Margins, Not Windows: Training-Free Per-Step Lossy Speculative Decoding

# Margins, Not Windows: Training-Free Per-Step Lossy Speculative Decoding
Source: [https://arxiv.org/html/2609.02897](https://arxiv.org/html/2609.02897)
Oszkár Urbán1Young D\. Kwon1,2Stylianos I\. Venieris2Cecilia Mascolo1 1University of Cambridge2Samsung AI Center\-Cambridge, UK

###### Abstract

Speculative decoding accelerates LLM inference by drafting candidate tokens and verifying them in parallel\. Tree\-attention drafters such as EAGLE\-3 are widely adopted, yet typically hold two decisions fixed: \(1\) a strict token\-match verification rule and \(2\) a static draft\-tree shape\. Prior work relaxes each in isolation under limiting assumptions: long draft chains for training\-free lossy verification, and adaptive tree shaping under a fixed token budget\. We introduce AdaptiveSpec, a training\-free per\-step speculative decoding method that adapts both decisions from internal signals already produced during decoding\. A per\-step margin rule promotes a mismatched draft\-proposed token when the ratio of the target’s probability on the drafted token to its top\-1 probability exceeds a threshold with no dependence on draft length or underlying drafter architecture\. A per\-step tree policy adjusts the draft tree’s depth, width, and node count directly from a fused signal of draft top\-1 confidence and a rolling acceptance history capturing recent draft\-target agreement, allowing the total draft count to vary rather than only be redistributed\. The two adaptations operate on orthogonal axes and compound in effect\. Implemented on the SGLang production\-grade serving engine, AdaptiveSpec improves throughput over the state\-of\-the\-art autoregressive speculative decoding method EAGLE\-3 by up to 56%, recovering 93% to fully lossless task accuracy across GSM8K, MATH\-500, and HumanEval on three target models \(DeepSeek\-R1\-Distill\-Llama\-8B,Llama\-3\.1\-8B\-Instruct,Qwen3\-8B\)\.

Margins, Not Windows: Training\-Free Per\-Step Lossy Speculative Decoding

Oszkár Urbán1††thanks:Corresponding author:ou222@cam\.ac\.ukYoung D\. Kwon1,2Stylianos I\. Venieris2Cecilia Mascolo11University of Cambridge2Samsung AI Center\-Cambridge, UK

## 1Introduction

Large language models \(LLMs\) are now widely adopted across natural language processing and beyond, solving diverse tasks\(Agarwal et al\.,[2025](https://arxiv.org/html/2609.02897#bib.bib1); Kamath et al\.,[2025](https://arxiv.org/html/2609.02897#bib.bib20)\)\. Their autoregressive design, however, fundamentally limits inference efficiency: each token is produced by a forward pass that must wait for the preceding token\. This cost grows as models scale, and is especially pronounced for chain\-of\-thought reasoning models\(DeepSeek\-AI,[2025](https://arxiv.org/html/2609.02897#bib.bib11)\), which emit long intermediate “thinking” traces, often longer than the final answer itself and disregarded once the final answer is produced\.

Speculative decoding\(Leviathan et al\.,[2023](https://arxiv.org/html/2609.02897#bib.bib22); Chen et al\.,[2023](https://arxiv.org/html/2609.02897#bib.bib6)\)addresses this autoregressive limitation while preserving the target model’s output distribution\. It follows a draft\-then\-verify pattern: a lightweight*draft*model proposes several candidate tokens, and the*target*model verifies them in parallel within a single forward pass, generating correctly predicted tokens at the cost of a single forward pass rather than one pass per token\. Tree\-attention drafters\(Li et al\.,[2024](https://arxiv.org/html/2609.02897#bib.bib24); Ringel and Romano,[2026](https://arxiv.org/html/2609.02897#bib.bib36)\)are a widely adopted implementation of this pattern: at each step, they propose a tree of candidate draft tokens allowing for several continuations\.

Recent work improves speculative decoding on two fronts: relaxing the verifier acceptance rule, and adjusting the draft tree shape\. On the*verifier*side, methods loosen the acceptance criterion from strict token match toward semantic equivalence, increasing throughput at moderate accuracy cost: training\-required verifier methods\(Bachmann et al\.,[2025](https://arxiv.org/html/2609.02897#bib.bib3); Dong et al\.,[2026](https://arxiv.org/html/2609.02897#bib.bib12)\)learn an external module from labelled or generated data, while the training\-free method, FLy\(Li et al\.,[2026](https://arxiv.org/html/2609.02897#bib.bib23)\), considers a mismatched token semantically equivalent only when a downstream window of the nextWWtokens \(typicallyW=6W\{=\}6\) contains no further mismatch\. On EAGLE\-3\(Li et al\.,[2025](https://arxiv.org/html/2609.02897#bib.bib25)\), however, per\-token acceptance collapses with draft depth, to below 10% by depths 7–9, so a window of this size is very likely to contain a mismatch\. As a result, FLy’s relaxation on EAGLE\-3 yields little net speedup and can fall below the static baseline\. On the*drafter*side, a complementary line adapts the shape and size of the draft tree, given the observation that confident steps benefit more from a deep chain, while uncertain ones need a wide tree of alternatives\. TALON\(Liu et al\.,[2026](https://arxiv.org/html/2609.02897#bib.bib28)\), the closest representative, adapts tree shape online from a confidence measure and produces deeper trees on easy steps and wider ones on hard steps\. The adaptation, however, happens within a total token budget, and TALON redistributes a node count between depth and width instead of adjusting the draft tree depth and width\(nsteps,top\-​k\)\(n\_\{\\text\{steps\}\},\\text\{top\-\}k\)directly\.

In this work, we address both limitations by introducing AdaptiveSpec, a training\-free, per\-step adaptive speculative decoding framework driven entirely by internal signals already computed during decoding\. First, we propose anovel per\-step lossy verification rulethat promotes a mismatched draft token when the ratio of the target’s probability on it to the target’s top\-1 probability exceeds a threshold, achieving higher throughput at minimal accuracy cost without requiring auxiliary training or an external verifier to judge semantic equivalence\. Second, we proposedynamic draft tree\-shapingthat directly adjusts the hyperparameters controlling the shape of the draft tree based on the draft’s top\-1 probability and a rolling acceptance history, without growing under a fixed budget\. In addition, we integrate the two axes into a single solution, AdaptiveSpec, compounding into further throughput speedup\. Our main contributions are summarised as follows:

1. 1\.We propose a novel, training\-free, lossy verification rule that promotes a mismatched draft token using only the ratio of the target’s probability on it to the target’s top\-1 probability at the mismatch position, with no requirements on draft chain length, applicable to any drafter\.
2. 2\.We introduce a dynamic tree\-shaping policy that adjusts all three tree\-shape drafter hyperparameters directly per decoding step, driven by combining draft confidence with a rolling acceptance rate\.
3. 3\.We combine these components into AdaptiveSpec, a unified, training\-free, internal\-signal\-driven adaptive speculative decoding method, that improves throughput by 18\-44% on average per target model over the EAGLE\-3 baseline, while retaining 93% to fully lossless downstream task accuracy\. Both our proposed components of AdaptiveSpec independently outperform state\-of\-the\-art \(SOTA\) speculative decoding in their own regime\.

## 2Related Work

#### Speculative Decoding\.

Speculative decoding\(Leviathan et al\.,[2023](https://arxiv.org/html/2609.02897#bib.bib22); Chen et al\.,[2023](https://arxiv.org/html/2609.02897#bib.bib6)\)breaks the sequential dependency of autoregressive decoding with a draft\-and\-verify approach\. A fast*draft*model proposesγ\\gammacandidate tokens, and the*target*model verifies them in a single forward pass\. Because verification runs in parallel, up toγ\\gammaaccepted draft tokens are committed per target forward pass\. Tree\-shaped drafters extend this pattern by proposing a*tree*of candidates per step rather than a chain, exposing multiple continuations to the same verify pass and raising the expected acceptance length\(Miao et al\.,[2024](https://arxiv.org/html/2609.02897#bib.bib32); Cai et al\.,[2024](https://arxiv.org/html/2609.02897#bib.bib5); Ankner et al\.,[2024](https://arxiv.org/html/2609.02897#bib.bib2); Du et al\.,[2024](https://arxiv.org/html/2609.02897#bib.bib13); Xiao et al\.,[2024](https://arxiv.org/html/2609.02897#bib.bib41)\)\. We adopt the SOTA autoregressive EAGLE\-3\(Li et al\.,[2025](https://arxiv.org/html/2609.02897#bib.bib25)\)as our drafter\. Each EAGLE\-3 decoding step alternates two phases:\(i\) Draft: the draft model performsn​s​t​e​p​snstepsforwards, branchingt​o​p​ktopkways per node and pruning to a verify budget ofn​d​tndttokens;\(ii\) Verify: the target model accepts the proposed tokens consistent with its own distribution\. The triplet\(nsteps,top\-​k,ndt\)\(n\_\{\\text\{steps\}\},\\text\{top\-\}k,\\mathrm\{ndt\}\)thus controls both the draft tree shape and the per\-step compute amount\.

