RGM: Combining Generation and Process Verification in One Model

Core positioning:“Test-Time Scaling with Reflective Generative Model” shares a backbone between policy and process reward model(PRM), adding only a5M–54M lightweight SPRM head. Filtering by outcome correctness×self-generated pseudo-label consistency reduces noise, allowing one network to generate and select reasoning trajectories.

• Date:2026-09-28
• Rotating field: LLM/NLP—reasoning, test-time scaling, post-training, evaluation
• Core paper: Zixiao Wang et al., Test-Time Scaling with Reflective Generative Model, ICLR 2026 Poster
• Final paper version:https://proceedings.iclr.cc/paper_files/paper/2026/hash/c1e854c0620b13668b93058455c7b183-Abstract-Conference.html
• Reporting convention: except differences and relative changes explicitly labeled as this report’s calculations, all numbers come from paper tables/text or public model cards actually read. Missing values are not inferred.

0. Search, deduplication, and random-selection audit

0.1 Deduplication over the preceding 14 days

First read ml-report-index.md. Closest recent coverage is ThinkSLM on 2026-09-14(small-model reasoning and compression evaluation) and HPS on 2026-09-21(preference optimization and hardest-negative sampling). These papers and their themes—post-compression reasoning matrices and hard-negative preference sampling—are excluded. RGM focuses on external test-time scaling, process verifiers, and shared backbones, without duplicating that coverage.

0.2 Candidate pool and source coverage

Candidates center on official ICLR2026 proceedings, cross-checked through arXiv, OpenReview, Hugging Face Daily Papers, Papers with Code, and Semantic Scholar. Semantic Scholar’s arXiv API link returned403, so it is marked inaccessible and its metadata supports no quantitative conclusion. Papers with Code yielded no standalone core-paper entry but did return the lineage paper Math-Shepherd. ACL Anthology verifies Math-Shepherd’s ACL 2024 long-paper entry. All24 candidates lie within 24 months, and their titles/official pages were individually opened or verified from the same proceedings results:

1. The End of Manual Decoding: Towards Truly End-to-End Language Models
2. Language Models are Injective and Hence Invertible
3. Plan and Budget: Effective and Efficient Test-Time Scaling on Reasoning Large Language Models
4. Language Models Use Lookbacks to Track Beliefs
5. Sequences of Logits Reveal the Low Rank Structure of Language Models
6. Soft-Masked Diffusion Language Models
7. On Predictive Power of Representation Dispersion in Language Models
8. Comparing Learning Dynamics of In-Context Learning and Fine-Tuning in Language Models
9. Do Large Language Models Know What They Are Capable Of?
10. Native Reasoning Models: Training Language Models to Reason on Unverifiable Data
11. SynthWorlds: Controlled Parallel Worlds for Disentangling Reasoning and Knowledge in Language Models
12. R-Horizon: How Far Can Your Large Reasoning Model Really Go in Breadth and Depth?
13. Log-Augmented Generation: Scaling Test-Time Reasoning with Reusable Computation
14. e3: Learning to Explore Enables Extrapolation of Test-Time Compute for LLMs
15. RL Squeezes, SFT Expands: A Comparative Study of Reasoning LLMs
16. Understanding the Role of Training Data in Test-Time Scaling
17. Are Reasoning LLMs Robust to Interventions on their Chain-of-Thought?
18. Test-Time Scaling with Reflective Generative Model
19. MoDr: Mixture-of-Depth-Recurrent Transformers for Test-Time Reasoning
20. ATTS: Asynchronous Test-Time Scaling via Conformal Prediction
21. TrimR: Verifier-based Training-Free Thinking Trimming for Efficient Test-Time Scaling
22. Sample Smart, Not Hard: Correctness-First Decoding for Better Reasoning in LLMs
23. Whatever Remains Must Be True: Filtering Drives Reasoning in LLMs, Shaping Diversity
24. OpenThoughts: Data Recipes for Reasoning Models

Actually executed shuf -i 1-24 -n 1 returned 18, namely RGM. The 18-page final paper contains five main evaluation sets,64 repeated evaluations, a complete main table, and 11 ablation/appendix comparisons, providing sufficient material, so zero redraws。

1. Link verification table

Version alert. The arXiv v2 abstract still gives additional parameters as 53M, whereas the ICLR final main table reports by base model 5M、26M、54M、54M、17M, summarized in the final abstract as approximately 50M. This is not a negligible typographical difference: it changes exact parameter-saving ratios against a72B reward model. The report follows per-model final-paper numbers, treating53M only as the older MetaStone-S1 convention.[arXiv abs lines 8–27; core Table 1, PDF p.6]

2. Motivation: why more samples do not guarantee effective scaling

External test-time scaling typically generates(k) complete reasoning trajectories with a policy, scores them with a reward model, and selects the best answer. Three problems arise.

