{"id":"59cd9c5c-e073-4e39-8abc-a5df4f621aed","arxiv_id":"2607.07674","paper_version":1,"verdict":"CONDITIONAL","confidence":"UNKNOWN","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":7,"one_line_summary":"AdaPrefix-GRPO treats solution-prefix length as a feedback controller targeting 50% rollout success rate during GRPO training, then anneals to zero prefix, yielding 1.6–2.1× accuracy gains over vanilla GRPO at matched compute on hard math.","lead":"The paper introduces a closed-loop controller that adjusts how much of a solution's prefix to show an LLM during reinforcement learning training, keeping the model's success rate near 50% where learning signal is strongest, then removing the assistance entirely. A smart generalist might read it because it could make RL training of small reasoning models substantially more efficient on hard problems.","discovery_kind":"new_method","skeptic_critique":{"model":"glm-5.2","headline":"The 3-seed AdaPrefix vs PrefixRL comparison is confounded by annealing; the clean attribution to closed-loop control rests on single-seed ablations (~2σ).","rationale":"The reader identified the FLOPs accounting (calibration overhead exclusion) as the weakest assumption. This is a valid concern but not load-bearing: the conservative-constant variant (no calibration sweep) still achieves 46.4 vs 48.2 (Table 3), and the base-only variant without per-sample offsets (and thus without the difficulty probe) still achieves 45.3, well above PrefixRL at 35.9. So even if all calibration overhead were included in the budget, the gain persists.\n\nThe more load-bearing concern is about attribution, not compute matching. The 3-seed comparison that supports the headline (48.2 vs 36.2 over PrefixRL) is confounded by annealing: AdaPrefix uses a delayed annealing envelope while PrefixRL does not. The clean comparison controlling for annealing (PrefixRL+anneal: 38.7 vs base-only: 45.3) is single-seed at ~2σ. This means the specific claim that 'closed-loop control, not prefixing per se' drives the gain has residual uncertainty, even though the broader claim (the full AdaPrefix method improves over fixed-prefix methods at matched FLOPs) is well-supported.\n\nThe paper provides partial mitigation: Prefix-RFT (annealing without closed-loop control) achieves only 36.8, suggesting annealing alone doesn't explain the gain. But this is single-seed. The iteration-matched control (Figure 3b) addresses the separate concern about extra optimizer steps but is also single-seed.\n\nNone of these concerns undermine the primary result (improvement at matched FLOPs over vanilla GRPO, 3-seed, ~6σ). They affect the secondary attribution claim. The reader's CONDITIONAL verdict is appropriate: the main result is trustworthy, but full confidence in the component-level attribution requires multi-seed ablations. No code release and hand-tuned offset map (without sensitivity analysis) are additional valid concerns that reinforce CONDITIONAL rather than ACCEPT, but neither is load-bearing for the central claim.\n\nI recommend UNCHANGED because the reader already identified the single-seed ablation issue among their concerns, and my analysis confirms it is the most consequential of the non-load-bearing concerns — moving to REJECT or UNVERDICTED would be unjustified given the strength of the 3-seed main comparison.","tokens_in":14687,"tokens_out":23205,"duration_ms":1082564,"concrete_test":"Re-run the two key ablation rows — PrefixRL+anneal and base-only (closed-loop, no offsets) — with 3 seeds each on Qwen3-1.7B at the same FLOPs budget. If the gap between them shrinks below ~3 pp (within CI), the claim that closed-loop control specifically (rather than the full method including annealing) drives the gain over fixed prefixing would need qualification. Additionally, running Prefix-RFT with 3 seeds would test whether annealing alone (without closed-loop control) truly adds negligible gain over PrefixRL.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central attribution — that 'closed-loop control, not prefixing per se, drives the improvement' (Section 5.3) — rests on a comparison between AdaPrefix-GRPO (which includes closed-loop control + per-sample offsets + annealing) and PrefixRL (which includes none of these). The 3-seed main table comparison (48.2 vs 36.2, gap = 12.0 pp) is solid but confounded: AdaPrefix uses a delayed annealing envelope (w=0.8) while PrefixRL does not. The ablation that controls for this confound — PrefixRL+anneal (38.7) vs base-only closed-loop (45.3), gap = 6.6 pp — is single-seed with CI ≈ ±3.1, making it approximately 2σ. If this gap shrinks with multiple seeds, the specific attribution to closed-loop control (as opposed to annealing + closed-loop jointly) weakens. Partial mitigation exists: Prefix-RFT (global decay, a form of annealing without closed-loop control) achieves only 36.8, close to PrefixRL's 35.9, suggesting annealing alone adds little. But Prefix-RFT is also single-seed in Table 1. The main claim — improvement at matched FLOPs over vanilla GRPO — is well-supported by 3-seed evidence (48.2 vs 30.1, ~6σ). The residual uncertainty is specifically about whether the gain over fixed-prefix methods is attributable to the closed-loop controller or to the combination of controller + annealing.","agreement_with_reader":"partial"},"referee_report":{"model":"glm-5.2","summary":"The paper introduces AdaPrefix-GRPO, a closed-loop controller that adjusts prefix length during GRPO training to hold the batch success rate near 50%, where group-relative gradient signal is maximized. The method addresses the 'dead zone' problem where all rollouts in a group fail and the gradient vanishes. Prefixes are annealed to zero so the deployed model operates without assistance. Experiments on hard math (DeepMath) across multiple model sizes and families show substantial gains over vanilla GRPO and fixed-prefix baselines at matched training FLOPs, with shorter traces and no pass@16 collapse. The experimental design is thorough: FLOPs-matched comparisons, multiple baselines isolating confounds, 3-seed main comparisons, cross-family validation, and component-level ablations.","tokens_in":15511,"tokens_out":1642,"duration_ms":445568,"significance":"The core contribution—treating prefix length as a tracked set-point rather than a fixed hyperparameter—is well-motivated and the mechanism is clearly articulated. The paper ships falsifiable predictions (the target sweep in Table 3 confirms the intermediate-optimum prediction), a parameter-light controller (secant/bisection with EMA, no learned components), and an honest limitations section. The FLOPs-matched comparison with a G=16 vanilla GRPO control and an iteration-matched view (Figure 3) are commendable controls that address the most obvious alternative explanations. The cross-family transfer (Qwen3.5, Gemma 4) rules out architecture-specific effects. The finding that a 0.6B model with AdaPrefix surpasses a 3x larger model with vanilla GRPO is practically significant.","major_comments":[{"comment":"Section 5.3, Table 3 (Control granularity row): The central attribution claim—that 'closed-loop control, not prefixing per se, drives the improvement'—rests on the comparison between base-only closed-loop (45.3) and PrefixRL+anneal (38.7), a gap of 6.6 pp. However, both of these are single-seed results with CI approximately +/-3.1, so the gap is roughly 2 sigma and could shrink with multiple seeds. The 3-seed main table comparison (AdaPrefix 48.2 vs PrefixRL 35.9, gap 12.3 pp) is confounded because AdaPrefix includes annealing while PrefixRL does not. The paper should either (a) add at least one more seed for the base-only vs PrefixRL+anneal comparison to tighten the attribution, or (b) explicitly acknowledge in the main text (not just the limitations) that the specific attribution to closed-loop control over the joint controller+annealing combination rests on single-seed evidence, and软化","section":null},{"comment":"Section 4.2 (Compute accounting): The FLOPs-matched comparison excludes the one-time calibration sweep (4 rollouts x 512 problems x 5 grid points) and difficulty probe (4 rollouts x ~6.8K problems) as 'amortized preprocessing.' This is defensible when multiple runs share the same model and data, but the paper's claim that gains are 'not attributable to extra training compute' is stated without qualification in the abstract and main results. For a practitioner training a single model once, this overhead is not amortized and represents non-trivial inference compute. The paper should state the absolute cost of calibration+probe in FLOPs or wall-clock time and note the breakeven point (how many training runs are needed before amortization holds), so readers can assess the practical accessibility claim.","section":null}],"minor_comments":[{"comment":"The abstract states 'more than doubles GRPO's accuracy' for the 0.6B model (2.1x). Table 2 shows 19.6 -> 41.8, which is indeed 2.1x. However, the abstract also says '1.6x on Qwen3-1.7B' — Table 2 shows 30.1 -> 48.2, which is 1.6x. These are consistent, but the abstract does not mention that these are DeepMath held-out numbers specifically; adding 'on held-out hard math' would avoid overpromising.","section":null},{"comment":"Table 1: PrefixRL shows a slight regression on GSM8K (90.4 vs 91.3 for vanilla GRPO). The text attributes this to 'over-prefixing easy problems.' It would help to verify whether the per-sample offset mechanism in AdaPrefix (which sets rho=0 on easy problems) is specifically responsible for the GSM8K recovery (92.4), or