#### Adaptive Draft Trees\.

A recent body of work has shown that no single draft tree is optimal across a generation; some steps benefit from a deep chain, while others from a wide branching tree\. To address this, several works have focused on adapting the tree at runtime\(Zhang et al\.,[2024](https://arxiv.org/html/2609.02897#bib.bib44); Xiong et al\.,[2024](https://arxiv.org/html/2609.02897#bib.bib42); Huang et al\.,[2025](https://arxiv.org/html/2609.02897#bib.bib18); Mamou et al\.,[2024](https://arxiv.org/html/2609.02897#bib.bib31); Huo et al\.,[2025](https://arxiv.org/html/2609.02897#bib.bib19); Liu et al\.,[2025](https://arxiv.org/html/2609.02897#bib.bib27); Gao et al\.,[2025](https://arxiv.org/html/2609.02897#bib.bib15)\)\. EAGLE\-2\(Li et al\.,[2024](https://arxiv.org/html/2609.02897#bib.bib24)\)reranks which tokens fill a fixed\-size tree budget\. OPT\-Tree\(Wang et al\.,[2025a](https://arxiv.org/html/2609.02897#bib.bib39)\)re\-solves the tree topology at every decoding step to maximise expected acceptance length within a fixed node budget, while Sequoia\(Chen et al\.,[2024](https://arxiv.org/html/2609.02897#bib.bib9)\)optimises the tree offline via dynamic programming for a given draft–target pair and hardware setup\.

Closest to our dynamic tree\-shaping axis is TALON\(Liu et al\.,[2026](https://arxiv.org/html/2609.02897#bib.bib28)\), which adapts the tree shape online via a confidence\-gated expansion rule: after a fixed top\-KKinitialisation at the root \(to mitigate early rejection\), deeper layers retain and further expand only those candidate tokens whose draft probability lies within a threshold ratio of the layer’s most\-confident token, growing the tree until a fixed global token budget is reached\. This yields topologies that are deep where the draft is confident and wide where it is not\. The limitation is that adaptation happens within that global token budget: TALON only redistributes a total node count across depth and width and cannot directly adjust the total draft compute\. In addition, as it has not been integrated into a performant inference engine such as SGLang, it remains unclear whether TALON’s performance gains would be maintained in a highly optimised production setup\.

Our AdaptiveSpec addresses both limitations directly\. It jointly adapts all three EAGLE\-3 draft\-tree hyperparameters\(nsteps,top\-​k,ndt\)\(n\_\{\\text\{steps\}\},\\text\{top\-\}k,\\mathrm\{ndt\}\)per decoding step from a confidence signal combining the draft model’s top\-1 probability and a running acceptance rate\. Because the candidate triplets span different total node counts, the policy genuinely contracts draft compute on weak\-draft steps rather than only redistributing a budget\. We implement this inside SGLang, retaining its production\-grade performance\.

#### Lossy Verification\.

Existing work has investigated how to relax the strict acceptance rule to admit mismatches the target considers near\-equivalent, raising acceptance rate at a small accuracy cost\(Sun et al\.,[2025](https://arxiv.org/html/2609.02897#bib.bib38); Garipov et al\.,[2025](https://arxiv.org/html/2609.02897#bib.bib16); Wang et al\.,[2025b](https://arxiv.org/html/2609.02897#bib.bib40)\)\. Judge Decoding\(Bachmann et al\.,[2025](https://arxiv.org/html/2609.02897#bib.bib3)\)andSemanticSpec\(Dong et al\.,[2026](https://arxiv.org/html/2609.02897#bib.bib12)\)showed that an external verifier, a judge classifier or a semantic probe over target hidden states, identifies and accepts such mismatches while preserving competitive task accuracy; their main limitation is that this module must be*trained*and therefore comes with limited transferability to new datasets and tasks\.

The training\-free FLy\(Li et al\.,[2026](https://arxiv.org/html/2609.02897#bib.bib23)\)instead promotes a mismatch when an entropy gate condition passes*and*a lookahead window of the nextWWtokens shows no further mismatch, designed so that the lookahead window can replace a trained verifier\.

The lookahead window builds on the idea that when LLMs are conditioned on genuinely incorrect tokens, they tend to self\-correct in subsequent generation steps\(Pan et al\.,[2023](https://arxiv.org/html/2609.02897#bib.bib34)\)\(a phenomenon referred to as the erroneous token pattern in Judge Decoding\(Bachmann et al\.,[2025](https://arxiv.org/html/2609.02897#bib.bib3)\)\)\. At a mismatch at positionjj, FLy implements this with an entropy gate followed by a lookahead window ofWWtokens; if no further mismatches occur within that window, the original token is interpreted as semantically equivalent and retained\. Otherwise, a subsequent mismatch signals a self\-correction, triggering a rollback\.

However, this lookahead window does not transfer cleanly to all speculative drafters \(§[4\.4](https://arxiv.org/html/2609.02897#S4.SS4)\)\. In particular, when the mean acceptance rate is low, subsequent mismatches are not necessarily evidence of the target course\-correcting an earlier error but rather a consequence of loose draft\-target coupling\. Additionally, the window is also structurally incompatible with drafters such as EAGLE\-3, whose mean acceptance length falls short of the long draft chains \(K=15K\{=\}15–2525\) that the FLy windowWWrule expects\.

Our proposed AdaptiveSpec sidesteps both problems by reading the target’s probability distribution at the mismatch position: a direct, single\-position measurement, independent of accepted token length and of any high\-level self\-correction idea\. It requires no lookahead and no trained module, only the target and draft probability distributions that the verify pass already maintains\. Unlike Judge Decoding and SemanticSpec, it incurs no training cost; unlike FLy, it makes no structural assumption about draft length or self\-correction pattern\.

## 3Method

#### Problem Formulation\.

A large language model generates one token per forward pass: tokenxtx\_\{t\}is sampled from the conditional distributionpθ​\(xt∣x<t\)p\_\{\\theta\}\(x\_\{t\}\\mid x\_\{<t\}\)over the vocabulary, given preceding tokensx<t=\(x1,…,xt−1\)x\_\{<t\}=\(x\_\{1\},\\dots,x\_\{t\-1\}\)\. Generation is therefore sequential; each step must wait for the one before it to finish, therefore decoding latency scales linearly with output length\(Pope et al\.,[2022](https://arxiv.org/html/2609.02897#bib.bib35)\)\. This sequential dependency is the bottleneck that speculative decoding aims to solve\.

### 3\.1Overview

AdaptiveSpec is a single system with two adaptive axes, one for each phase of EAGLE\-3’s decoding step \(draft and verify\), driven only by internal model signals already produced during the decode step and requiring no auxiliary training\. The first axis reshapes the draft tree at every step, driven by a draft\-confidence signal; the second relaxes the verification rule using the target’s probability\-distribution margin\.

- •Draft phase\(§[3\.3](https://arxiv.org/html/2609.02897#S3.SS3)\): a Draft Confidence Score \(DCS\) selects the tree shape\(nsteps,top\-​k,ndt\)\(n\_\{\\text\{steps\}\},\\text\{top\-\}k,\\mathrm\{ndt\}\)per step, contracting compute on uncertain drafts and expanding it on confident ones\.
- •Verify phase\(§[3\.2](https://arxiv.org/html/2609.02897#S3.SS2)\): a margin\-based rule promotes drafted tokens at the first mismatch position when the target’s distribution indicates the disagreement is semantically close, recovering acceptances that the strict exact\-match rule would discard\.