First, the verifier may exceed the policy in size. The core comparator is Qwen2.5-Math-RM/PRM-72B, versus RGM’s5M–54M SPRM head. Passing each candidate through a separate 72B verifier pushes inference compute and deployment memory back toward large-model costs.[Core Sec.1, PDF pp.1–2; Table 1, p.6]

Second, process labels are expensive and unreliable. Even after filtering, PRM800K requires approximately 800K human step labels covering 75K solutions and 12K problems. Although its large PRM reaches 78.2%on a particular MATH subset, this approach bases verification quality on human process review.[Let’s Verify Step by Step, arXiv HTML lines 23–30,52–55,171]

Third, final-answer-only supervision contaminates process labels. Math-Shepherd estimates step quality by continuing from intermediate steps and measuring final-answer success, avoiding human labels. Lessons of Developing PRMs later observes that MC labels can reward wrong reasoning ending in correct answers, and finds that most open PRMs except its own Qwen2.5-Math-PRM have error-step detection accuracy below 50%. Thus, best-of-N final accuracy can rise without the verifier actually learning logical-error detection.[Math-Shepherd PDF pp.1–2; Lessons Sec.3, arXiv HTML lines 95–125,178–179]

RGM therefore asks:Can a policy use its own hidden states with an extremely lightweight process-scoring head, learning only when its process judgment agrees with the final outcome, to reduce noisy propagation of outcome labels to every step?

3. Argument, assumptions, and trade-offs

The narrative has four steps:

1. Unified interface. Generation and SPRM heads share one Transformer backbone. Scoring reads step-token hidden states from the policy’s penultimate layer rather than requiring a separate LLM forward pass.
2. Self-supervised filtering. Final-answer correctness(y) supplies only a trajectory-level weak label. The current SPRM produces per-step pseudo-labels\hat y_n; only steps with(y=\hat y_n) enter BCE, while conflicts are discarded.
3. Length debiasing. The geometric mean of step scores defines trajectory score, avoiding exponential decay with step count under direct products.
4. Inference scaling. One model samples(k) reasoning paths, SPRM scores each, and the policy head outputs an answer from the highest-scoring path. Main experiments use(k=8).

Implicit assumption A is that penultimate-layer hidden states retain sufficient process-quality information. Table 9 supports this: on DeepScaleR-1.5B, penultimate-layer SPRM AIME24 is 53.1versus final-layer 48.8, a gain of 4.3 pp; HMMT25 is 21.5 vs 18.8, a gain of 2.7 pp.[Core Table 9, PDF pp.13–14]

Implicit assumption B is that consistency filtering eventually separates correct and incorrect trajectories despite noisy early pseudo-labels. Figure 5 defines the aha moment as the first training step where the correct-trajectory curve’s slope becomes positive and the incorrect one negative. QwQ-32B reaches it around 60 steps , prompting60 extra steps for a total of 140 steps.[Core Sec.5.4, PDF p.8]

Implicit assumption C is that parameter/forward savings outweigh multitask interference. Table 8 supplies the key counterevidence: standalone RGM8 adds 1.5B parameters and exceeds the shared5M head on all four math benchmarks by 0.6–1.6 pp. Sharing is therefore an efficiency–accuracy compromise, not the accuracy optimum.[Core Table 8, PDF p.13]

4. Equation-level formalization

For question(Q), a policy generates(k) reasoning trajectories(\tau_i). Traditional external TTS is:

[ i^=\arg\max_{i\in{1,\dots,k}} R_\phi(\tau_i),\qquad a=G_\theta(Q,\tau_{i^}), ]

where(G_\theta) and(R_\phi) are two large models. RGM instead shares backbone(H_\theta), separating only generation and lightweight scoring heads:

[ h_{i,n}=H_\theta^{(L-1)}(\tau_i)[t_{i,n}], ]

[ s_{i,n}=\sigma\bigl(W_2,\mathrm{Dropout}{0.5}(\mathrm{ReLU}(W_1h{i,n}))\bigr), ]

where(t_{i,n}) is the(n)-th step-token,(W_1:c\rightarrow2c), and(W_2:2c\rightarrow1). English mathematical reasoning is split at tokens containing .\n\n ; consecutive step-tokens retain only the first, and leading step-tokens are ignored.[Core Sec.4.1, PDF pp.3–4]

Trajectory scores use a geometric mean:

[ S_i=\left(\prod_{n=1}^{N_i}s_{i,n}\right)^{1/N_i} =\exp\left(\frac{1}{N_i}\sum_{n=1}^{N_i}\log s_{i,n}\right). ]

The equivalent second form reveals that it compares mean log-scores, avoiding an inherent penalty on long trajectories from multiplying more probabilities below 1. Table 3’s direct-product AIME24/AIME25/BRUMO25/HMMT25 values are 44.2/31.1/40.0/17.9versus geometric-mean values of 53.1/35.7/43.2/21.5; the largest gain is AIME24’s 8.9 pp.[Core Eq.5 and Table 3, PDF pp.4,8]

SPRM’s key is masked rather than ordinary BCE:

[ \hat y_{i,n}=\mathbb{I}[s_{i,n}>0.5],\qquad \mathcal{L}{SPR}=\frac{1}{N}\sum_n\mathbb{I}[y_i=\hat y{i,n}],\mathrm{BCE}(s_{i,n},\hat y_{i,n}). ]

A step is not updated when the final answer is correct but currently judged wrong, or the final answer is wrong but currently judged correct. This does not prove pseudo-label correctness; it avoids forcing visibly conflicting trajectory-level labels onto every step.

4.1 Training and inference pseudocode

for question Q, gold answer a*:
    trajectories = policy.sample(Q, group_size)
    outcome y_i = exact_match(final_answer_i, a*)
    GRPO_update(policy, trajectories, y)

    for each trajectory i:
        steps = split_by_step_token(trajectory_i)
        for each step n:
            h = penultimate_hidden_state(step_token_n)
            s = SPRM_head(h)
            pseudo = 1[s > threshold]
            if pseudo == y_i:
                BCE_update(SPRM_head, s, pseudo)

inference(Q, k=8):
    sample k complete thoughts
    score each thought by geometric_mean(step_scores)
    select argmax score
    generate final answer conditioned on selected thought

Note: the paper calls this joint training, but policy GRPO and SPRM masked BCE are parallel objectives; scoring-head gradients need not influence the policy through sampling selection. Complete total-loss weights and gradient-coupling ablations are absent, so superiority over alternating training cannot be inferred.

5. Key mechanisms and engineering details

6. Datasets, benchmarks, and metrics

Training combines NuminaMath, OpenR1-Math-220k, DeepScaleR, LIMR, and OREAL-RL, filters easy questions using a MATH difficulty classifier, then samples by pass rate, yielding 40K examples. Source proportions, deduplication counts, and contamination checks against AIME/HMMT/BRUMO are absent.40K establishes quantity, not evaluation independence.[Core Sec.5.1, PDF p.5]

Pass@1 can be misunderstood here: configurations are repeatedly sampled and averaged over 64 evaluations, but each run submits only one RGM-selected answer. This is not conventional pass@k, where any correct candidate counts as success.[Core PDF pp.5–6, lines 324–374]

7. Complete main-results matrix

7.1 Six methods × five benchmarks: QwQ-32B as the shared comparison base

Source: core Table 1(PDF p.6). Bold has two scopes: RGM wins all five columns among the four same-base QwQ rows; including external closed/671B references, it leads the full table only on AIME24 and HMMT25. Against same-base PRM-72B, absolute gains are +0.9/+1.1/+1.6/+1.4/+1.0 ppand relative gains +1.08%/+1.52%/+2.09%/+2.71%/+1.59%(calculated from the table). Against o3-mini, RGM gains on AIME24 +4.6 ppand HMMT25 +0.1 pp, but trails on AIME25/BRUMO25/LiveCodeBench by 1.4/1.9/3.4 pp. “Outperforms o3-mini” therefore holds in only two columns, not overall.

