of inference.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Early-stopping protocol bundles a pre-announced deadline warning with a fixed α=25 answer reservation; the headline rankings may be protocol artifacts.","rationale":"The paper's contribution is empirical and its five findings are clearly stated. The load-bearing premise is that the early-stopping protocol measures the intended quantity. I find this premise insufficiently isolated. The early-stopping condition changes both the prompt (advance warning about 'Time's Up!') and the decoding trajectory (injection at Budget − α with α=25). All later findings are reported exclusively under this condition after Section 5.1, so the protocol is not a neutral measurement instrument. This does not make the experiments uninformative—the protocol is a coherent intervention and could be adopted in deployment—but it does make the findings conditional on protocol parameters and on the warning prompt. The paper's own limitations section does not list this dependency, which is a gap. The proposed test is feasible: vary α and remove the warning prompt; if rankings are stable, the concern is resolved. I therefore keep the reader's CONDITIONAL verdict.","tokens_in":25775,"tokens_out":8103,"duration_ms":77334,"concrete_test":"Re-run the headline comparisons (GSM8K budgets 50/150, MATH500 budgets 100/200, at least Qwen-2.5 7B/14B/32B and one reasoning model such as QwQ-32B) under early stopping with α ∈ {5, 50, 100} and, separately, with the same concluding injection but without the pre-generation 'Time's Up!' warning in the system prompt. Then check whether (a) the early-stopping-over-direct-terminating gap and (b) the best prompt/model ordering or the 7B>14B crossover survive. If the ordering flips or the gap disappears, Findings 2–5 are protocol-dependent; if it is unchanged, the concern is settled.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that model and prompt rankings under strict output budgets are captured by Findings 2–5—rests on the early-stopping protocol of Section 3.2, but that protocol differs from the direct-termination baseline in two bundled ways that are never disentangled. First, early stopping changes the system prompt before generation: the model is told that it may be interrupted by '**Time's Up!**' and is instructed to 'stop reasoning immediately' and 'conclude with: Therefore, the final answer is: \\boxed{...}' (Appendix A.2). Direct terminating uses no such warning. Thus the comparison in Finding 1 and all subsequent rankings measure a model's ability to follow a pre-announced deadline protocol, not simply its reasoning under an output cap. Second, the deadline fires at Budget − α with α fixed at 25 (footnote 1), and no sensitivity analysis is reported. α simultaneously sets how much reasoning is allowed before the signal and how many tokens are reserved for the answer, so a different α reallocates the budget between thinking and answering. If the best prompt style or the 'smaller is better' ordering changes when α is varied or when the warning is removed, the findings are artifacts of the protocol rather than stable properties of constrained reasoning.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper presents an empirical study of open-source LLM reasoning under strict output length constraints. The authors evaluate 30 models on GSM8K and MATH500 under varying token budgets, comparing two ways of imposing the constraint: directly terminating generation at the budget, and an 'early stopping' method that injects a concluding message ('Time\\'s Up! Therefore, the final answer is:') at Budget-α tokens. Three prompt styles (step-by-step, coarse-to-fine, answer-and-verify) are tested. The paper reports five findings: (1) early stopping consistently outperforms direct termination; (2) coarse-to-fine and answer-and-verify prompts outperform step-by-step under budgets in most cases; (3) larger models are not always better, with non-monotonic accuracy within Qwen-2.5 and Phi-3 families; (4) reasoning-specialized models do not always outperform instruction-tuned or math models; (5) when token budgets are converted to latency on an NVIDIA A800, mid-sized models (around 7B) are latency-optimal. The authors acknowledge limitations in the final section and release code and data.","tokens_in":25990,"tokens_out":2542,"duration_ms":24982,"significance":"If the findings hold, they provide practically relevant guidance for deploying LLMs in latency-sensitive applications, showing that model choice depends on the output budget rather than on unconstrained accuracy. The study is broad in model coverage, uses external benchmarks with no fitted parameters, and is transparent about its limitations. The central empirical observations—that ranking and optimal prompt style change with budget—are plausible and worth reporting. However, the strength of the claims currently exceeds what the experimental design can support because the early-stopping protocol is not isolated from other prompt changes, no statistical uncertainty is reported, and the latency analysis rests on a single hardware profile.","major_comments":[{"comment":"The early-stopping method differs from direct termination in two bundled ways: the system prompt pre-announces the deadline and instructs the model to conclude with a specific format, and the injection fires at Budget−α with α=25 fixed. The comparison in Finding 1 and all