![Refer to caption](https://arxiv.org/html/2609.02897v1/overview.png)Figure 1:Overview of AdaptiveSpec\. Each decoding step adapts along two axes driven by signals the model already produces\.\(Bottom Left\)During drafting, the Draft Confidence Score \(DCS\), the product of the draft’s top\-1 probability and a running acceptance rate \(RAR\), selects a\(nsteps,top\-​k,ndt\)\(n\_\{\\text\{steps\}\},\\text\{top\-\}k,\\mathrm\{ndt\}\)triplet: confident steps get a deep narrow chain, uncertain steps a wide shallow tree\.\(Bottom Right\)During verification, at the first mismatch position the target margin rule promotes the drafted token when it exceedsκ\\kappa, accepting semantically equivalent disagreements that lossless decoding would discard\.
### 3\.2Margin\-based Lossy Verification

Lossless speculative decoding in its original form accepts a drafted token only on exact match with the target, discarding even continuations that are semantically equivalent and unnecessarily lowering acceptance rates\. To address this, we propose a margin\-based rule that enables lossy, yet controlled, verification\. We define the margin rule at the first mismatch positionjjas the ratio of the probability the target model assigned the draft\-proposed token to its own top\-1 probability choice\. Formally:

margin​\(j\)=ptarget​\(draftj\)ptarget​\(top1j\)∈\[0,1\],\\mathrm\{margin\}\(j\)\\;=\\;\\frac\{p\_\{\\text\{target\}\}\(\\text\{draft\}\_\{j\}\)\}\{p\_\{\\text\{target\}\}\(\\text\{top1\}\_\{j\}\)\}\\;\\in\\;\[0,1\],\(1\)We define the acceptance rule that promotes the drafted token whenmargin​\(j\)≥κ\\mathrm\{margin\}\(j\)\\geq\\kappa, and rejects otherwise\. A margin near11means the target nearly chose the drafted token \(a semantically equivalent disagreement, safe to promote\), while a margin near0means the target was confident that the draft was wrong\. The proposed rule is parametrised with thresholdκ\\kappato provide tunable control over the relaxation\-strictness during verification\.

Our method effectively overcomes the main limitation of FLy’s lookahead\-window verifier \(§[4\.4](https://arxiv.org/html/2609.02897#S4.SS4)\); it reads the target’s distribution at the mismatched token position, a direct single\-position measurement, independent of chain depth and of any high\-level self\-correction pattern\. It requires no lookahead and no trained module, only target probabilities that the verify phase already computes\.

### 3\.3Dynamic Draft Tree\-Shaping

Holding the draft tree shape fixed across decoding is wasteful, since speculative steps are not uniformly hard: confident steps admit a deep chain, while uncertain ones benefit from a wider tree that covers plausible alternatives\. EAGLE\-3 controls the tree with three hyperparameters, namely, branching factortop\-​k\\text\{top\-\}k, depthnstepsn\_\{\\text\{steps\}\}, and verify\-time token budgetndt\\mathrm\{ndt\}, all fixed upon deployment\.

AdaptiveSpec selects the values of the triplet via a Draft Confidence Score \(DCS\), which is computed once per decoding step:

DCSt=pdraft​\(top1t\)⋅RARt,\\mathrm\{DCS\}\_\{t\}\\;=\\;p\_\{\\text\{draft\}\}\(\\text\{top1\}\_\{t\}\)\\cdot\\mathrm\{RAR\}\_\{t\},\(2\)
wherepdraft​\(top1t\)p\_\{\\text\{draft\}\}\(\\text\{top1\}\_\{t\}\)is the draft model’s top\-1 softmax probability at decode steptt, andRARt\\mathrm\{RAR\}\_\{t\}is the rolling acceptance rate \(EMA,α=0\.3\\alpha=0\.3\) of the fraction of drafted tokens the target accepted, serving as a measure of acceptance history\. Before mapping, the score is rescaled by a divisordd, so thatDCS\\mathrm\{DCS\}saturates to11once the draft confidencepdraft​\(top1\)⋅RARp\_\{\\text\{draft\}\}\(\\text\{top1\}\)\\cdot\\mathrm\{RAR\}reachesdd\. A smallerddsaturates the score sooner and biases the policy toward the deep\-narrow configuration\. We show a search overddhyperparameter value per model and benchmark in Table[3](https://arxiv.org/html/2609.02897#S4.T3)\.

Depth interpolates linearly with DCS and branching with1−D​C​S1\{\-\}DCS\{\}over a range\(nsteps,top\-​k,ndt\)=\(3,4,4\)↔\(7,1,8\)\(n\_\{\\text\{steps\}\},\\text\{top\-\}k,\\mathrm\{ndt\}\)=\(3,4,4\)\\leftrightarrow\(7,1,8\): a confident draft is given a deep narrow chain, an uncertain draft a wide shallow tree, following the convention adopted by prior work\(Liu et al\.,[2026](https://arxiv.org/html/2609.02897#bib.bib28)\)\. Crucially, the range spans different total node counts, so the policy genuinely shrinks draft compute on weak\-draft steps rather than only redistributing a fixed budget\. A circuit breaker reverts to the starting configuration for any request with five consecutive zero\-accept steps\.

Production\-grade inference engines such as SGLang rely on CUDA graphs, which requires static tensor shapes and therefore the values oftop\-​k\\text\{top\-\}k,nstepsn\_\{\\text\{steps\}\}, andndt\\mathrm\{ndt\}\. To preserve this acceleration under a per\-step policy, we pre\-capture at startup one CUDA graph for every\(nsteps,top\-​k,ndt\)\(n\_\{\\text\{steps\}\},\\text\{top\-\}k,\\mathrm\{ndt\}\)triplet the policy could select and swap between them during decoding\.

### 3\.4AdaptiveSpec

AdaptiveSpec combines the two axes within a single decoding step\. During drafting, DCS selects the tree shape\(nsteps,top\-​k,ndt\)\(n\_\{\\text\{steps\}\},\\text\{top\-\}k,\\mathrm\{ndt\}\), adjusting how the candidate tree is built\. During verification, the margin\-based rule decides promotion at proposed mismatches\. Each axis acts on a different sub\-step of the speculative decoding step; tree\-shaping during drafting, the margin rule during verification, and their gains compound into increased throughput\. Both are driven by signals the decode loop already produces with no extra computation\.

## 4Experiments

### 4\.1Experimental Setup

#### Models\.

We evaluate across three target models;Llama\-3\.1\-8B\-InstructDubey et al\. \([2024](https://arxiv.org/html/2609.02897#bib.bib14)\),DeepSeek\-R1\-Distill\-Llama\-8B\(DeepSeek\-AI,[2025](https://arxiv.org/html/2609.02897#bib.bib11)\), andQwen3\-8B\(Yang et al\.,[2025](https://arxiv.org/html/2609.02897#bib.bib43)\), each paired with its publicly released EAGLE\-3 draft model\. The pairings are shown in Appendix[A](https://arxiv.org/html/2609.02897#A1)\.

#### Evaluation\.

Benchmarks span mathematical reasoning GSM8K\(Cobbe et al\.,[2021](https://arxiv.org/html/2609.02897#bib.bib10)\)and MATH\-500\(Lightman et al\.,[2024](https://arxiv.org/html/2609.02897#bib.bib26)\), and code generation HumanEval\(Chen et al\.,[2021](https://arxiv.org/html/2609.02897#bib.bib8)\)tasks\.

#### Metrics\.

We report output throughput speedup relative to vanilla autoregressive decoding, and mean accepted tokensτ\\tau, adding task accuracy recovery for lossy methods, defined as a ratio of task accuracy retained relative to the lossless EAGLE\-3\. All runs use greedy decoding \(temperature=0=0\) at batch size 1 on a single NVIDIA A100, executed on SGLang\(Zheng et al\.,[2024](https://arxiv.org/html/2609.02897#bib.bib45)\)and benchmarked with the SpecForge\(LMSYS Org,[2025](https://arxiv.org/html/2609.02897#bib.bib29)\)framework\.

#### Baselines\.

We compare AdaptiveSpec against three SOTA methods spanning the lossless and lossy regimes: EAGLE\-3\(Li et al\.,[2025](https://arxiv.org/html/2609.02897#bib.bib25)\)for static lossless speculative decoding; an adapted TALON\(Liu et al\.,[2026](https://arxiv.org/html/2609.02897#bib.bib28)\)implementation for dynamic draft\-tree lossless decoding; and an adapted FLy\(Li et al\.,[2026](https://arxiv.org/html/2609.02897#bib.bib23)\)implementation for lossy decoding with a static draft tree\. Adapted implementations of TALON and FLy were necessary because the aforementioned works are not currently supported in the SGLang inference engine, and because of drafter limitations, as explained in Section[4\.4](https://arxiv.org/html/2609.02897#S4.SS4)\. The hyperparameters for EAGLE\-3 were selected as \(3,1,4\), matching the configuration reported in the EAGLE\-3 SGLang experiments, while dynamic draft tree shapes span the range from\(3,4,4\)↔\(7,4,8\)\(3,4,4\)\{\\leftrightarrow\}\(7,4,8\), following the configurations present in SpecForge’s benchmark table\(LMSYS Org,[2025](https://arxiv.org/html/2609.02897#bib.bib29)\)\.

As the reference point for all speedup measurements, we report throughput speedup against standard autoregressive decoding, in which the target model produces a single token per forward pass\.

#### Implementation Details\.

We re\-implement both FLy and TALON on SGLang using the EAGLE\-3 drafters so that all baselines share the same highly optimised inference engine and drafter family\.