7.2 Five policy backbones: RGM versus each backbone’s strongest72B reward model

Cells show RGM score(versus the stronger same-base RM-72B/PRM-72B: absolute pp; relative %)。

Source: core Table 1(PDF p.6); relative percentages computed by this report. Across 25 architecture×task cells, RGM wins 23against the strongest same-base72B reward model. Exceptions are Qwen3-32B/HMMT25(−0.4 pp) and GPT-OSS-20B/AIME24(−0.3 pp). This is more precise than “consistently surpasses”: broadly consistent, without cellwise dominance.

8. Component ablations: where do gains arise?

Sources: core Tables 2–5,7–13(PDF pp.8–15). Three mutually constraining conclusions matter most: process signals help; sharing sacrifices about 1 pp for substantial parameter savings; fixed thresholds and two-layer heads are reasonable defaults, not universal task optima.

9. Hyperparameter sensitivity and transitions

9.1 Candidate count(k)

Figure 3 shows1.5B and 7B improving with candidate count on AIME24, AIME25, and LiveCodeBench, with SPRM usually above72B RM/PRM. Exact coordinates for each(k) are absent from PDF text, so this report invents none from images. The main table uses(k=8); appendix RGM32 appears only in the SPRLoss comparison. More candidates generally help, but superiority at equal FLOPs or latency over 72B PRM is unproven.

9.2 Search budget

MCTS AIME24 rises from the 0-token score of 43.8 to the 160K-token score of 52.8, monotonically over five points, with marginal gains of +5.0、+1.2、+1.7、+1.1 pp. The first 40K is most cost-effective, with clear diminishing returns thereafter.[Table 5, PDF p.9] The paper acknowledges excessive depth and compute for tree search on long reasoning, which still underperforms BoN.

9.3 The training aha moment

The authors define a transition by diverging slope signs: correct-trajectory scores turn positive from negative/flat, while incorrect-trajectory scores turn negative. QwQ-32B reaches it around 60 steps, then trains60 more. This threshold depends on smoothing, evaluation batches, and randomness, yet no confidence intervals or automatic detector are given. It is an informative diagnostic, not an established universal phase-transition law.

9.4 Thresholds and formatting

The four-benchmark average at threshold0.5 is 38.38, versus mean-threshold 37.78and median-threshold 37.30(computed from Table 7), only 0.60–1.08 points better on average. On BRUMO25, mean exceeds hard by 1.8 pp. Moreover, English uses .\n\nwhile Chinese switches to all tokens containing \n , showing that zero format fine-tuning still requires manual rule transfer.

10. Statistical significance and evaluation credibility

Each question/configuration is evaluated repeatedly 64 timesand mean accuracy reported, more reliable than a single run.[Core PDF p.6] However, the paper reports no standard deviations, standard errors, confidence intervals, significance tests, or random-seed counts. Therefore:

• QwQ-RGM’s five means exceed same-base PRM-72B;
• small gaps such as+0.5 pp or+0.9 pp cannot be declared statistically significant;
• the+0.1 pp HMMT25 lead over o3-mini especially should not be described as robust, since closed-model evaluation may use unequal compute;
• winning23/25 cells supports directional consistency, not significance.

End-to-end latency, tokens/s, peak memory, energy, and P95/P99 are also absent. The model card claims99% lower PRM inference cost, while the final paper mainly uses extra parameter count as an efficiency proxy. Without serving measurements, parameter savings must not be equated with 99% latency savings.

11. Genuine contributions, reusable design, and transfer potential

Actual contribution 1: a verifier need not be a second model. If generation exposes suitable intermediate states, process scoring can use an auxiliary head on the same backbone. This extends to code-execution traces, tool plans, retrieval chains, and agent actions.

Actual contribution 2: consistency masks reduce process contamination from weak outcome labels. SPRLoss is simple, but demotes answer correctness from hard truth for every step to a screening signal used only when the model’s local judgment agrees. The reusable template is global weak label(y) + local pseudo-label\hat y + consistency mask.