subsequent findings therefore measure a model's ability to follow a pre-announced deadline protocol, not simply its reasoning under an output cap. Because a different α reallocates the budget between reasoning and answer-writing, and because the warning itself may change model behavior, the headline rankings in Findings 2–5 may be artifacts of this specific protocol. I request an ablation that separates the warning from the message injection, and a sensitivity analysis over α (e.g., α∈{10,25,50,100}) at least for a subset of models and budgets.","section":"Section 3.2, Appendix A.2"},{"comment":"All results are from a single greedy decoding run with no confidence intervals, standard errors, or statistical tests. Many reported differences are small (e.g., Table 2 shows gaps of 1–3 accuracy points between prompt styles for several models), and the claim in Finding 1 that early stopping 'consistently improves' accuracy on all combinations is based on visual inspection of the plotted curves. I request bootstrap confidence intervals over sampled problems (or per-problem standard errors) and, for the pairwise model comparisons in Findings 3–4, a test of whether the observed gaps are distinguishable from noise. Without this, the generality of the findings is not established.","section":"Section 4.4, Table 2, Figures 2–5"},{"comment":"Finding 5 (mid-sized models are latency-optimal) is derived from a latency model profiled on a single NVIDIA A800 GPU with a fixed input length of 200 tokens and a linear output-token-to-latency mapping. The manuscript's own limitation section acknowledges that the token-latency assumption 'does not account for hardware-specific variations,' but the finding is stated as a general deployment recommendation. The optimal size under a latency budget depends on the prefill/decode speed ratio, which varies across hardware, batch size, and quantization. I request either a second device profile or an explicit parametric sensitivity analysis (e.g., varying decode throughput) to show that the 7B-optimal conclusion is not an artifact of one GPU's characteristics.","section":"Section 5.5, Appendix C.4"},{"comment":"Findings 3 and 4 compare models that differ not only in size or reasoning specialization but also in training data, training procedure, and architecture. The limitations paragraph correctly identifies this as a threat to validity, but the body text presents the findings with general force ('larger is not always better'). I recommend either confining the claims to within-family comparisons (e.g., Qwen-2.5 and Phi-3 series, as is already partly done) or adding a caveat in the finding statements themselves so that 'larger' and 'reasoning model' are not read as causal categories. A within-family comparison with controlled training data would be the strongest fix.","section":"Sections 5.3, 5.4, Limitations"}],"minor_comments":[{"comment":"There is a typo 'reasoing' in the paragraph on efficient reasoning techniques; please correct it.","section":"Section 2"},{"comment":"The text writes 'Qwen-2,5-1.5B' with a comma; the model name should be 'Qwen-2.5-1.5B'.","section":"Section 5.3"},{"comment":"Footnote 1 justifies α=25 as 'large enough to cover the correct final answers,' but no supporting measurement is given. If the claim refers to observed correct answers, state it explicitly with statistics; otherwise this is a tuning choice that needs sensitivity analysis.","section":"Section 3.2"},{"comment":"The phrase 'mid-sized models are latency-optimal' is stated as a general finding, but the supporting figures (Figures 20–21) show only a subset of model families; the Qwen-2.5 series is the main evidence. Please clarify how much the conclusion generalizes beyond the families shown.","section":"Section 5.5"},{"comment":"The contribution statement claims 'the first thorough empirical study of LLM reasoning under strict output length constraints.' Given the growing literature on token-budget-aware reasoning (some cited in Section 2), 'first' may be hard to verify; consider softening to 'a systematic empirical study.'","section":"Section 1"}],"recommendation":"major_revision","confidential_remarks":"The paper is likely to have impact if the protocol-ablation and statistical robustness issues are addressed. The 'early stopping' protocol is a reasonable evaluation choice, but the current manuscript does not establish that its findings generalize across reasonable protocol variations. I would also ask the editor to ensure the 'first thorough empirical study' claim is checked against concurrent work on length constraints in reasoning, as the paper itself cites several closely related papers in Section 2."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read the paper. Here's my take: it's a serious empirical study that fills a gap, but the central evaluation protocol has a confound that needs airing before the findings become deployment rules.\n\nWhat's new: they systematically map accuracy against hard token budgets for 30 open-source LLMs on GSM8K and MATH500, with three prompt styles, and compare direct termination against an early-stopping method that injects a \"Time's Up!