whether the controller alone suffices. A one-line mention of whether the GSM8K slice was tracked during training would clarify this.","section":null},{"comment":"Section 5.4 ('Why traces shorten'): The hypothesis that holding k/G near 0.5 'rewards efficient correct completions rather than long, lucky explorations' is plausible but unverified. The paper itself notes 'We treat this as a hypothesis to verify with length-conditioned analyses at rho=0.' This is fine as stated, but the claim in the abstract and Table 1 that traces are 'roughly halved' is a headline result; a brief note in the results section (not just the analysis) flagging that the mechanism is hypothesized would be more transparent.","section":null},{"comment":"Figure 2a is labeled as 'illustrative' in the caption. Since the paper has actual calibration data (512 problems x 5 grid points), replacing the illustrative panel with a real measured kappa(rho) curve would strengthen the empirical foundation at no additional cost.","section":null},{"comment":"The paper does not release training code or per-step data (acknowledged in Limitations). Given that the method is described as 'data preparation plus a loss mask on prefix tokens; the trainer is otherwise stock,' releasing the data preparation script would be low-effort and would significantly aid reproducibility.","section":null},{"comment":"Section 4.2: The offset map delta is described as 'a small monotone (linear) map with a hand-tuned slope, spanning +/-0.15 around the base across the difficulty range.' The exact slope and how the difficulty range is normalized (quantile? raw pass rate?) are not specified. A one-line formula or a footnote with the exact mapping would be useful for reproduction.","section":null},{"comment":"References to concurrent work (Setlur et al. 2026, Qu et al. 2026) use future-dated arXiv IDs. If these are genuinely concurrent submissions, noting 'concurrent work' explicitly in the Related Work section (as is done) is sufficient, but ensuring the arXiv IDs are correct at publication time would help readers.","section":null}],"recommendation":"minor_revision","confidential_remarks":"The paper is a single-author independent submission. The experimental work is substantial (5 model sizes/families, 8 baselines, 7 ablation factors) and the writing is above average for the venue. The main concern is the single-seed attribution ablation, but this is a local issue: the primary claim (improvement over vanilla GRPO at matched FLOPs) is well-supported by 3-seed evidence, and the method is clearly described and falsifiable. I lean toward minor revision: the authors should tighten the attribution claim language and add the compute accounting caveat, but the core contribution is sound. The stress-test concern about the annealing confound is valid but partially mitigated by the Prefix-RFT baseline (global decay = annealing without closed-loop control, achieving only 36.8). The concern does not undermine the main result."},"author_rebuttal":{"model":"glm-5.2","summary":"We thank the referee for the careful reading and the constructive recommendation. Both major comments are well-taken and will be addressed in revision. Below we respond point by point.","responses":[{"response":"The referee is correct on both counts. The 3-seed main-table comparison (48.2 vs 35.9) does conflate closed-loop control with annealing, since AdaPrefix-GRPO includes the annealing envelope and PrefixRL does not. The clean attribution to closed-loop control specifically—rather than to the joint controller+annealing combination—rests on the single-seed Table 3 rows: base-only closed-loop (45.3) vs PrefixRL+anneal (38.7), a gap of 6.6 pp with CI ±3.1, i.e., approximately 2 sigma. This is not the level of evidence we would want for a central attribution claim, and we agree it should be characterized honestly in the main text rather than only in the limitations section. We will revise Section 5.3 to state explicitly that the specific attribution to closed-loop control over the joint controller+annealing combination rests on single-seed evidence and that the gap, while directionally consistent with the claim, is not conclusive at conventional significance thresholds. We will also soften the related claim in Section 2 ('We additionally show it is closed-loop control, not prefixing per se, that carries the gain') to reflect this qualification. Regarding option (a): we will attempt to add at least one additional seed for the base-only closed-loop and PrefixRL+anneal rows during the revision period. If compute permits, this would tighten the CI; if not, the main-text qualification will stand. Either way, the revision will not overstate the strength of the attribution.","revision_made":"partial","referee_comment":"Major Comment 1 (Section 5.3, Table 3): The attribution claim that 'closed-loop control, not prefixing per se, drives the improvement' rests on single-seed evidence (base-only closed-loop 45.3 vs PrefixRL+anneal 38.7, gap 6.6 pp, CI ±3.1, roughly 2 sigma). The 3-seed main table comparison (AdaPrefix 48.2 vs PrefixRL 35.9) is confounded because AdaPrefix includes annealing while PrefixRL does not. The referee requests either (a) additional seeds for the base-only vs PrefixRL+anneal comparison, or (b) explicit acknowledgment in the main text that the specific attribution rests on single-seed evidence."