Actual contribution 3: aggregation is central to TTS. Replacing products with geometric means alone adds on AIME24 8.9 pp. PRM comparisons must therefore include step segmentation, score calibration, and cross-length aggregation, beyond model size.

Transfer potential. Table 13’s32B→1.5B transfer aligns dimensions through a linear projection and exceeds the native SPRM on two of four tasks. This suggests general process-scoring representations adapted through small projections. A valuable next question is whether quality signals linearly align across architectures, languages, and tasks, rather than simply enlarging standalone PRMs.

12. Technical lineage: problem solved—remaining gap—RGM’s response—design transfer

12.1 Let’s Verify Step by Step（ICLR 2024）

Addresses whether process supervision is more reliable than outcome supervision, using PRM800K human step labels to reach 78.2%on a particular MATH subset and improve data efficiency through active learning by 2.6×. Remaining gaps are 800K human-label costs, closed large models, and math-only scope. RGM accepts the value of process scores but replaces human labels with outcome–pseudo-label consistency. Per-step aggregatable scores transfer, while supervision shifts from humans to the model itself.

12.2 Math-Shepherd（ACL 2024 Main Long）

Uses MC success rates from intermediate-step rollouts to generate process labels automatically, removing manual annotation. Process RL raises Mistral-7B from 77.9→84.1（GSM8K）、28.6→33.0on MATH, followed by verification reaching 89.1/43.5.[ACL PDF pp.1–2] Each intermediate step still needs multiple rollouts, and wrong steps can accidentally lead to correct answers, contaminating labels. RGM avoids extra MC completions, filtering outcome labels through current SPRM binary judgments. Outcomes remain weak process supervision, but cost shifts from rollouts to one shared forward pass.

12.3 Scaling LLM Test-Time Compute Optimally（ICLR 2025）

Addresses allocation of fixed compute budgets, showing that search strategy depends on difficulty and compute-optimal strategies can save over 4× relative to best-of-N, while smaller models beat 14× larger ones at some difficulties.[Official PDF pp.1–3] The remaining gap is per-question difficulty estimation using 2048 sampleswhose cost is explicitly excluded; models and PRMs are also unreleased. RGM chooses fixed(k=8) and a shared verifier, addressing verifier cost rather than per-question budget routing. It inherits the proposer–verifier abstraction, not dynamic allocation.

12.4 Lessons of Developing PRMs（2025）

Tests whether high BoN scores imply good process verification, finding opposite trends for MC, LLM-judge, and human labels on BoN versus ProcessBench. Consensus filtering retains only about 40% of data while approaching LLM-judge ProcessBench performance. It still requires a72B judge or extensive MC. RGM’s mask is endogenous single-model consensus: train only when global outcomes and local heads agree. It inherits filtering instead of indiscriminate data growth, but never tests process-error detection on ProcessBench.

12.5 ReasonFlux-PRM（NeurIPS 2025 Spotlight）

Addresses different trajectory and final-response distributions in long CoT through step- and trajectory-level supervision for distillation, RL, and BoN. Its abstract reports mean SFT gains of 12.1%、RL 4.5%、TTS 6.3%. It still needs a separate 1.5B/7B PRM. RGM shrinks the head to 5M–54M but uses one geometric mean without trajectory-structure encoding. A next step is transferring ReasonFlux’s two-granularity supervision to a shared backbone while retaining low overhead.

13. Nonlinear technical evolution, drivers, and turning points

                                                  ┌─ Human process supervision ─ PRM800K(2023/ICLR2024)
                         │      └─ Strong process discrimination; costly labels
Final-answer supervision ┤
                         └─ Automatic process supervision ─ Math-Shepherd(ACL 2024)
                                ├─ MC rollout labels; costly, potentially wrong
                                └─ Lessons of PRMs(2025)
                                       └─ Consensus filtering + ProcessBench critique

External best-of-N scaling ─ Snell et al.(ICLR2025)
       ├─ Dynamic difficulty routing: search selection under fixed budgets
       └─ Separate verifier; expensive difficulty estimation

Long-CoT distribution shift ─ ReasonFlux-PRM(NeurIPS 2025)
       └─ Step + trajectory supervision, still an external1.5B/7B model

Branches converge ─ RGM(ICLR2026)
       ├─ Shared backbone +5M–54M scoring head
       ├─ Outcome × pseudo-label consistency filtering
       └─ Fixed k=8: addresses verifier cost, not dynamic budget allocation

Three shifts drive this evolution: from correct final answers to trustworthy processes; from costly human labels to automatic weak supervision, exposing MC/BoN biases; and from larger standalone PRMs to embedding discrimination within generators. RGM’s main shift redefines deployment around whetherverification can reuse representations from a generation forward pass.

