SpecRoll: Fast-Slow Verifier-Feedback Adaptation for Speculative Reinforcement Learning Rollouts

Duy Tung Doan; Khac-Hoai Nam Bui; Nhat Minh Pham; Thi Duyen Ngo; Vinh Van Nguyen

REVIEW 3 major objections 4 minor 28 references

SpecRoll: Fast-Slow Verifier-Feedback Adaptation for Speculative Reinforcement Learning Rollouts

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read SpecRoll claims 1.26x–2.15x faster GRPO rollout generation with the target sampling distribution and the GRPO objective exactly unchanged, via cheap future-token heads, a gradient-free fast memory, and a drift-triggered slow learner.

desk verdict A genuinely new fast-slow speculative rollout engine with a real proof gap at the top-p verifier boundary; worth reviewing, but the 'distribution unchanged' claim needs a fix. read the letter →

arxiv 2608.04962 v1 pith:MPW4LJNO submitted 2026-08-05 cs.LG cs.CL

Nhat Minh Pham , Duy Tung Doan , Thi Duyen Ngo , Vinh Van Nguyen , Khac-Hoai Nam Bui This is my paper

classification cs.LGcs.CL

keywords speculativedecodingGRPOreinforcementlearningrolloutaccelerationfuture-tokenheadsverifierfeedbackdriftadaptationmathematicalreasoning

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

SpecRoll claims that the rollout-generation bottleneck in Group Relative Policy Optimization (GRPO), a standard reinforcement-learning method for improving mathematical reasoning in large language models, can be removed without disturbing the training objective. Autoregressive response generation dominates RL wall-clock time, but speculative decoding has been hard to apply inside training because the target policy moves at every update: a static drafter goes stale, while retraining a drafter frequently costs nearly as much as it saves. The paper's resolution is a two-timescale design: lightweight future-token heads propose several positions in parallel from the target's hidden state; a gradient-free Reflex module converts delayed verifier errors into bounded, trajectory-local hidden-state corrections; and a slow path updates head parameters only after sustained degradation is detected. Claimed results are 1.26x–2.15x generation and 1.21x–2.04x end-to-end speedups over vanilla GRPO across five models and three mathematical-reasoning datasets, with SpecRoll faster than the online-drafter baseline in all 15 matched settings while exact verification keeps the committed-token distribution and GRPO objective unchanged.

What carries the argument

The load-bearing object is the future-token head, a residual map $z_{t,h} = g_{\phi_h}(h_t) + h_t$ that reuses the frozen target vocabulary projection $W$ to predict horizon-$h$ positions in parallel, so no second autoregressive drafter or drafter KV cache exists. Two derived mechanisms carry the adaptation argument. First, the distribution–coverage decomposition $p(C^\star_K) - \tilde{A}_C = d_{\mathrm{dist}} + d_{\mathrm{cov}}$ is derived under the conservative acceptance surrogate $\tilde{A}_C = p(C)\Omega_C$, where $\Omega_C$ is the overlap coefficient between the target and proposal distributions renormalized on the candidate set $C$; each error term maps to a hidden-space direction that is a strict descent direction of a pointwise KL surrogate. Second, a trajectory–horizon memory $m_{i,h}$ updated by an exponential moving average, and gated by the lower confidence bound $dRel = \bar{a} - z_\delta s_a/\sqrt{n}$ on delayed alignment, decides when the accumulated correction is applied to later prefixes of the same trajectory. A concurrency-aware tree budget $N_t = \mathrm{clip}(C_{\mathrm{hw}}/B_t, N_{\min}, N_{\max})$ keeps packed verification within the hardware envelope, and node-wise rejection sampling with residual fallback is what carries the exactness claim.

What would settle it

Run SpecRoll and vanilla GRPO on the same prompts with the same seed and identical hyperparameters, record the committed token at every verified position, and compare the empirical next-token distributions at matched prefixes (for example by total variation or a two-sample token-frequency test): a measurable divergence contradicts the unchanged-distribution claim. A more direct check is to instrument the verifier's acceptance rule $\min\{1, p(y)/q(y)\}$ and log whether $p$ is the full softmax or the top-p-renormalized softmax; the released code makes this observable.