},{"response":"The referee is right that the unqualified statement in the abstract and main results is misleading for a practitioner training a single model once. The calibration sweep and difficulty probe are real inference compute that we exclude from the training budget only because they are shared across all runs on the same model and data (seeds, ablations, hyperparameter sweeps). For a single-run practitioner this overhead is not amortized and should be disclosed. We will add the following to Section 4.2: (1) The absolute cost of calibration+probe in terms of total rollout count: the calibration sweep performs 4 × 512 × 5 = 10,240 rollouts and the difficulty probe performs 4 × ~6,800 = ~27,200 rollouts, for a combined ~37,440 short rollouts. (2) Expressed as a fraction of the training budget: for the 1.7B model, this preprocessing amounts to approximately 3% of the per-run training FLOPs budget (the exact figure depends on average rollout length, which is shorter for prefixed episodes). (3) The breakeven point: amortization holds once the same model+data combination is used for 2 or more training runs (e.g., a seed sweep or hyperparameter search), which is the typical use case in RL post-training. For a single run, the overhead is small but nonzero. We will also add a brief qualification to the abstract ('at matched training compute, excluding one-time per-model calibration') so that the claim is not overgeneralized. The conservative-constant cold-start variant (Table 3, 46.4), which skips the calibration sweep and retains only the difficulty probe, provides a lower-overhead fallback that we will mention alongside the cost disclosure.","revision_made":"yes","referee_comment":"Major Comment 2 (Section 4.2, Compute accounting): The FLOPs-matched comparison excludes the calibration sweep (4 rollouts × 512 problems × 5 grid points) and difficulty probe (4 rollouts × ~6.8K problems) as 'amortized preprocessing.' The abstract and main results state gains are 'not attributable to extra training compute' without qualification. For a practitioner training a single model once, this overhead is not amortized and represents non-trivial inference compute. The referee requests the absolute cost of calibration+probe in FLOPs or wall-clock time, and the breakeven point for amortization."}],"tokens_in":14383,"tokens_out":1811,"duration_ms":171117,"standing_objections":[]},"desk_editor":{"model":"glm-5.2","letter":"The headline result is real: AdaPrefix-GRPO more than doubles GRPO accuracy on hard math at matched FLOPs (48.2 vs 30.1 on DeepMath held-out, 3 seeds, ~6σ). The method is simple — prefix length becomes a feedback controller tracking 50% success rate, then anneals to zero — and the implementation is clean: loss masking on prefix tokens, stock trainer, everything else in data prep. The cross-family transfer (Qwen, Gemma) and the scaling pattern (bigger gains on smaller models, which makes sense given deeper dead zones) are convincing. The FLOPs accounting is fair: prefix prefill is counted, and the iteration-matched control in Figure 3b shows the baselines lose even with more compute. The 50% set-point is adopted from Bae et al. and Gao et al., not invented here, which is fine — the contribution is the mechanism that reaches and tracks it. The target sweep ablation (Table 3) confirms the intermediate optimum empirically, which is a nice check. The paper is honest about limitations: no code released, offset map is hand-tuned, and the author explicitly flags that 50% on a short remainder may be an easier signal than 50% on a full trajectory. That last point is a real subtlety and I'm glad it's acknowledged rather than buried. Now the soft spots. The stress-test concern about confounding is legitimate but partially mitigated. The 3-seed AdaPrefix vs PrefixRL gap (12.0 pp) is confounded by annealing, yes. The clean comparison — PrefixRL+anneal (38.7) vs base-only closed-loop (45.3), gap 6.6 pp — is single-seed with CI ±3.1, so roughly 2σ. That's not nothing. The partial mitigation: Prefix-RFT (global decay, a form of annealing without closed-loop) gets 36.8, barely above PrefixRL's 35.9, suggesting annealing alone adds little. But Prefix-RFT is