13.1 Cross-paper comparison

14. Limitations acknowledged by the paper

1. Complete-trajectory latency. All(k) complete trajectories must first be generated. The authors acknowledge added latency and use(k=8), versus common external TTS counts64–512. Parallel batching can reduce wall-clock time, but not total tokens or memory-bandwidth cost.[Appendix D, PDF p.15]
2. Limited benefit on short reasoning/knowledge tasks. Factual QA or tasks requiring little reasoning lack sufficient step-tokens/trajectories for RGM; the authors view knowledge, not TTS, as the bottleneck.[Appendix D, PDF p.15]
3. Bound to the target policy. Different hidden dimensions prevent direct cross-model SPRM use, requiring linear projection and separate head fine-tuning.[Appendix D, PDF p.15] Table 13 shows one transfer, but not genuine plug-and-play portability.

15. Independent critique: evidence and implications

1. [Evaluation validity] Because evaluation uses final-answer accuracy and BoN selection without ProcessBench or human error-step localization, while Lessons of PRMs shows BoN can move opposite to actual process verification, Table 1 does not establish logical-step understanding. SPRM may learn trajectory styles correlated with success.
2. [Statistics] Because64 repeats lack standard deviations, confidence intervals, or tests, and most gains are only 0.2–1.6 pp,23/25 higher means do not imply cellwise significance. The+0.1 pp over o3-mini is especially difficult to interpret.
3. [Efficiency] Because inference still generates8 full paths, each up to 38K math tokens, without tokens/s, TTFT, P99, or GPU-hours, a lightweight head proves only low verifier parameter count—not cheap overall serving. Generation may dominate scoring cost.
4. [Fairness] Because GPT-OSS-20B uses temperature 1.0while other models use 0.6, and diversity directly affects the BoN ceiling, cross-base gains do not use identical protocols. Table 1 should prioritize within-base comparisons over cross-base rankings.
5. [Data contamination] Because40K training problems combine public math sources without reported deduplication or temporal cutoffs against AIME24/25, HMMT25, and BRUMO25, exact or near-duplicate leakage cannot be excluded. AIME24 predates the training paper and especially needs auditing.
6. [Mechanism attribution] Because standalone RGM8 adds 1.5B parameters and exceeds shared RGM by 0.6–1.6 pp across four math sets, sharing is not the source of accuracy superiority. Its contribution compresses most standalone verification ability into 5M parameters, rather than proving shared representations inherently better.
7. [Pseudo-label bias] Because only(y=\hat y) steps train, uncertain or outcome-conflicting hard steps are systematically discarded, potentially creating confirmation bias. Figure 5’s aha moment indicates this risk, but failure rates across initializations/seeds are absent.
8. [Versions and reproduction] Because arXiv v2 says 53M, the ICLR table5M–54M, its abstract about 50M, and the repository uses XBai o4 branding, model identity and parameter reporting have drifted. Reproduction must calculate from checkpoint hidden size/head configuration, not treat50M as constant.

16. Open challenges requiring head-to-head experiments

16.1 Theory

• Does consistency masking converge to true process labels? Fix policy, data, and compute; compare SPRLoss, ordinary BCE, co-teaching, and confidence-weighted soft labels. On human step-error data, report AUROC/F1, calibration, and final BoN accuracy, tracking erroneous pseudo-label transition matrices across training.
• Is the geometric mean merely implicit length regularization? Compare product, arithmetic, geometric, minimum-step, and learned-attention aggregation, reporting selection accuracy by trajectory-length bucket. Use identical candidates to exclude generation differences.
• Where is the best shared-representation layer? Train equal-parameter linear/two-layer heads at every layer with frozen backbones, forming a layer×task×model matrix. Compare against a standalone1.5B verifier at equal FLOPs to test for a universal middle-layer process-quality peak.