FLy reimplementation on SGLangFLy’s promotion windoww=6w=6was designed for7070B\-405405B target models paired with deep draft chains \(nsteps=15n\_\{\\text\{steps\}\}=15\-2525\) \(window ratio 24\-40%\)\. We adopt this by decreasing the window size tow=3w=3given the generally shorter mean accepted tokens length as described in Analysis[4\.4](https://arxiv.org/html/2609.02897#S4.SS4), maintaining a window\-to\-draft\-depth ratio of40%~40\\%\. Matching this setup by lengthening the draft chain would not be possible, as FLy’s authors themselves highlight, pushing the draft length to1515\-2525tokens on lightweight drafters degrades draft quality and causes the target to reject drafted tokens substantially more often\.

TALON reimplementation on SGLangTALON’s original formulation gates per draft\-tree layer, growing the tree node\-by\-node under a global token budgetndt\\mathrm\{ndt\}\. We preserve TALON’s defining property, budget\-constrained adaptive shape selection driven by a confidence\-margin thresholdμ\\mu, but apply it at our per\-decode\-step granularity\. At each step we apply TALON’s rule to identify the retained set𝒫\\mathcal\{P\}, the candidates within the hyperparameterμ\\muvalue\. When\|𝒫\|\|\\mathcal\{P\}\|is large, the policy selects shallow and wide, when small, it selects deep and narrow across the\(nsteps,top\-​k\)\(n\_\{\\text\{steps\}\},\\text\{top\-\}k\)configuration\. We use the paper’s defaultμ=0\.03\\mu=0\.03\.

The detailed experiment configuration for each run can be found in Appendix[B](https://arxiv.org/html/2609.02897#A2)\.

### 4\.2Main Results

GSM8KMATH\-500HumanEvalModelMethodSpeedupMATτ\\tauRec\.%SpeedupMATτ\\tauRec\.%SpeedupMATτ\\tauRec\.%Llama\-3\.1\-8BEAGLE\-31\.932\.83\-1\.382\.08\-1\.812\.55\-TALON\*2\.113\.73\-1\.903\.19\-2\.303\.77\-AdaptiveSpec \(Dynamic\-only\)2\.223\.80\-2\.053\.28\-2\.433\.99\-FLy\*2\.174\.06951\.833\.26882\.604\.6392AdaptiveSpec \(Lossy\-only\)2\.284\.35931\.633\.28922\.754\.8994AdaptiveSpec \(Combined\)2\.434\.32942\.133\.47962\.824\.80103Qwen3\-8BEAGLE\-31\.682\.39\-1\.562\.21\-1\.502\.10\-TALON\*1\.772\.89\-1\.492\.41\-1\.532\.46\-AdaptiveSpec \(Dynamic\-only\)1\.913\.03\-1\.642\.54\-1\.722\.65\-FLy\*1\.602\.83991\.262\.23821\.342\.3793AdaptiveSpec \(Lossy\-only\)1\.662\.95981\.342\.38821\.402\.5096AdaptiveSpec \(Combined\)2\.003\.23991\.832\.97991\.772\.82109DeepSeek\-R1\-8BEAGLE\-32\.283\.27\-2\.153\.02\-2\.052\.86\-TALON\*2\.884\.98\-2\.524\.23\-2\.263\.77\-AdaptiveSpec \(Dynamic\-only\)2\.904\.98\-2\.644\.32\-2\.413\.90\-FLy\*3\.075\.59992\.574\.56922\.324\.1282AdaptiveSpec \(Lossy\-only\)3\.205\.78962\.935\.24972\.584\.5582AdaptiveSpec \(Combined\)3\.205\.66973\.095\.24912\.644\.3992

Table 1:Main results across the three target models and benchmarks evaluating AdaptiveSpec\. AdaptiveSpec \(Combined\) attains the best speedup in every \(model, benchmark\) cell, improving over the EAGLE\-3 baseline by1717\-56%56\\%\. speedup is reported relative to vanilla autoregressive decoding; MATτ\\tauis the mean accepted token length; Rec\. % is the task accuracy retained relative to lossless EAGLE\-3\(3,1,4\)\(3,1,4\)\. Best per\-cell speedup andτ\\tauin the AdaptiveSpec model block is in bold\.∗TALON and FLy are evaluated using our SGLang re\-implementations on the EAGLE\-3 drafter\.Table[1](https://arxiv.org/html/2609.02897#S4.T1)reports throughput speedup, mean accepted tokens lengthτ\\tau, and task\-accuracy recovery for lossy methods, on the three target models across GSM8K, MATH\-500, and HumanEval\.

#### Dynamic draft tree adaptation improves throughput at full accuracy retention\.

AdaptiveSpec \(Dynamic\-only\) reshapes the draft tree per step from internal signals and improves over static EAGLE\-3 on every \(model, benchmark\) cell at a lossless setting\. The largest single\-cell gain is on Llama\-3\.1\-8B MATH\-500, where Dynamic\-only reaches2\.05×2\.05\\timesagainst the static1\.38×1\.38\\times\(\+49%\+49\\%\)\. On average across the three benchmarks, Dynamic\-only improves over EAGLE\-3 by\+30%\+30\\%on Llama\-3\.1\-8B \(2\.23×2\.23\\timesvs\.1\.71×1\.71\\times\),\+11%\+11\\%on Qwen3\-8B \(1\.76×1\.76\\timesvs\.1\.58×1\.58\\times\), and\+23%\+23\\%on DeepSeek\-R1\-8B \(2\.65×2\.65\\timesvs\.2\.16×2\.16\\times\)\.

#### Margin\-rule lossy verification outperforms FLy while maintaining accuracy recovery\.

AdaptiveSpec \(Lossy\-only\) exceeds FLy on throughput in all cells except Llama\-3\.1\-8B MATH\-500 and maintains task accuracy recovery\. The clearest single\-cell advantage is on DeepSeek\-R1\-8B MATH\-500, where Lossy\-only attains2\.93×2\.93\\timesvs\. FLy’s2\.57×2\.57\\times\(\+14%\+14\\%\) at higher recovery \(97%97\\%vs\.92%92\\%\)\. On average, Lossy\-only matches or exceeds FLy on every target:2\.22×2\.22\\timesvs\.2\.20×2\.20\\timeson Llama\-3\.1\-8B \(\+1%\+1\\%\),1\.47×1\.47\\timesvs\.1\.40×1\.40\\timeson Qwen3\-8B \(\+5%\+5\\%\), and2\.90×2\.90\\timesvs\.2\.65×2\.65\\timeson DeepSeek\-R1\-8B \(\+9%\+9\\%\)\.

#### Combined leverages both axes and outperforms all baselines\.

AdaptiveSpec \(Combined\) achieves the best speedup on every \(model, benchmark\) cell, improving over the static EAGLE\-3 baseline by1717\-56%56\\%across the cells\. The largest single\-cell improvement is on Llama\-3\.1\-8B HumanEval, where Combined reaches2\.82×2\.82\\timesagainst EAGLE\-3’s1\.81×1\.81\\times\(\+56%\+56\\%\) at103%103\\%accuracy retention\. On average, Combined exceeds EAGLE\-3 by\+44%\+44\\%on Llama\-3\.1\-8B \(2\.46×2\.46\\timesvs\.1\.71×1\.71\\times\),\+18%\+18\\%on Qwen3\-8B \(1\.87×1\.87\\timesvs\.1\.58×1\.58\\times\), and\+38%\+38\\%on DeepSeek\-R1\-8B \(2\.98×2\.98\\timesvs\.2\.16×2\.16\\times\), the highest average speedup\. Combined also recovers accuracy lost by Lossy\-only on the cells where static lossy underperformed \(Llama\-3\.1\-8B MATH\-500,92%→96%92\\%\\\!\\to\\\!96\\%; Qwen3\-8B MATH\-500,82%→99%82\\%\\\!\\to\\\!99\\%\), which can be explained by the fact that dynamic shaping, paired with a more lenient verifier, proposes several plausible paths per step and allows acceptance of continuations that a fixed tree under strict verification would have rejected\.

### 4\.3Analysis and Ablation Study

We show the contribution of each adaptation axis with a2×22\{\\times\}2ablation crossing tree shaping \(static, dynamic\) with verification \(strict, lossy\), averaged across GSM8K, MATH\-500, and HumanEval in Table[2](https://arxiv.org/html/2609.02897#S4.T2)\.

Each axis improves over the EAGLE\-3 baseline \(Static×\\timesStrict\) on its own\. Dynamic tree shaping lifts the average speedup by\+21\.4%\+21\.4\\%\(1\.82×→2\.21×1\.82\\times\\to 2\.21\\times\) at no accuracy cost, driven by a40%40\\%rise in mean accepted token length \(τ:2\.59→3\.61\\tau\{:\}\\,2\.59\\to 3\.61\)\. Static lossy verification reaches a\+20\.9%\+20\.9\\%speedup \(1\.82×→2\.20×1\.82\\times\\to 2\.20\\times\) at an average8%8\\%accuracy cost\.