Watch

Extended reading notes

Core claim

On its own terms, the paper's central discovery is that verifier feedback in speculative rollouts decomposes into two independent failure modes — distribution error, where probability mass is misallocated among the retained candidates, and coverage error, where target-important tokens are omitted entirely — and that both can be converted into explicit hidden-space correction directions computed from the verifier's own output. These directions are combined, RMS-normalized, and accumulated in a trajectory-local exponential moving average whose application is gated by a conservative reliability score; the paper proves the combined direction is a strict descent direction of a pointwise KL-based surrogate. Because the corrections are detached and trajectory-local, the target backbone receives no gradient from them, and because the tree verifier commits tokens by node-wise rejection sampling with target-residual fallback, the paper argues the committed continuation has exactly the distribution of ordinary autoregressive sampling from the current policy. Persistent mismatch that recurs across trajectories is absorbed into the proposal-head parameters on a drift-triggered schedule, so the proposer adapts without constant retraining. The package is presented as evidence that speculation and policy drift need not conflict: a cheap proposer plus gradient-free fast correction plus rare slow consolidation keeps the GRPO objective exact while cutting end-to-end training time.

Load-bearing premise

Exact target verification is proven for the full-softmax target distribution, but the rollouts are generated with nucleus (top-p 0.95) sampling, and the paper never states how the top-p threshold enters the packed verifier; if the verifier accepts candidates against the full softmax while vanilla GRPO samples from the truncated distribution, the committed-token distributions differ and the claim that the GRPO objective is unchanged is unsupported.

Editorial extensions

If this is right

GRPO training time falls by roughly 1.21x–2.04x end to end with no change to reward computation, advantage estimation, or the policy-update rule, because only the rollout sampler is replaced.
Three small heads sharing the frozen target vocabulary projection suffice to keep acceptance high during training, so proposer overhead stays a small fraction of rollout cost instead of requiring a second autoregressive model.
The fast and slow adaptation paths each improve a heads-only baseline and are strongest combined, indicating that transient within-trajectory mismatch and cross-trajectory drift are genuinely different failure modes requiring different fix mechanisms.
The efficiency lever is acceptance rate — the fraction of tested proposal tokens that commit — rather than raw accepted-token length, since SpecRoll wins on acceptance rate in 14 of 15 settings even where the baseline achieves longer accepted continuations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the top-p gap is real, part of the measured speedup could come from a distribution shift — the verifier committing tokens the nucleus-truncated baseline could never sample — which would still reduce wall-clock time but would invalidate the distribution-preservation claim; comparing committed-token frequencies against vanilla GRPO settles which story is true.
The distribution-versus-coverage decomposition is a general diagnostic for proposal quality that could be reused outside RL training, for example in request-adaptive speculation where a drafter cannot be retrained quickly but verifier feedback is cheap.
The reliability-gate pattern — apply a correction only when its delayed-alignment evidence clears a noise floor set by the mean minus z times the standard error — is a transferable design rule for any online adaptation loop that must survive noisy feedback.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Two things to know. First, this is a genuinely new mechanism: Reflex, a gradient-free trajectory-local hidden-state correction with a reliability gate, plus a two-timescale split where a slow path updates head parameters only after sustained drift. That combination is not in the prior work they cite. Second, the paper's headline claim—exact target verification preserving the GRPO objective—has a gap: the proof in Appendix B assumes the full-softmax target, but the implementation (Appendix C.1) rolls out with top-p 0.95. The paper never says how top-p enters the packed verifier. If the verifier uses full softmax, SpecRoll's committed tokens come from a different distribution than the vanilla GRPO baseline, and the 'unchanged objective' claim fails. If it uses the truncated distribution, the exactness proof needs to be redone. Either way it's fixable with a clear statement and a re-derived lemma, but it's load-bearing.