16.2 Engineering and applications

• Actual serving cost. On the same 8×H200 or 8×H100 node, compare Majority@8,72B-PRM@8,RGM@8, and dynamic-k RGM. Report TTFT, total latency, P50/P95/P99, tokens/s, peak memory, joules/query, and accuracy. Deployment superiority requires this table.
• Early stopping instead of eight complete paths. With the same RGM head, compare post-completion scoring against online pruning triggered by step scores at fixed mean generated tokens. Measure accuracy–latency Pareto frontiers, especially errors caused by prematurely pruning exploratory paths.
• Cross-language formatting robustness. Across Chinese, English, Japanese, Korean, and code, compare manual delimiters, syntactic segmentation, and learned boundary heads at a fixed checkpoint. Report step coverage, segmentation errors, and final performance to test whether .\n\n rules are a hidden engineering dependency.

16.3 Emerging directions

• RGM × dynamic budget routing. At fixed total FLOPs, directly compare fixed(k=8) with Plan-and-Budget/ATTS-style per-question routing over(k\in{1,2,4,8,16}). Include difficulty-estimation FLOPs; report accuracy per difficulty bucket and overcomputation rates.
• Two-granularity shared verification. On one backbone, compare RGM’s step-only geometric mean with ReasonFlux-style step+trajectory heads at fixed 54M extra parameters. Use ProcessBench, AIME, and LiveCodeBench to measure both error detection and answer selection.
• Agent/tool trajectories. For executable-code or tool tasks, use executor-provided sparse outcome rewards. Compare shared SPRM, standalone verifiers, and execution-result-only reranking on first-error action localization, task success, and tool-call cost.

17. Eight recent works to follow

1. Plan and Budget: Effective and Efficient Test-Time Scaling on Reasoning LLMs: frames reasoning duration as planning and budgeting, suitable for equal-FLOP comparison with fixed(k=8) RGM.
2. e3: Learning to Explore Enables Extrapolation of Test-Time Compute: learns exploration during training for test-budget extrapolation, testing whether RGM scores remain calibrated at larger(k).
3. ATTS: Asynchronous Test-Time Scaling via Conformal Prediction: manages candidates with asynchrony and conformal prediction, targeting fixed-batch tail latency.
4. MoDr: Mixture-of-Depth-Recurrent Transformers for Test-Time Reasoning: places extra compute into deep recursion rather than parallel candidates, representing an internal-TTS architectural route.
5. TrimR: Verifier-based Training-Free Thinking Trimming: uses verifiers to trim redundant reasoning, addressing RGM’s inability to reduce tokens online rather than merely selecting completed paths.
6. Sample Smart, Not Hard: shifts decoding from likelihood-first to correctness-first; combined with shared SPRM, it could reduce useless candidates rather than only rerank afterward.
7. Log-Augmented Generation: reuses computation logs for reasoning, pursuing caching/reuse instead of resampling every time.
8. Test-Time Scaling in Reasoning LLMs: Inference Regimes, Evaluation, and Reproducibility: unifies sequential, leaf-level, and prefix-level scaling as budgeted prefix trees, emphasizing compute, repeated sampling, and uncertainty reporting—a stricter audit framework for RGM.

18. Conclusion: how to read this paper

RGM’s value lies in changing external TTS’s system boundary: verification need not require a second large model, since process scores can be read from existing generator states. QwQ-32B +RGM8-54M exceeds same-base PRM-72B across five tasks by 0.9–1.6 ppand reaches on AIME24/HMMT25 84.2/53.1; across five backbones, it beats the strongest72B reward model in23/25 cells. Yet standalone RGM remains about 1 pp better, full eight-path serving lacks measurements, process-error detection lacks an independent benchmark, and small gains lack statistical tests. The defensible conclusion is:RGM establishes that lightweight shared verifiers can be competitive, but not that they comprehensively outperform standalone PRMs at equal total compute, equal latency, and actual process reliability.

Footnote: updated local ml-report-index.mdwith 2026-09-28, LLM/NLP, core paper, venue, and a one-sentence conclusion; persistent-index replacement follows the save result. Semantic Scholar API returned403, so none of its numbers are cited. No standalone Papers with Code core entry was found; this is marked rather than substituting a different page.