Combined AdaptiveSpec \(Dynamic×\\timesLossy\) reaches2\.44×2\.44\\timesthroughput on average, the best of all four configurations\. Llama\-3\.1\-8B illustrates both effects most clearly: each axis contributes substantially in isolation \(1\.71×→2\.23×1\.71\\times\\to 2\.23\\timesfrom dynamic draft tree shaping,1\.71×→2\.22×1\.71\\times\\to 2\.22\\timesfrom lossy verification\), and combining them yields2\.46×2\.46\\times\(\+44%\+44\\%\) at98%98\\%recovery\. The Dynamic×\\timesLossy combination shows robustness, as this configuration delivers the best speedup across every target model\.

Static treeDynamic treeModelVerif\.Spd\.τ\\tauRec\.%Spd\.τ\\tauRec\.%Llama\-3\.1\-8BStrict1\.712\.491002\.233\.69100Lossy2\.224\.17932\.464\.2098Qwen3\-8BStrict1\.582\.231001\.762\.74100Lossy1\.472\.61921\.873\.01102DeepS\-R1\-8BStrict2\.163\.051002\.654\.40100Lossy2\.905\.19922\.985\.1093AverageStrict1\.822\.591002\.213\.61100Lossy2\.203\.99922\.444\.1098Table 2:Ablation across draft\-tree construction \(static, dynamic\) and verification rule \(strict, lossy\), per target model and averaged across GSM8K, MATH\-500, and HumanEval\. Each axis improves over the EAGLE\-3 baseline \(Static×\\timesStrict\) in isolation\. Speedup is over vanilla AR;τ\\tauis the mean accepted token length; Rec\. % is accuracy retained vs\. EAGLE\-3\(3,1,4\)\(3,1,4\)\. Best speedup per row is in bold\.#### Hyperparameter search\.

We evaluate each component of AdaptiveSpec by searching its hyperparameters in isolation: \(1\) the divisorddin DCS, which sets how quickly the signal saturates the tree\-shape range \(Table[3](https://arxiv.org/html/2609.02897#S4.T3)\); \(2\) the margin thresholdκ\\kappain the lossy verifier \(Table[4](https://arxiv.org/html/2609.02897#S4.T4)\)\. We search overddon dynamic\-only \(lossless verification\) andκ\\kappaon lossy\-only \(static chain\(7,1,8\)\(7,1,8\)\)\. We then run a finalκ\\kappasearch on the joint dynamic and lossy configuration that represents the AdaptiveSpec Combined\.

#### Draft tree shape \(dd\)

The divisorddcontrols how rapidly DCS saturates the tree\-shape range\. A smallddpushes the policy toward the deep\-narrow extreme, producing chains that maximise accept length when the draft is strong\. A largeddkeeps the policy in the shallow\-wide regime when the draft is uncertain\. Across the swept range,d=0\.5d\{=\}0\.5wins on nearly every \(model, benchmark\) cell\. We therefore fixd=0\.5d\{=\}0\.5for the Combined hyperparameter search\.

GSM8KM\-500HEModelddSτ\\tauSτ\\tauSτ\\tauLlama\-3\.1\-8B0\.22\.023\.681\.933\.212\.343\.860\.32\.153\.741\.993\.232\.363\.910\.42\.183\.772\.033\.282\.413\.960\.52\.223\.802\.053\.282\.433\.99Qwen3\-8B0\.21\.762\.901\.522\.441\.562\.500\.31\.842\.971\.592\.501\.652\.610\.41\.893\.021\.612\.521\.692\.640\.51\.913\.031\.642\.541\.722\.65DeepSeek\-R1\-8B0\.22\.844\.952\.564\.302\.273\.810\.32\.854\.972\.634\.382\.333\.850\.42\.894\.992\.634\.352\.363\.880\.52\.904\.982\.644\.322\.413\.90Table 3:Divisor hyperparameter search for AdaptiveSpec’s \(Dynamic\-only\) draft tree construction overd∈\{0\.2,0\.3,0\.4,0\.5\}d\\in\\\{0\.2,0\.3,0\.4,0\.5\\\}\. S is the speedup over vanilla autoregressive decoding andτ\\tauthe mean accepted token length\. M\-500 denotes MATH\-500, HE denotes HumanEval\. Smallerddsaturates the policy toward the deep\-narrow end of the\(3,4,4\)↔\(7,1,8\)\(3,4,4\)\{\\leftrightarrow\}\(7,1,8\)range; largerddkeeps it shallow\-wide\. Asd=0\.5d\{=\}0\.5wins on most cells, we fixd=0\.5d\{=\}0\.5for all AdaptiveSpec \(Combined\) runs in Table[1](https://arxiv.org/html/2609.02897#S4.T1)\.GSM8KM\-500HEModelκ\\kappaSτ\\tauRSτ\\tauRSτ\\tauR\(a\) Lossy\-only: search overκ\\kappa, chain\(7,1,8\)\(7,1,8\)Llama\-3\.1\-8B0\.102\.484\.66881\.913\.31802\.704\.86890\.202\.284\.35931\.853\.33862\.754\.89940\.302\.224\.17951\.633\.28922\.684\.7998Qwen3\-8B0\.101\.662\.95981\.132\.51761\.562\.82840\.201\.612\.85981\.342\.38821\.492\.64930\.301\.572\.78991\.322\.33791\.402\.5096DeepSeek\-R1\-8B0\.103\.346\.08932\.935\.24972\.774\.53890\.203\.205\.78961\.803\.281112\.584\.55820\.303\.145\.60991\.663\.201092\.484\.4282\(b\) Combined:d=0\.5d\{=\}0\.5, search overκ\\kappaLlama\-3\.1\-8B0\.052\.644\.72892\.263\.72712\.774\.70940\.102\.554\.55912\.193\.59842\.574\.35910\.202\.434\.32942\.153\.49902\.824\.801030\.302\.404\.22942\.133\.47962\.784\.74102Qwen3\-8B0\.052\.033\.291001\.802\.86791\.933\.08890\.102\.003\.23991\.782\.82791\.893\.02980\.201\.953\.17991\.832\.97991\.822\.901040\.301\.943\.12981\.682\.66831\.772\.82109DeepSeek\-R1\-8B0\.053\.436\.14893\.095\.24912\.934\.93820\.103\.355\.93922\.183\.561112\.834\.72830\.203\.205\.66972\.203\.571082\.744\.60880\.303\.145\.51972\.113\.531052\.644\.3992Table 4:Margin rule threshold hyperparameter search for AdaptiveSpec overκ∈\{0\.05,0\.10,0\.20,0\.30\}\\kappa\\in\\\{0\.05,0\.10,0\.20,0\.30\\\}\. S is the speedup over vanilla autoregressive decoding andτ\\tauthe mean accepted token length\. M\-500 denotes MATH\-500, HE denotes HumanEval\. \(a\) Lossy\-only with the fixed chain\(7,1,8\)\(7,1,8\); \(b\) Combined withd=0\.5d\{=\}0\.5and the dynamic range\(3,4,4\)↔\(7,1,8\)\(3,4,4\)\{\\leftrightarrow\}\(7,1,8\)\.
#### Lossy threshold \(κ\\kappa\)

The thresholdκ\\kappacontrols how strictly the lossy verifier promotes a draft token: a token is promoted when its margin against the target meets or exceedsκ\\kappa\. A lowerκ\\kappaadmits more mismatches and increases accept length\. Table[4](https://arxiv.org/html/2609.02897#S4.T4)searchesκ∈\{0\.05,0\.10,0\.20,0\.30\}\\kappa\\in\\\{0\.05,0\.10,0\.20,0\.30\\\}on the static lossy chain\(7,1,8\)\(7,1,8\)\. The search shows a direct throughput\-recovery trade\-off: lowerκ\\kappaincreases throughput and decreases recovery, while higherκ\\kapparecovers accuracy at a throughput cost\. We pickκ\\kappaper \(model, benchmark\) cell to balance the two, since different models find different tasks hard and the optimalκ\\kappashifts accordingly\.

#### Jointκ\\kappasearch

Fixingd=0\.5d\{=\}0\.5, we searchκ\\kappaon the Combined configuration in Table[4](https://arxiv.org/html/2609.02897#S4.T4)\. The throughput\-recovery trade\-off seen in the static search persists, and the per\-cellκ\\kappapicks transfer between Lossy\-only to Combined experiments, except MATH\-500 and HumanEval on DeepSeek\-R1\-8B\. Full per\-cell picks for both configurations are shown in Table[8](https://arxiv.org/html/2609.02897#A2.T8)\(Appendix[B](https://arxiv.org/html/2609.02897#A2)\)\.