What the paper does well: the exact verification proof (Theorem B.1) is careful and, under the full-softmax assumption, sound. The surrogate acceptance analysis in Appendix B.4 is a nice decomposition. The experimental design is more careful than most systems papers: matched target checkpoints, same prompt order and reward, a runtime-scaling check in Appendix D. The ablations isolating Reflex and the aux path are the right way to test the two-timescale claim.

Soft spots beyond the top-p gap: every table entry is a single run, no variance or seeds beyond a single seed 42. For a speedup claim, one run is thin, even if the timing is wall-clock. Also, the k=48 support budget was selected from a sweep on one model-dataset (Appendix F) and then used for all main results; that's benchmark-suite calibration, and the sweep itself shows non-monotonic behavior. The Appendix A theory is real but it is a pointwise descent argument with fixed supports; the paper itself notes (A4) is not implied, and the transfer to acceptance only gives a certificate on the candidate support, not a guarantee on the verifier support. That is a fair limitation, not fatal.

Send it to peer review. The idea deserves a careful referee, and the top-p issue is addressable. Ask the authors to state the verifier's target distribution, re-derive the exactness lemma for the truncated case, and at least report a second seed. If they do that, the central claim has a real chance of holding.

Referee Report

3 major / 4 minor

Summary. The paper introduces SpecRoll, a speculative decoding engine for GRPO rollout generation that combines lightweight future-token heads, a gradient-free trajectory-local correction module called Reflex, and a slower persistent head-adaptation mechanism, all under a concurrency-aware sparse-tree verifier. The central claims are that these mechanisms preserve the target rollout distribution and the GRPO objective, and that SpecRoll achieves 1.26–2.15x generation speedup and 1.21–2.04x end-to-end speedup over vanilla GRPO, while outperforming FastGRPO on all 15 matched model–dataset settings. The paper includes theoretical appendices for exact tree verification and for the descent properties of the Reflex feedback, along with ablations and hyperparameter sensitivity experiments.

Significance. If the distribution-preservation claim holds, SpecRoll is a practical and well-motivated contribution to RL post-training efficiency: it addresses the non-stationarity of the target policy without an extra autoregressive drafter, and its two-timescale adaptation has a clear design rationale. The manuscript ships substantial formal support for its core components: the exact node-wise tree verification proof (Appendix B) is rigorous and the pointwise surrogate analysis (Appendix A) is honest about the conditions under which the feedback is a descent direction. The experimental coverage is broad for a systems paper (five models, three datasets, ablations, runtime scaling diagnostic). The main weakness is a gap between the theoretical exactness statement and the implemented sampling configuration, which directly affects the validity of the headline claims.

major comments (3)

[Appendix C.1 vs. Appendix B / Eq. (2)] The implemented rollout uses nucleus sampling with temperature 1.0 and top-p 0.95 (Appendix C.1), but the theoretical exactness statement is proved for the full-softmax target: Eq. (2) defines x_{t+1} ~ p_t = softmax(W h_t), and Theorem B.1 establishes exactness for p_u(v) = pi_theta(v | prefix). The manuscript never states whether the packed verifier logits are the full-softmax distribution or a top-p-truncated and renormalized distribution. If the verifier evaluates full-softmax targets while the vanilla GRPO baseline samples from the top-p-0.95-truncated distribution, then the committed-token distribution under SpecRoll differs from vanilla GRPO, and the abstract, Section 3.1, and Section 5 claims that the target rollout distribution and GRPO objective are unchanged are unsupported. If the verifier instead uses top-p-truncated targets, Theorem B.1 and the residual update in Algorithm 1 must be re-derived for the censored target, and the manuscript must confirm that the vanilla GRPO baseline uses the identical truncation procedure. This issue is load-bearing because both the exactness identity and the apples-to-apples speedup comparison rest on the sampling distribution being the same across methods.
[Appendix F / Table 1 / Table 3] The sparse-support top-k budget in Eq. (12) is selected on Qwen2.5-3B with SimpleRL-Abel-Level3to5: Appendix F states that k=48 is chosen because it gives the best speedup, AAL, and acceptance rate in that sweep, and this same configuration is used in the main results on the same model–dataset pair. More generally, Tables 3 and 4 report many calibrated thresholds (reliability coefficient z_delta, correction intervals, feedback stride, auxiliary trigger conditions) without stating whether any of these were tuned on the evaluation suite. Since the headline claim is that SpecRoll is faster than FastGRPO in all 15 matched settings, the manuscript should either use a held-out tuning set or provide a sensitivity analysis showing that the qualitative 15/15 result is robust to the calibrated hyperparameters. As written, the strength of the empirical claim exceeds what the tuning protocol supports.
[Appendix D / Figure 4] The runtime-scaling diagnostic fits a linear model to cumulative wall-clock time and reports R^2 values (0.998 and 0.988) as evidence that the speedup is not concentrated in one phase. Cumulative runtime is monotonically increasing by construction, so high R^2 on cumulative curves is expected and is not informative about whether the per-segment speedup is stable. The partial-run completion estimates (23.53 vs. 21.41 hours, and 22.67 vs. 29.95 hours) also show nontrivial error. Please report per-segment slope or per-20%-interval speedup, and state the implied uncertainty, to support the claim of a stable runtime advantage.