\" message at Budget−25 and lets the model generate a concluding answer. That protocol is genuinely new and does improve accuracy over abrupt cutoff. The findings—early stopping helps, c2f/aav prompts beat step-by-step under tight budgets, larger models are not always better, reasoning models are not always better, and mid-sized models are latency-optimal—are plausible and practically relevant. The paper is well written, the appendix gives the full prompt templates and chat format details, and they are upfront in the Limitations section about math-only focus, limited prompt designs, and hardware-specific latency.\n\nThe soft spots are real, though not fatal. Most important: the early-stopping protocol is a bundled treatment. The model is warned before generation that it may be interrupted and told to stop and conclude when it sees \"Time's Up!\". Direct termination has no such warning. So Finding 1 and all subsequent rankings compare models on their ability to follow a pre-announced deadline protocol, not simply on reasoning under an output cap. The two effects are never separated. Second, α=25 is fixed without sensitivity analysis. That number decides how much of the budget is thinking vs. answering; rankings could change if α shifts. Third, no error bars or statistical tests, and only greedy decoding. For a study meant to guide deployment, we don't know how stable these curves are to sampling or seed. Fourth, the latency-optimality claim rests on one A800 profile, as they admit.\n\nThat said, the qualitative direction of the findings likely holds; the exact rankings and optimal budget numbers should be treated as preliminary. The paper deserves a serious referee. The empirical map is valuable, and the protocol critique is testable—authors could run α sensitivity and a no-warning variant to see if the rankings survive, and they should ship code and data as promised.\n\nFor reading group: yes, this will provoke a good discussion about evaluation methodology for time-constrained reasoning.","headline":"A useful, extensive empirical study of LLM reasoning under token budgets, but the early-stopping protocol bundles a pre-deadline warning with the answer injection and fixes α=25 without sensitivity analysis, so the rankings may be protocol artifacts.","tokens_in":26512,"tokens_out":2476,"would_cite":true,"duration_ms":22224,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Under strict output-length constraints, the largest model and the best unconstrained reasoner are often not the best choices; budgets change which model, prompt, and size win.","keywords":["large language models","strict output length constraint","budget-aware reasoning","early stopping","model size scaling","latency budget","prompt styles","math reasoning"],"falsifier":"Vary the early-stopping margin $\\alpha$ (for example 0, 10, 25, 50, 100) and the concluding-message wording across all 30 models on MATH500, and check whether the best model, best prompt style, and best size band stay the same; if the rankings flip, the five findings are artifacts of the protocol.","tokens_in":25593,"feed_emoji":"⏱️","tokens_out":8560,"duration_ms":68052,"temperature":0.7,"pith_summary":"This paper sets out to establish how open-source large language models behave when forced to answer within a fixed output-token budget, the setting that real time-sensitive deployments create. It tests 30 models on two math datasets across a wide range of budgets and introduces an early-stopping protocol that injects a concluding message before the budget is reached. The central claim is that constrained reasoning is not just slower unconstrained reasoning: the best model size, the best prompt style, and the best model type all change with the budget, and mid-sized models are often latency-optimal. The findings matter because they give practitioners a budget-specific, latency-aware basis for model selection instead of assuming unconstrained accuracy rankings transfer.","feed_headline":"Smaller models can beat larger ones under tight token budgets","feed_subtitle":"Early stopping, prompt style, and model size all change rankings once answers must fit a strict output limit.","key_machinery":"The load-bearing mechanism is the early-stopping protocol. Before generation, the model is warned that the keyword 'Time's Up!' means: stop reasoning and conclude with 'Therefore, the final answer is: $\\boxed{[answer]}$'. When generation reaches $B-\\alpha$ tokens, with $\\alpha=25$, the message '**Time’s Up!** Therefore, the final answer is:' is appended to the output, and decoding continues within the total budget $B$. The paper argues that this reveals genuine constrained reasoning ability because the model must compress its completed reasoning into a final answer rather than being cut off mid-thought. The supporting machinery is the comparison grid: three prompt styles (step-by-step, coarse-to-fine, answer-and-verify), token budgets spanning dozens to thousands of tokens, and a measured near-linear mapping from output tokens to inference latency on a single GPU that converts token budgets into latency budgets.","core_discovery":"The paper's central discovery is a set of five budget-dependent phenomena. First, interrupting reasoning early and appending the message 'Time's Up! Therefore, the final answer is:' consistently improves accuracy over abruptly truncating at the budget, on every dataset and prompt style tested. Second, no single prompt style dominates, but coarse-to-fine and answer-and-verify styles outperform step-by-step prompting in most constrained scenarios, although the benefit shrinks as tasks get harder. Third, accuracy does not scale monotonically with model size under