### 4\.4Limitation Analysis of FLy’s Verifier

FLy’s window rule assumes that the lookahead windowwwfits comfortably inside the typical accepted prefix, a premise that holds for the long draft chains \(n​s​t​e​p​s=15nsteps\{=\}15\-2525\) FLy was designed for, but breaks on other drafters, such as EAGLE\-3\. EAGLE\-3’s mean accepted token length sits between2\.082\.08and3\.273\.27across our three targets in Table[5](https://arxiv.org/html/2609.02897#S4.T5), strictly shorter than FLy’sw=6w\{=\}6in every cell, which makes it impossible for the window to fit meaningfully inside the proposed draft tokens\.

Target ModelGSM8Kτ\\tauMATH\-500τ\\tauHumanEvalτ\\tauLlama\-3\.1\-8B2\.832\.082\.55Qwen3\-8B2\.392\.212\.10DeepSeek\-R1\-8B3\.273\.022\.86Table 5:Mean accepted token lengthτ\\taufor static EAGLE\-3\(3,1,4\)\(3,1,4\)across the three target models and three benchmarks\.τ\\tauranges from2\.082\.08to3\.273\.27, showing the limitation of FLy’s lookahead window that requires lengthw=6w\{=\}6\.This structural mismatch underlines the importance of AdaptiveSpec’s window\-free design: by reading the target’s distribution at the mismatch position rather than looking ahead, the verifier becomes independent of draft depth and applicable regardless ofτ\\tau\.

## 5Conclusion

We presented AdaptiveSpec, a training\-free per\-step adaptive speculative decoder\. Its primary contribution is a novel lossy verification rule that converts near\-miss draft tokens into accepted tokens using only the target distribution at the verification step, without requiring an external verifier for equivalence checking\. Another contribution is a per\-step dynamic tree\-shape policy that adjusts all three EAGLE\-3 hyperparameters independently, removing the fixed total\-budget assumption common to prior adaptive\-tree work\. The two components are empirically orthogonal axes of throughput and their gains compound: AdaptiveSpec improves end\-to\-end throughput by 18\-44% on average per target model \(peak \+56%\) at 93% to fully lossless downstream task accuracy retention on three target models, all inside SGLang\.

## 6Future Work

There are a number of areas limited by sequential decoding, where AdaptiveSpec could be adapted as a potential solution to increase inference efficiency\.

#### Speculative Decoding Beyond Language Domain

The bottleneck AdaptiveSpec addresses is not specific to language generation\. Any autoregressive architecture is constrained by the same sequential dependency, and the draft\-then\-verify pattern could be adapted to units beyond language tokens\. This matters as generative models move into the physical domain: a growing body of work applies Transformer\-based architectures to embodied settings, such as vision\-language\-action models for roboticsBrohan et al\. \([2023](https://arxiv.org/html/2609.02897#bib.bib4)\); Kim et al\. \([2024](https://arxiv.org/html/2609.02897#bib.bib21)\)\. There, latency is not a matter of user experience but a requirement for effective coordination; an agent acting in the world cannot wait seconds between perceiving and moving\. Although AdaptiveSpec is specific to language, we believe its central idea, adapting speculative decoding to the per\-step difficulty of the task, is a valuable foundation for extending the draft\-then\-verify paradigm to these physical domains\.

#### Retrieval\-Based Drafting for Agentic Workloads

In agentic settings, sequential decoding is an even greater bottleneck: agents emit long traces that are repetitive across similar requests\. This repetition allows sequences generated once to be reused in future steps\. A line of work exploits this by replacing the draft model with retrieval, drawing candidate tokens from prior outputs, or a datastore rather than an autoregressive generationSaxena \([2023](https://arxiv.org/html/2609.02897#bib.bib37)\); He et al\. \([2024](https://arxiv.org/html/2609.02897#bib.bib17)\); Luo et al\. \([2025](https://arxiv.org/html/2609.02897#bib.bib30)\)\. SuffixDecodingOliaro et al\. \([2025](https://arxiv.org/html/2609.02897#bib.bib33)\)applies this to agentic workloads specifically, caching past sequences in a suffix tree\. These methods change the source of the draft tokens, whereas our AdaptiveSpec adapts the draft tree shape and the verification rule\. A direction for future work is replacing autoregressive drafters with retrieval\-based drafters, and maintaining the AdaptiveSpec’s per\-step signals adaptive mechanism to improve inference efficiency in repetitive agentic settings\.

## 7Limitations

The per\-step margin rule does not preserve the target distribution in the formal sense ofLeviathan et al\. \([2023](https://arxiv.org/html/2609.02897#bib.bib22)\); accuracy retention is reported empirically and may vary on tasks outside our evaluation\.

We evaluate only at batch size 1, where latency is memory\-bandwidth bound and per\-step speculation gains are largest\. At higher batch sizes we expect AdaptiveSpec’s gains to persist but leave multi\-batch evaluation to future work\.

We instantiate and evaluate AdaptiveSpec on EAGLE\-3 and do not report results on diffusion\-based drafters such as DFlash, DDTree\(Chen et al\.,[2026](https://arxiv.org/html/2609.02897#bib.bib7); Ringel and Romano,[2026](https://arxiv.org/html/2609.02897#bib.bib36)\), a recent SOTA diffusion tree drafter that appeared close to our submission\. We believe that AdaptiveSpec’s lossy verification and the tree\-shape principle would transfer to DDTree; empirical confirmation is left to future work\.