minor comments (4)

[Eq. (11) and Eq. (16)] The notation d_dist and d_cov is overloaded: in Eq. (11) they denote the two gap components of the acceptance surrogate, while in Eq. (16) they are nonnegative combination weights. Please rename one of the two uses to avoid confusion.
[Table 1] Each table entry appears to come from a single matched run. Please state whether runs were repeated across seeds or initialization, or explicitly say that the table reports a single run by design, so readers can calibrate the strength of the 15/15 improvement claim.
[Section 4.2, RQ2] The discussion of acceptance rate versus AAL is clear, but the interpretation that SpecRoll is 'more effective' at using the proposal budget is based on a single aggregate statistic; a breakdown by dataset or trajectory length would strengthen the claim.
[Appendix G] The training-reward dynamics figure shows comparable raw-reward trajectories, but the extracted text around Figure 6 contains garbled rendering artifacts; please ensure the figure and its caption are clean in the final version.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the exactness theorem is a self-contained rejection-sampling proof with stated assumptions, and the speedups are measured wall-clock outcomes; the nucleus top-p mismatch and k=48 benchmark calibration are correctness caveats, not reductions to inputs.

full rationale

Walking the paper's derivation chain shows no circular reduction. The central identity claim, that Algorithm 1 commits tokens from the target conditional, is proven in Appendix B (Proposition B.1, Theorem B.1) by the standard node-wise residual rejection-sampling argument; the conclusion is not assumed in the premises. The verifier-error analysis in Section 3.3 is exact algebra following from the definitions of p_C, q_C, and the overlap coefficient, with the key inequality p(C)Omega_C <= A_ver_C <= p(C) proven in Proposition B.2. The Appendix A.1 'pointwise surrogate representation' is an explicit construction: the surrogate L_cov is defined in Eq. 24 after the feedback direction r_cov in Eq. 22, with coefficients chosen so that -grad_Phi = r, and the paper states this construction openly, so the equivalence is a stated representation theorem rather than a hidden circularity. Theorem A.1 is a self-contained martingale and concentration argument under stated drift and noise assumptions. Empirically, the headline speedups are wall-clock outcomes measured against matched vanilla-GRPO and FastGRPO runs; no fitted parameter is renamed as a derived prediction. The reference list contains no papers by the present authors, so no self-citation chain exists. Two caveats are correctness risks, not circularity. First, Appendix C.1 states rollouts use nucleus sampling at top-p 0.95, while the exactness theorem is stated and proven for the full-softmax target p_u(v) = pi_theta(v | prefix) (Eq. 86); the manuscript never specifies whether the packed verifier targets are full-softmax or truncated, so the identity with vanilla GRPO's distribution and the 'unchanged GRPO objective' claim are unsupported as written. Second, the k=48 support budget is selected on the same benchmark where a headline speedup is reported (Appendix F, Qwen2.5-3B SimpleRL), with the paper honestly reporting the selection; this is a benchmark-calibration concern, not a fitted-parameter-renamed-as-prediction reduction, since the speedup remains a measured outcome. Neither issue makes a prediction equivalent to an input by construction.