also single-seed. So the specific attribution to closed-loop control (as opposed to controller+annealing jointly) is the weakest link in the paper. The main claim — improvement over vanilla GRPO at matched compute — is rock solid. The secondary claim — that the controller specifically drives the gain over fixed-prefix methods — is probably right but under-powered. The FLOPs accounting excludes calibration overhead (4 rollouts × 512 problems × 5 grid points plus difficulty probe), which the reader flags. For a lab running multiple seeds and sweeps this is genuinely amortized. For a practitioner training once, it's a real cost that shrinks the effective advantage. Minor concern, worth noting but not disqualifying. No code or data is released. For a method whose entire appeal is simplicity of implementation, this is a gap that should be fixed before publication. The offset map has no sensitivity analysis. The author calls it a hand-tuned heuristic, which is honest, but a reader can't assess robustness without seeing how performance varies with the slope parameter. Who is this for? Anyone doing RL post-training of reasoning models, especially with small models where the dead zone is most severe. The method is practical and the gains are large enough to matter. This deserves a serious referee. The main results warrant publication; the attribution claim needs either multi-seed ablations or softer language about what specifically drives the gain. I'd recommend accept with revisions: require multi-seed on at least the PrefixRL+anneal vs base-only comparison, code release, and sensitivity analysis on the offset map.","headline":"Solid paper. The closed-loop prefix controller for GRPO is a genuinely new mechanism with strong main results. The attribution claim (controller vs. annealing) rests on single-seed ablations and needs tightening, but the core improvement over vanilla GRPO is well-established.","tokens_in":15538,"tokens_out":849,"would_cite":true,"duration_ms":98522,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"glm-5.2","headline":"Closed-loop prefix control doubles GRPO accuracy on hard math","keywords":["GRPO","reinforcement learning","prefix conditioning","closed-loop control","difficulty curriculum","mathematical reasoning","language model training","dead zone"],"falsifier":"Run AdaPrefix-GRPO with the calibration and difficulty-probe costs included in the training budget. If the gains over vanilla GRPO and fixed-prefix baselines shrink substantially under full-cost accounting, the claim that improvements are not attributable to extra compute weakens.","tokens_in":14903,"feed_emoji":"🎛️","tokens_out":1135,"duration_ms":255131,"temperature":0.7,"pith_summary":"Group Relative Policy Optimization (GRPO), a standard method for training language models to reason, has a structural blind spot: on problems the model almost never solves, all sampled attempts fail identically, producing zero gradient signal. The hardest problems, which matter most for learning, contribute nothing. This paper introduces AdaPrefix-GRPO, which treats the length of a correct solution prefix given to the model as a feedback-controlled dial on problem difficulty. Rather than fixing the prefix length once at the start, the method continuously adjusts it throughout training to hold each problem's success rate near 50 percent, the regime where GRPO's learning signal is strongest. It then anneals all prefixes to zero so the deployed model solves problems unaided. The central claim is that closed-loop control of prefix length, not prefixing itself, drives the improvement: fixed-prefix and global-decay baselines trail by roughly 12 and 11 percentage points respectively on held-out hard math problems. At matched training compute, AdaPrefix-GRPO improves pass@1 accuracy over vanilla GRPO by 22.2 points on a 0.6B model and 18.1 points on a 1.7B model, while roughly halving output trace length. The gain is larger for smaller models, which sit deeper in the dead zone. The method requires only a loss mask on prefix tokens and data preparation changes; the underlying GRPO trainer is otherwise unmodified.","feed_headline":"Closed-loop prefix control doubles GRPO accuracy on hard math","feed_subtitle":"Holding each problem's success rate near 50% extracts signal where standard RL gets none, with smaller models gaining most.","key_machinery":"The central mechanism is a one-dimensional root-finding controller that adjusts a single global base prefix ratio to hold the batch-mean success rate k/G near a target (default 0.5). Per-sample difficulty offsets (static, estimated from a cold-start probe) compress the spread of success rates across problems of varying difficulty. An annealing envelope forces all prefixes to zero in the final training phase so the