## References

- Agarwal et al\. \(2025\)Sandhini Agarwal, Lama Ahmad, Jason Ai, Sam Altman, Andy Applebaum, Edwin Arbus, Rahul K\. Arora, Yu Bai, Bowen Baker, Haiming Bao, Boaz Barak, Ally Bennett, Tyler Bertao, Nivedita Brett, Eugene Brevdo, Greg Brockman, Sebastien Bubeck, Che Chang, Kai Chen, and 106 others\. 2025\.[gpt\-oss\-120b & gpt\-oss\-20b model card](https://arxiv.org/abs/2508.10925)\.*Preprint*, arXiv:2508\.10925\.
- Ankner et al\. \(2024\)Zachary Ankner, Rishab Parthasarathy, Aniruddha Nrusimha, Christopher Rinard, Jonathan Ragan\-Kelley, and William Brandon\. 2024\.Hydra: Sequentially\-dependent draft heads for medusa decoding\.*arXiv preprint arXiv:2402\.05109*\.
- Bachmann et al\. \(2025\)Gregor Bachmann, Sotiris Anagnostidis, Albert Pumarola, Markos Georgopoulos, Artsiom Sanakoyeu, Yuming Du, Edgar Schönfeld, Ali Thabet, and Jonas Kohler\. 2025\.Judge decoding: Faster speculative sampling requires going beyond model alignment\.*arXiv preprint arXiv:2501\.19309*\.
- Brohan et al\. \(2023\)Anthony Brohan, Noah Brown, Justice Carbajal, Yevgen Chebotar, Xi Chen, Krzysztof Choromanski, Tianli Ding, Danny Driess, Avinava Dubey, Chelsea Finn, Pete Florence, Chuyuan Fu, Montse Gonzalez Arenas, Keerthana Gopalakrishnan, Kehang Han, Karol Hausman, Alexander Herzog, Jasmine Hsu, Brian Ichter, and 35 others\. 2023\.[Rt\-2: Vision\-language\-action models transfer web knowledge to robotic control](https://arxiv.org/abs/2307.15818)\.*Preprint*, arXiv:2307\.15818\.
- Cai et al\. \(2024\)Tianle Cai, Yuhong Li, Zhengyang Geng, Hongwu Peng, Jason D Lee, Deming Chen, and Tri Dao\. 2024\.[Medusa: Simple llm inference acceleration framework with multiple decoding heads](https://arxiv.org/abs/2401.10774)\.In*International Conference on Machine Learning \(ICML\)*\.
- Chen et al\. \(2023\)Charlie Chen, Sebastian Borgeaud, Geoffrey Irving, Jean\-Baptiste Lespiau, Laurent Sifre, and John Jumper\. 2023\.[Accelerating large language model decoding with speculative sampling](https://arxiv.org/abs/2302.01318)\.*arXiv preprint arXiv:2302\.01318*\.
- Chen et al\. \(2026\)Jian Chen, Yesheng Liang, and Zhijian Liu\. 2026\.[Dflash: Block diffusion for flash speculative decoding](https://arxiv.org/abs/2602.06036)\.*Preprint*, arXiv:2602\.06036\.
- Chen et al\. \(2021\)Mark Chen, Jerry Tworek, Heewoo Jun, Qiming Yuan, Henrique Ponde de Oliveira Pinto, Jared Kaplan, Harri Edwards, Yuri Burda, Nicholas Joseph, Greg Brockman, and 1 others\. 2021\.Evaluating Large Language Models Trained on Code\.*arXiv preprint arXiv:2107\.03374*\.
- Chen et al\. \(2024\)Zhuoming Chen, Avner May, Ruslan Svirschevski, Yuhsun Huang, Max Ryabinin, Zhihao Jia, and Beidi Chen\. 2024\.Sequoia: Scalable, Robust, and Hardware\-aware Speculative Decoding\.*arXiv preprint arXiv:2402\.12374*\.
- Cobbe et al\. \(2021\)Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Mark Chen, Heewoo Jun, Lukasz Kaiser, Matthias Plappert, Jerry Tworek, Jacob Hilton, Reiichiro Nakano, and 1 others\. 2021\.Training verifiers to solve math word problems\.*arXiv preprint arXiv:2110\.14168*\.
- DeepSeek\-AI \(2025\)DeepSeek\-AI\. 2025\.DeepSeek\-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning\.*arXiv preprint arXiv:2501\.12948*\.
- Dong et al\. \(2026\)Ximing Dong, Shaowei Wang, Dayi Lin, Boyuan Chen, and Ahmed E\. Hassan\. 2026\.Beyond Tokens: Semantic\-Aware Speculative Decoding for Efficient Inference by Probing Internal States\.*arXiv preprint arXiv:2602\.03708*\.
- Du et al\. \(2024\)Cunxiao Du, Jing Jiang, Xu Yuanchen, Jiawei Wu, Sicheng Yu, Yongqi Li, Shenggui Li, Kai Xu, Liqiang Nie, and Zhaopeng Tu\. 2024\.[Glide with a cape: A low\-hassle method to accelerate speculative decoding](https://arxiv.org/abs/2402.02082)\.In*International Conference on Machine Learning \(ICML\)*\.
- Dubey et al\. \(2024\)Abhimanyu Dubey and 1 others\. 2024\.The Llama 3 Herd of Models\.*arXiv preprint arXiv:2407\.21783*\.
- Gao et al\. \(2025\)Xiangxiang Gao, Weisheng Xie, Yiwei Xiang, and Feng Ji\. 2025\.Falcon: Faster and parallel inference of large language models through enhanced semi\-autoregressive drafting and custom\-designed decoding tree\.In*AAAI Conference on Artificial Intelligence \(AAAI\)*\.
- Garipov et al\. \(2025\)Roman Garipov, Fedor Velikonivtsev, Ruslan Svirschevski, Vage Egiazarian, and Max Ryabinin\. 2025\.Autojudge: Judge decoding without manual annotation\.*arXiv preprint arXiv:2504\.20039*\.
- He et al\. \(2024\)Zhenyu He, Zexuan Zhong, Tianle Cai, Jason D\. Lee, and Di He\. 2024\.[Rest: Retrieval\-based speculative decoding](https://arxiv.org/abs/2311.08252)\.*Preprint*, arXiv:2311\.08252\.
- Huang et al\. \(2025\)Kaixuan Huang, Xudong Guo, and Mengdi Wang\. 2025\.Specdec\+\+: Boosting speculative decoding via adaptive candidate lengths\.*arXiv preprint arXiv:2405\.19715*\.
- Huo et al\. \(2025\)Feiye Huo, Mingyuan Tan, Jiawen Zhou, Muzhi Yao, Jiangchuan Pang, and Kai Lu\. 2025\.C2t: A classifier\-based tree construction method in speculative decoding\.*arXiv preprint arXiv:2502\.13652*\.
- Kamath et al\. \(2025\)Aishwarya Kamath, Johan Ferret, Shreya Pathak, Nino Vieillard, Ramona Merhej, Sarah Perrin, Tatiana Matejovicova, Alexandre Ramé, Morgane Rivière, Louis Rouillard, Thomas Mesnard, Geoffrey Cideron, Jean bastien Grill, Sabela Ramos, Edouard Yvinec, Michelle Casbon, Etienne Pot, Ivo Penchev, Gaël Liu, and 196 others\. 2025\.[Gemma 3 technical report](https://arxiv.org/abs/2503.19786)\.*Preprint*, arXiv:2503\.19786\.
- Kim et al\. \(2024\)Moo Jin Kim, Karl Pertsch, Siddharth Karamcheti, Ted Xiao, Ashwin Balakrishna, Suraj Nair, Rafael Rafailov, Ethan Foster, Grace Lam, Pannag Sanketi, Quan Vuong, Thomas Kollar, Benjamin Burchfiel, Russ Tedrake, Dorsa Sadigh, Sergey Levine, Percy Liang, and Chelsea Finn\. 2024\.[Openvla: An open\-source vision\-language\-action model](https://arxiv.org/abs/2406.09246)\.*Preprint*, arXiv:2406\.09246\.
- Leviathan et al\. \(2023\)Yaniv Leviathan, Matan Kalman, and Yossi Matias\. 2023\.[Fast inference from transformers via speculative decoding](https://arxiv.org/abs/2211.17192)\.In*International Conference on Machine Learning \(ICML\)*\.
- Li et al\. \(2026\)Jinze Li, Yixing Xu, Guanchen Li, Shuo Yang, Jinfeng Xu, Xuanwu Yin, Dong Li, Edith C\. H\. Ngai, and Emad Barsoum\. 2026\.[Training\-Free Loosely Speculative Decoding: Accepting Semantically Correct Drafts Beyond Exact Match](https://arxiv.org/abs/2511.22972)\.In*International Conference on Learning Representations \(ICLR\)*\.
- Li et al\. \(2024\)Yuhui Li, Fangyun Wei, Chao Zhang, and Hongyang Zhang\. 2024\.[EAGLE\-2: Faster Inference of Language Models with Dynamic Draft Trees](https://arxiv.org/abs/2406.16858)\.In*Conference on Empirical Methods in Natural Language Processing \(EMNLP\)*\.
- Li et al\. \(2025\)Yuhui Li, Fangyun Wei, Chao Zhang, and Hongyang Zhang\. 2025\.[EAGLE\-3: Scaling up Inference Acceleration of Large Language Models via Training\-Time Test](https://arxiv.org/abs/2503.01840)\.In*Annual Conference on Neural Information Processing Systems \(NeurIPS\)*\.
- Lightman et al\. \(2024\)Hunter Lightman, Vineet Kosaraju, Yura Burda, Harri Edwards, Bowen Baker, Teddy Lee, Jan Leike, John Schulman, Ilya Sutskever, and Karl Cobbe\. 2024\.[Let’s Verify Step by Step](https://arxiv.org/abs/2305.20050)\.In*International Conference on Learning Representations \(ICLR\)*\.
- Liu et al\. \(2025\)Tianyu Liu, Yun Li, Qitan Lv, Kai Liu, Jianchen Zhu, Winston Hu, and Xiao Sun\. 2025\.[Pearl: Parallel speculative decoding with adaptive draft length](https://arxiv.org/abs/2408.11850)\.In*International Conference on Learning Representations \(ICLR\)*\.
- Liu et al\. \(2026\)Tianyu Liu, Qitan Lv, Yuhao Shen, Xiao Sun, and Xiaoyan Sun\. 2026\.[Talon: Confidence\-aware speculative decoding with adaptive token trees](https://doi.org/10.48550/arXiv.2601.07353)\.*arXiv preprint arXiv:2601\.07353*\.
- LMSYS Org \(2025\)LMSYS Org\. 2025\.Specforge: A training framework for speculative decoding draft models\.[https://github\.com/sgl\-project/SpecForge](https://github.com/sgl-project/SpecForge)\.
- Luo et al\. \(2025\)Xianzhen Luo, Yixuan Wang, Qingfu Zhu, Zhiming Zhang, Xuanyu Zhang, Qing Yang, and Dongliang Xu\. 2025\.[Turning trash into treasure: Accelerating inference of large language models with token recycling](https://arxiv.org/abs/2408.08696)\.*Preprint*, arXiv:2408\.08696\.
- Mamou et al\. \(2024\)Jonathan Mamou, Oren Pereg, Daniel Korat, Moshe Berchansky, Nadav Timor, Moshe Wasserblat, and Roy Schwartz\. 2024\.Dynamic speculation lookahead accelerates speculative decoding of large language models\.*arXiv preprint arXiv:2405\.04304*\.
- Miao et al\. \(2024\)Xupeng Miao, Gabriele Oliaro, Zhihao Zhang, Xinhao Cheng, Zeyu Wang, Zhengxin Zhang, Rae Ying Yee Wong, Alan Zhu, Lijie Yang, Xiaoxiang Shi, and 1 others\. 2024\.[Specinfer: Accelerating large language model serving with tree\-based speculative inference and verification](https://arxiv.org/abs/2305.09781)\.In*ASPLOS*\.
- Oliaro et al\. \(2025\)Gabriele Oliaro, Zhihao Jia, Daniel Campos, and Aurick Qiao\. 2025\.[Suffixdecoding: Extreme speculative decoding for emerging ai applications](https://arxiv.org/abs/2411.04975)\.*Preprint*, arXiv:2411\.04975\.
- Pan et al\. \(2023\)Liangming Pan, Michael Saxon, Wenda Xu, Deepak Nathani, Xinyi Wang, and William Yang Wang\. 2023\.Automatically Correcting Large Language Models: Surveying the Landscape of Diverse Self\-Correction Strategies\.*arXiv preprint arXiv:2308\.03188*\.
- Pope et al\. \(2022\)Reiner Pope, Sholto Douglas, Aakanksha Chowdhery, Jacob Devlin, James Bradbury, Anselm Levskaya, Jonathan Heek, Kefan Xiao, Shivani Agrawal, and Jeff Dean\. 2022\.Efficiently scaling transformer inference\.*arXiv preprint arXiv:2211\.05102*\.
- Ringel and Romano \(2026\)Liran Ringel and Yaniv Romano\. 2026\.[Accelerating speculative decoding with block diffusion draft trees](https://arxiv.org/abs/2604.12989)\.*Preprint*, arXiv:2604\.12989\.
- Saxena \(2023\)Apoorv Saxena\. 2023\.[Prompt lookup decoding](https://github.com/apoorvumang/prompt-lookup-decoding/)\.
- Sun et al\. \(2025\)Ziteng Sun, Uri Mendlovic, Yaniv Leviathan, Asaf Aharoni, Ananda Theertha Suresh, and Ahmad Beirami\. 2025\.[Block verification accelerates speculative decoding](https://arxiv.org/abs/2403.10444)\.In*International Conference on Learning Representations \(ICLR\)*\.
- Wang et al\. \(2025a\)Jikai Wang, Yi Su, Juntao Li, Qingrong Xia, Zi Ye, Xinyu Duan, Zhefeng Wang, and Min Zhang\. 2025a\.OPT\-Tree: Speculative Decoding with Adaptive Draft Tree Structure\.*Transactions of the Association for Computational Linguistics \(TACL\)*\.
- Wang et al\. \(2025b\)Yixuan Wang, Yijun Liu, Shiyu Ji, Yuzhuang Xu, Yang Xu, Qingfu Zhu, and Wanxiang Che\. 2025b\.Think before you accept: Semantic reflective verification for faster speculative decoding\.*arXiv preprint arXiv:2505\.18629*\.
- Xiao et al\. \(2024\)Zilin Xiao, Hongming Zhang, Tao Ge, Siru Ouyang, Vicente Ordonez, and Dong Yu\. 2024\.Parallelspec: Parallel drafter for efficient speculative decoding\.*arXiv preprint arXiv:2410\.05589*\.
- Xiong et al\. \(2024\)Yunfan Xiong, Ruoyu Zhang, Yanzeng Li, Tianhao Wu, and Lei Zou\. 2024\.Dyspec: Faster speculative decoding with dynamic token tree structure\.*arXiv preprint arXiv:2410\.11744*\.
- Yang et al\. \(2025\)An Yang, Anfeng Li, Baosong Yang, Beichen Zhang, Binyuan Hui, Bo Zheng, Bowen Yu, Chang Gao, Chengen Huang, Chenxu Lv, Chujie Zheng, Dayiheng Liu, Fan Zhou, Fei Huang, Feng Hu, Hao Ge, Haoran Wei, Huan Lin, Jialong Tang, and 41 others\. 2025\.[Qwen3 Technical Report](https://arxiv.org/abs/2505.09388)\.*Preprint*, arXiv:2505\.09388\.
- Zhang et al\. \(2024\)Situo Zhang, Hanqi Wang, Da Liu, Zheng Wang, Junlong Wang, Su Zhu, Lu Chen, and Kai Yu\. 2024\.Adaeagle: Optimizing speculative decoding via explicit modeling of adaptive draft structures\.*arXiv preprint arXiv:2412\.18910*\.
- Zheng et al\. \(2024\)Lianmin Zheng, Liangsheng Yin, Zhiqiang Xie, Chuyue Sun, Jeff Huang, Cody Hao Yu, Shiyi Cao, Christos Kozyrakis, Ion Stoica, Joseph E\. Gonzalez, Clark Barrett, and Ying Sheng\. 2024\.[SGLang: Efficient Execution of Structured Language Model Programs](https://arxiv.org/abs/2312.07104)\.In*Advances in Neural Information Processing Systems \(NeurIPS\)*\.