Assumptions & free parameters 9 free parameters · 5 assumptions · 0 invented entities

The central speedup claim depends on many hand-set parameters, the most load-bearing being the feedback weights, support budget k=48, tree budget, and the unspecified calibrated baselines. The exactness proof is independent of these, but the measured speedups are not. The only truly unstated assumption is the compatibility of the full-softmax verifier in the proof with the nucleus sampling in the implementation.

free parameters (9)

Feedback direction weights = d_dist=0.15, d_cov=1.25
Equation 16 combines distribution and coverage correction directions; these weights are hand-set and directly affect Reflex behavior.
Sparse support top-k = 48
Equation 12 defines the feedback support; k=48 was selected as best in the Appendix F sweep on Qwen2.5-3B SimpleRL and used in all main runs.
Reflex reliability coefficient z_delta = 0.60
Table 3 sets the conservative lower-bound coefficient in Equation 18; controls how much evidence is required before Reflex fires.
Horizon memory decay rates = rho=(0.85, 0.90, 0.95)
Per-horizon EMA decays in Equation 17 are hand-set in Table 3.
Correction interval bounds = [1.0-2.5%, 0.4-1.0%, 0.25-0.6%] of hidden-state RMS
Table 3 bounds the alpha factor in Equation 19; chosen per horizon.
Tree budget parameters = C_peak=512, N_min=1, N_max=10
Equation 106 maps active concurrency to node budget; tuned for the B200 hardware used in all runs.
Feedback severity coefficients = 0.3 TV + 0.7 p_out, threshold 0.03
Equation 107 decides which matured proposals update the Reflex memory; coefficients are hand-set.
Calibrated per-head baselines = not stated
Section 3.5 and Equation 109 require comparing current discrepancy and acceptance against calibrated baselines; the calibration procedure is not specified and is effectively fit to run data.
Auxiliary loss coefficients = 1.0, 0.1, 1.5, lambda_p=0.020
Equation 110 weights distillation, effective-distillation, ranking, and proximity terms; chosen by hand.

assumptions (5)

standard math Standard probability and concentration inequalities (KL, TV, Pinsker, sub-Gaussian concentration, covering number argument).
Used in Appendix A and B for the descent guarantee and the acceptance certificate; standard results invoked without proof.
domain assumption Assumptions A2-A4 in Appendix A.2: bounded drift of the predictable field, sub-Gaussian noise, and current-field calibration ||h_t - g_t|| <= b.
Theorem A.1's descent bound holds only under these unproved assumptions about the verifier-feedback process.
domain assumption Verifier errors at matured proposals remain predictive over nearby positions within the same trajectory.
This is the core motivation of Reflex in Section 3.4 and is empirically probed in Appendix E, but not proven.
ad hoc to paper The exact verifier target distribution equals the actual GRPO sampling distribution, including the nucleus top-p truncation.
Appendix B proves exactness for the full-softmax target p_u, while Appendix C.1 specifies nucleus sampling with top-p 0.95. The paper does not state how top-p enters the packed verifier, so this compatibility is assumed without evidence.
domain assumption ShareGPT-pretrained future-token heads transfer to math RL rollouts.
The heads are pretrained on ShareGPT-derived data (Appendix C.1) and used without additional domain pretraining on math data.

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Cite this review

Pith. "Pith review of SpecRoll: Fast-Slow Verifier-Feedback Adaptation for Speculative Reinforcement Learning Rollouts." pith.science (2026). https://pith.science/paper/MPW4LJNO