deployed policy needs no prefix. Gradients are masked on prefix tokens; the reward is computed on the full completion.","core_discovery":"The paper identifies that the binding constraint on GRPO for hard problems is not model capacity but sampling failure: when no rollout in a group succeeds, the group-relative advantage is exactly zero and no gradient flows. Prefix length converts this binary barrier into a continuous, controllable dial on difficulty. The key finding is that the dial must be closed-loop rather than fixed, because the relationship between prefix length and success rate shifts as the policy improves, causing any static choice to drift out of the signal-maximizing regime. A simple root-finding controller (secant with bisection fallback) tracking a 50 percent success-rate set-point, combined with per-sample难度-d难度","pith_inferences":["The calibration sweep and difficulty probe, while excluded from the training budget, represent non-trivial one-time inference compute. For practitioners training a single model on a single dataset without multiple seeds or sweeps, this overhead does not amortize and the effective compute advantage over vanilla GRPO shrinks.","The per-sample difficulty offset is a static heuristic that cannot correct individual mis-estimations during training. A genuine per-sample second control loop, if it could be made feasible with denser rollout estimates, might recover the remaining spread the global loop leaves unaddressed.","The method's reliance on reference solutions and binary verifiers means its applicability to domains with noisy rewards, multiple valid solution styles, or no available reference traces remains untested. The controller's behavior under reward noise may differ from the clean math setting.","If the 50 percent set-point is not universal but depends on reward noise and solution-path multiplicity (as the paper acknowledges), an adaptive target that itself responds to measured signal quality could outperform the fixed 0.5 default."],"forward_implications":["Smaller models stuck in GRPO's dead zone can be trained to surpass larger models trained with vanilla GRPO, shifting the cost-benefit tradeoff between scaling parameters and improving the training recipe.","The principle of closed-loop difficulty targeting via controllable scaffolds could extend beyond prefix injection to any mechanism that modulates problem difficulty, such as hint granularity, tool access, or context window budget.","The finding that traces shorten as a side effect suggests that holding problems at moderate success rates may preferentially reinforce efficient solution paths rather than lengthy exploration, a hypothesis with implications for inference cost at deployment.","If the 50 percent success-rate set-point generalizes beyond math reasoning, curriculum design for code generation or logical reasoning tasks could adopt the same closed-loop targeting rather than static difficulty filtering."],"fun_headline_variants":["Feedback-controlled prefix hints double GRPO accuracy on hard math","Adaptive prefix control keeps GRPO at 50% success and doubles accuracy","Closed-loop prefix length more than doubles GRPO gains on hard math","Static prefix length drifts; adaptive controller extracts 2.1x GRPO signal","Smaller models gain most from closed-loop prefix control in GRPO"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The compute-matched comparison excludes the one-time calibration sweep and difficulty probe as amortized preprocessing. If a practitioner trains a model once rather than running multiple seeds or sweeps, this overhead is not amortized and the effective compute advantage over baselines shrinks.","fun_headline_variants_meta":{"raw":{"variants":["Feedback-controlled prefix hints double GRPO accuracy on hard math","Adaptive prefix control keeps GRPO at 50% success and doubles accuracy","Closed-loop prefix length more than doubles GRPO gains on hard math","Static prefix length drifts; adaptive controller extracts 2.1x GRPO signal","Smaller models gain most from closed-loop prefix control in GRPO"]},"model":"glm-5.2","effort":"high","cost_usd":0.0,"raw_usage":{"total_tokens":650,"prompt_tokens":572,"completion_tokens":78,"prompt_tokens_details":null},"tokens_in":572,"tokens_out":78,"duration_ms":57714,"temperature":1.0,"reasoning_tokens":null,"cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-09T02:43:19.038644+00:00","model_set":{"reader":"glm-5.2"},"falsifier":"Run AdaPrefix-GRPO with the calibration and difficulty-probe costs included in the training budget. If the gains over vanilla GRPO and fixed-prefix baselines shrink substantially under full-cost accounting, the claim that improvements are not attributable to extra compute weakens.","supporting_citations":[],"review_version":1}