strict budgets: for example, Qwen-2.5-7B outperforms Qwen-2.5-14B in parts of the GSM8K budget range, and Phi-3-small matches or beats Phi-3-medium on MATH500 at some budgets. Fourth, reasoning-specialized models are not always better than instruction-tuned or math-specialized models when tokens are scarce, because their accuracy curves rise too slowly at low budgets. Fifth, after mapping token budgets to on-device latency, mid-sized models around 7B are the best choice under tight latency limits, with larger models catching up only as the constraints relax.","pith_inferences":["The early-stopping margin $\\alpha=25$ and the exact wording of the concluding message are free parameters; if model rankings shift when they are varied, the reported findings are properties of the protocol rather than of constrained reasoning.","The token-to-latency mapping was measured on one GPU type in single-request decoding; batch serving, quantization, or smaller accelerators could move the optimal size band, even if the qualitative mid-size advantage remains.","The evaluation protocol itself could be turned into training signal: fine-tuning models to conclude cleanly when interrupted at an arbitrary token count might directly improve budget-aware accuracy.","The data suggest plotting an accuracy-per-token frontier for each model family and prompt style, letting practitioners read off the optimal configuration for any latency budget without re-running full sweeps."],"forward_implications":["Practitioners should select models and prompts using budget-specific accuracy curves, because rankings under unconstrained evaluation do not transfer to strict output limits.","For latency-critical on-device deployment, a mid-sized model around 7B is often the best choice, and larger models only become worthwhile once the latency budget is relaxed.","Prompt style is a controllable lever under constraints: answer-and-verify or coarse-to-fine prompting can recover accuracy that step-by-step reasoning loses at low token budgets.","Evaluations of constrained reasoning should report early-stopping results, since direct truncation understates model capability, with differences reaching about 5% on MATH500."],"supporting_citations":[{"why":"Supplies the GSM8K grade-school math benchmark that is one of the two testbeds for constrained reasoning.","marker":"Cobbe et al., 2021"},{"why":"Supplies MATH500, the harder benchmark where early stopping's advantage reaches about 5%.","marker":"Lightman et al., 2023"},{"why":"Provides the evaluation and scoring procedure used to measure accuracy across models.","marker":"Yang et al., 2024b"},{"why":"Supplies the serving engine used to enforce the max_new_token budget in direct termination.","marker":"Kwon et al., 2023"},{"why":"Defines the DRD-Qwen reasoning-model family whose slow accuracy rise under tight budgets grounds Finding 4.","marker":"DeepSeek-AI et al., 2025"},{"why":"Defines Sky-T1, one of the reasoning models whose budget-dependent behavior is compared with instruction-tuned models.","marker":"Team, 2025"},{"why":"The Phi-3 technical report provides the training-data explanation the paper uses to interpret why Phi-3-medium fails to beat Phi-3-small under budgets.","marker":"Abdin et al., 2024a"},{"why":"The scaling-law result that Finding 3 explicitly disagrees with under output constraints.","marker":"Kaplan et al., 2020"}],"fun_headline_variants":["Token budget flips which LLM size wins","Under tight token limits, smaller LLMs can excel","'Time's Up' interruption helps budget-constrained reasoning","Reasoning model rankings shift under strict token budgets","On-device latency favors mid-size LLMs for reasoning"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The early-stopping protocol assumes that appending 'Time's Up! Therefore, the final answer is:' and allowing 25 extra tokens reveals a model's genuine constrained reasoning ability rather than measuring prompt compliance, and this assumption is not tested by varying $\\alpha$ or the message.","fun_headline_variants_meta":{"raw":{"variants":["Token budget flips which LLM size wins","Under tight token limits, smaller LLMs can excel","'Time's Up' interruption helps budget-constrained reasoning","Reasoning model rankings shift under strict token budgets","On-device latency favors mid-size LLMs for reasoning"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000243,"raw_usage":{"total_tokens":1542,"prompt_tokens":974,"completion_tokens":568,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":590,"completion_tokens_details":{"reasoning_tokens":493}},"tokens_in":590,"tokens_out":568,"duration_ms":5337,"temperature":1.0,"reasoning_tokens":493,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T11:50:05.054824+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Vary the early-stopping margin $\\alpha$ (for example 0, 10, 25, 50, 100) and the concluding-message wording across all 30 models on MATH500, and check whether the best model, best prompt style, and best size band stay the same; if the rankings flip, the five findings are artifacts of the protocol.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the serving engine used to enforce the max_new_token budget in direct termination."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines Sky-T1, one of the reasoning models whose budget-dependent behavior is compared with instruction-tuned models."}],"review_version":1}