@misc{pith2026260804962,
  author       = {Pith},
  title        = {Pith review of: SpecRoll: Fast-Slow Verifier-Feedback Adaptation for Speculative Reinforcement Learning Rollouts},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MPW4LJNO}},
  note         = {Machine review of arXiv:2608.04962}
}

read the original abstract

Reinforcement learning (RL) post-training improves the reasoning capabilities of large language models, but autoregressive rollout generation remains a major efficiency bottleneck. Speculative decoding can accelerate generation, yet applying it during RL is difficult because the target policy continually evolves: static proposers become stale, while frequent drafter updates add substantial overhead. We introduce SpecRoll, a speculative rollout engine that preserves the target model's sampling distribution while adapting at two timescales. Lightweight future-token heads generate parallel proposals, while our proposed Reflex module uses delayed verifier feedback to perform bounded, trajectory-local hidden-state corrections without backpropagation. A complementary slow path updates the head parameters only when sustained degradation is detected. SpecRoll combines these mechanisms with concurrency-aware sparse-tree verification and exact target verification, leaving the target rollout distribution and GRPO objective unchanged. Across five models ranging from 1.5B to 14B and three mathematical reasoning datasets, SpecRoll achieves 1.26-2.15x generation speedup and 1.21-2.04x end-to-end speedup over vanilla GRPO. It also outperforms FastGRPO in both generation and end-to-end time across all 15 matched settings, with an average pairwise end-to-end gain of 1.18x. Controlled ablations show that the fast and slow adaptation paths provide complementary benefits. Our source code is available at https://anonymous.4open.science/r/SpecRoll-26062006.

Figures

Figures reproduced from arXiv: 2608.04962 by the authors.

**Figure 1.** SpecRoll delivers plug-and-play rollout acceleration for RL. On a single NVIDIA B200 at $6.88 per GPU-hour, SpecRoll saves approximately $14 and $325 per run relative to FastGRPO and GRPO, respectively. vantages from groups of sampled responses without requiring a learned value model (Shao et al., 2024; DeepSeek-AI, 2025). However, each update still requires multiple long autoregressive responses, making rollou… view at source ↗

**Figure 2.** Overview of SpecRoll across one GRPO iteration. Future-token heads construct proposals from the current target hidden state, and Reflex optionally applies trajectory-local corrections before sparse-tree verification. Mature verifier feedback updates the fast memory and reliability records, while persistent head parameters are updated only after sustained drift is detected. Reward computation and the GRPO policy upda… view at source ↗

**Figure 3.** Two proposal errors under a fixed candidate [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: Cumulative end-to-end runtime as a function of the fraction of training examples processed for Qwen2.5- [PITH_FULL_IMAGE:figures/full_fig_p020_4.png]

**Figure 5.** Figure 5: Predictive validity of the proposal-time Reflex reliability score on Qwen2.5-1.5B with SimpleRL-Abel [PITH_FULL_IMAGE:figures/full_fig_p021_5.png]

**Figure 6.** Figure 6: Training-reward dynamics on GSM8K. SpecRoll and vanilla GRPO exhibit comparable raw-reward trajectories for Qwen2.5-1.5B and Qwen2.5-3B. ceptance rate by 0.006. This suggests that the support budget has a modest, non-monotonic effect on the restricted error geometry a…

**Figure 7.** Figure 7: Wall-clock latency of triggered auxiliary updates. Each point denotes one update; dashed and dotted lines indicate the mean and median latency, respectively [PITH_FULL_IMAGE:figures/full_fig_p023_7.png]

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Works this paper leans on

28 extracted references · 18 canonical work pages

[1]

Advances in Neural Information Processing Systems , volume =

Using Fast Weights to Attend to the Recent Past , author =. Advances in Neural Information Processing Systems , volume =. 2016 , url =

work page 2016
[2]

and Chen, Deming and Dao, Tri , booktitle =

Cai, Tianle and Li, Yuhong and Geng, Zhengyang and Peng, Hongwu and Lee, Jason D. and Chen, Deming and Dao, Tri , booktitle =. Medusa: Simple. 2024 , eprint =

work page 2024
[3]

arXiv preprint arXiv:2302.01318 , year =

Accelerating Large Language Model Decoding with Speculative Sampling , author =. arXiv preprint arXiv:2302.01318 , year =. 2302.01318 , archivePrefix =

arXiv
[4]

arXiv preprint arXiv:2110.14168 , year =

Training Verifiers to Solve Math Word Problems , author =. arXiv preprint arXiv:2110.14168 , year =. 2110.14168 , archivePrefix =

arXiv
[5]