## Appendix AEAGLE3 target–draft model pairings

Target/Draft checkpointLlamameta\-llama/Llama\-3\.1\-8B\-Instructlmsys/sglang\-EAGLE3\-LLaMA3\.1\-Instruct\-8BDeepSeekdeepseek\-ai/DeepSeek\-R1\-Distill\-Llama\-8Byuhuili/EAGLE3\-DeepSeek\-R1\-Distill\-LLaMA\-8BQwenQwen/Qwen3\-8BAngelSlim/Qwen3\-8B\_eagle3Table 6:Target–draft model pairings used in our experiments\. The target model is listed on the first line of each pair and the EAGLE\-3 draft checkpoint on the second\.
## Appendix BExperiment configurations

Method/Tree shape\(nsteps,top\-​k,ndt\)\(n\_\{\\text\{steps\}\},\\text\{top\-\}k,\\mathrm\{ndt\}\); hyperparameter detailsEAGLE\-3\(3,1,4\)\(3,1,4\); StrictTALON\*\(nsteps,top\-​k\)\(n\_\{\\text\{steps\}\},\\text\{top\-\}k\)adaptable,ndt=8\\mathrm\{ndt\}\{=\}8fixed; Strict;μ=0\.03\\mu\{=\}0\.03FLy\*\(7,1,8\)\(7,1,8\); Lossy \(window\);nsteps=7n\_\{\\text\{steps\}\}\{=\}7,w=3w\{=\}3,θ=0\.30\\theta\{=\}0\.30AdaptiveSpec \(Dyn\-only\)\(3,4,4\)↔\(7,1,8\)\(3,4,4\)\{\\leftrightarrow\}\(7,1,8\); Strict;d=0\.5d\{=\}0\.5AdaptiveSpec \(Lossy\-only\)\(7,1,8\)\(7,1,8\); Lossy \(margin\);κ\\kappaper cell†AdaptiveSpec \(Combined\)\(3,4,4\)↔\(7,1,8\)\(3,4,4\)\{\\leftrightarrow\}\(7,1,8\); Lossy \(margin\);d=0\.5d\{=\}0\.5,κ\\kappaper cell†Table 7:Method hyperparameter configurations used in Table[1](https://arxiv.org/html/2609.02897#S4.T1)\. “Tree shape” is the triplet\(nsteps,top\-​k,ndt\)\(n\_\{\\text\{steps\}\},\\text\{top\-\}k,\\mathrm\{ndt\}\)or the dynamic rangeA↔BA\{\\leftrightarrow\}B\.ddis the DCS divisor;κ\\kappamargin threshold of the lossy margin rule\. TALON:μ\\muconfidence\-margin threshold\. FLy:wwlookahead window,θ\\thetaentropy threshold\.†Per\-cellκ\\kappahyperparameter search is reported in Table[8](https://arxiv.org/html/2609.02897#A2.T8)\.∗TALON and FLy are re\-implementations on SGLang using the EAGLE\-3 drafter\.ModelGSM8KMATH\-500HumanEvalLlama0\.200\.200\.300\.300\.200\.20DeepSeek0\.200\.200\.050\.05\(0\.10\)\(0\.10\)0\.300\.30\(0\.20\)\(0\.20\)Qwen30\.100\.100\.200\.200\.300\.30Table 8:Per\-\(model, benchmark\) cell margin thresholdκ\\kappafor AdaptiveSpec’s lossy verifier in Table[1](https://arxiv.org/html/2609.02897#S4.T1)\. Values shown are the picks used by AdaptiveSpec \(Combined\)\. The two DeepSeek cells where Lossy\-only deviates from the Combined configuration show the Lossy\-onlyκ\\kappain parentheses\.
## Appendix CSpecForge Benchmarking Implementation Details

All experiments use greedy decoding \(temperatureT=0T=0\) at batch size11on a single NVIDIA A100, executed through SGLang and benchmarked with the SpecForge harness\. Maximum generation length follows the SpecForge benchmarker defaults: 2048 tokens for GSM8K, and 4096 tokens for MATH\-500 and HumanEval\.