2501.12948 , archivePrefix =

arXiv preprint arXiv:2501.12948 , year =. 2501.12948 , archivePrefix =

arXiv
[6]

Grattafiori, Aaron and others , journal =. The. 2024 , eprint =

work page 2024
[7]

Accelerating

Iso, Hayate and Mitra, Tiyasa and Mondal, Sudipta and Shafipour, Rasoul and Elango, Venmugil and Kong, Terry and Huang, Yuki and Na, Seonjin and Putterman, Izzy and Chislett, Benjamin and Ashkenazi, Maor and Guman, Joseph and Shen, Gerald and Konuk, Tugrul and Aithal, Ashwath and Borkar, Ritika and Zilberstein, Ran and Rouhani, Bita , journal =. Accelerat...

work page 2026
[8]

2026 , eprint =

Kim, Minseo and Lee, Minjae and Oh, Seunghyuk and Galim, Kevin and Kim, Donghoon and Hooper, Coleman and Singh, Harman and Gholami, Amir and Koo, Hyung Il and Kang, Wonjun , journal =. 2026 , eprint =

work page 2026

Show all 28 references

[9]

arXiv preprint arXiv:2605.09329 , year =

Test-Time Speculation , author =. arXiv preprint arXiv:2605.09329 , year =. 2605.09329 , archivePrefix =

arXiv
[10]

Proceedings of the 40th International Conference on Machine Learning , series =

Fast Inference from Transformers via Speculative Decoding , author =. Proceedings of the 40th International Conference on Machine Learning , series =. 2023 , url =

2023
[11]

2024 , url =

Li, Yuhui and Wei, Fangyun and Zhang, Chao and Zhang, Hongyang , booktitle =. 2024 , url =

2024
[12]

2024 , doi =

Li, Yuhui and Wei, Fangyun and Zhang, Chao and Zhang, Hongyang , booktitle =. 2024 , doi =

2024
[13]

2025 , eprint =

Li, Yuhui and Wei, Fangyun and Zhang, Chao and Zhang, Hongyang , booktitle =. 2025 , eprint =

2025
[14]

Proceedings of the 41st International Conference on Machine Learning , series =

Online Speculative Decoding , author =. Proceedings of the 41st International Conference on Machine Learning , series =. 2024 , url =

2024
[15]

arXiv preprint arXiv:2603.12617 , year =

When Drafts Evolve: Speculative Decoding Meets Online Learning , author =. arXiv preprint arXiv:2603.12617 , year =. 2603.12617 , archivePrefix =
[16]

2412.15115 , archivePrefix =

arXiv preprint arXiv:2412.15115 , year =. 2412.15115 , archivePrefix =

arXiv
[17]

Shao, Zhihong and Wang, Peiyi and Zhu, Qihao and Xu, Runxin and Song, Junxiao and Bi, Xiao and Zhang, Haowei and Zhang, Mingchuan and Li, Y. K. and Wu, Y. and Guo, Daya , journal =. 2024 , eprint =

2024
[18]

Beat the Long Tail: Distribution-Aware Speculative Decoding for

Shao, Zelei and Srivatsa, Vikranth and Srivastava, Sanjana and Wu, Qingyang and Ariyak, Alpay and Wu, Xiaoxia and Patel, Ameen and Wang, Jue and Liang, Percy and Dao, Tri and Zhang, Ce and Zhang, Yiying and Athiwaratkun, Ben and Xu, Chenfeng and Wang, Junxiong , booktitle =. B...

2026
[19]

2025 , eprint =

Yu, Qiying and others , journal =. 2025 , eprint =

2025
[20]

2025 , eprint =

Zeng, Weihao and Huang, Yuzhen and Liu, Qian and Liu, Wei and He, Keqing and Ma, Zejun and He, Junxian , journal =. 2025 , eprint =

2025
[21]

International Conference on Learning Representations , year =

Learning Harmonized Representations for Speculative Sampling , author =. International Conference on Learning Representations , year =. 2408.15766 , archivePrefix =

arXiv
[22]

2025 , eprint =

Zhang, Yizhou and Lv, Ning and Wang, Teng and Dang, Jisheng , journal =. 2025 , eprint =

2025
[23]

arXiv preprint arXiv:2509.19128 , year =

Pich. arXiv preprint arXiv:2509.19128 , year =. 2509.19128 , archivePrefix =
[24]

2023 , eprint =

Yao, Zhewei and Yazdani Aminabadi, Reza and Ruwase, Olatunji and Rajbhandari, Samyam and Wu, Xiaoxia and Awan, Ammar Ahmad and Rasley, Jeff and Zhang, Minjia and Li, Conglong and Holmes, Connor and Zhou, Zhongzhu and Wyatt, Michael and Smith, Molly and Kurilenko, Lev and Qin, ...

2023
[25]

2024 , eprint =

Hu, Jian and Wu, Xibin and Shen, Wei and Liu, Jason Klein and Zhu, Zilin and Wang, Weixun and Jiang, Songlin and Wang, Haoran and Chen, Hao and Chen, Bin and Fang, Weikai and Xianyu and Cao, Yu and Xu, Haotian and Liu, Yiming , journal =. 2024 , eprint =

2024
[26]

2024 , eprint =

Mei, Zhiyu and Fu, Wei and Li, Kaiwei and Wang, Guangju and Zhang, Huanchen and Wu, Yi , journal =. 2024 , eprint =

2024
[27]

2025 , publisher =

Sheng, Guangming and Zhang, Chi and Ye, Zilingfeng and Wu, Xibin and Zhang, Wang and Zhang, Ru and Peng, Yanghua and Lin, Haibin and Wu, Chuan , booktitle =. 2025 , publisher =

2025
[28]

2025 , eprint =

Wang, Siqi and Yang, Hailong and Zhu, Junjie and Wang, Xuezhu and Xu, Yufan and Qian, Depei , journal =. 2025 , eprint =

2025

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

Advances in Neural Information Processing Systems , volume =

Using Fast Weights to Attend to the Recent Past , author =. Advances in Neural Information Processing Systems , volume =. 2016 , url =

work page 2016

[2] [2]

and Chen, Deming and Dao, Tri , booktitle =

Cai, Tianle and Li, Yuhong and Geng, Zhengyang and Peng, Hongwu and Lee, Jason D. and Chen, Deming and Dao, Tri , booktitle =. Medusa: Simple. 2024 , eprint =

work page 2024

[3] [3]

arXiv preprint arXiv:2302.01318 , year =

Accelerating Large Language Model Decoding with Speculative Sampling , author =. arXiv preprint arXiv:2302.01318 , year =. 2302.01318 , archivePrefix =

arXiv

[4] [4]

arXiv preprint arXiv:2110.14168 , year =

Training Verifiers to Solve Math Word Problems , author =. arXiv preprint arXiv:2110.14168 , year =. 2110.14168 , archivePrefix =

arXiv

[5] [5]

2501.12948 , archivePrefix =

arXiv preprint arXiv:2501.12948 , year =. 2501.12948 , archivePrefix =

arXiv

[6] [6]

Grattafiori, Aaron and others , journal =. The. 2024 , eprint =

work page 2024

[7] [7]

Accelerating

Iso, Hayate and Mitra, Tiyasa and Mondal, Sudipta and Shafipour, Rasoul and Elango, Venmugil and Kong, Terry and Huang, Yuki and Na, Seonjin and Putterman, Izzy and Chislett, Benjamin and Ashkenazi, Maor and Guman, Joseph and Shen, Gerald and Konuk, Tugrul and Aithal, Ashwath and Borkar, Ritika and Zilberstein, Ran and Rouhani, Bita , journal =. Accelerat...

work page 2026

[8] [8]

2026 , eprint =

Kim, Minseo and Lee, Minjae and Oh, Seunghyuk and Galim, Kevin and Kim, Donghoon and Hooper, Coleman and Singh, Harman and Gholami, Amir and Koo, Hyung Il and Kang, Wonjun , journal =. 2026 , eprint =

work page 2026