Where and When to Commit: Candidate-Aware Decoding for Diffusion Language Models

# Where and When to Commit: Candidate-Aware Decoding for Diffusion Language Models
Source: [https://arxiv.org/html/2607.28166](https://arxiv.org/html/2607.28166)
Chia\-Ming Lee1,2, Ming\-Ching Chang2, Xin Li2, Yu\-Lun Liu1, Chih\-Chung Hsu1 1National Yang Ming Chiao Tung University2University at Albany, SUNY

###### Abstract

Diffusion language models \(DLMs\) expose a provisional prediction at every denoising step, creating an opportunity for generation\-time*early exit*that stops decoding before the schedule is exhausted\. Existing early\-exit gates decide termination from fixed\-region confidence statistics or schedule\-dependent rules, evidence too coarse for a decision that freezes every remaining position at once, so they fire prematurely on long chain\-of\-thought outputs whose answers stabilize only near the end\.*Adaptive sampling*, the other axis of training\-free acceleration, paces how quickly positions commit while decoding continues but never verifies that the output itself has stabilized\. We introduce a training\-free, candidate\-aware early\-exit framework that keeps the two axes separate and matches each decision to evidence of its own scope\.Confidence\-Verified Commit \(CVC\)governs*when*the sequence may stop by verifying confidence and sustained argmax stability over the dynamically extracted candidate span using a deterministic parser specified from each task’s output format\.Block\-Wise Early Commit \(BWEC\)governs*where*to accelerate by applying a cheaper local rule to non\-final blocks, while leaving the final block and global termination under CVC\. We refer to their combination asLATCH\(*Localized Acceleration with Tracked\-Candidate Halting*\)\. Unlike prior methods, LATCH needs no suffix\-prompt construction; it is prompt\-anchor\-free but format\-aware\. We evaluate LATCH end to end on1111tasks under zero\-shot settings using LLaDA and Dream\. LATCH stays within2\.02\.0percentage points of full\-decoding accuracy across all2222evaluation settings, with one frozen hyperparameter set that transfers cross\-backbone untuned, while achieving end\-to\-end TPS speedups of9\.39\.3–17\.8×17\.8\\timeson short\-answer tasks and2\.02\.0–3\.3×3\.3\\timeson long\-reasoning tasks\. Code is available at[https://github\.com/ming053l/LATCH\-dLLM](https://github.com/ming053l/LATCH-dLLM)\.

## 1Introduction

Diffusion language models \(DLMs\) generate text by iteratively denoising a fully\-masked sequence, in contrast to autoregressive models’ left\-to\-right pass\(Nieet al\.,[2025](https://arxiv.org/html/2607.28166#bib.bib33); Yeet al\.,[2025](https://arxiv.org/html/2607.28166#bib.bib34)\); at every intermediate step the model already holds a*provisional*guess for every position, and on many tasks this candidate matches its full\-decoding value well before the last denoising step\. Training\-free acceleration exploits that slack along two separate axes;*adaptive\-sampling*rules such asWuet al\.\([2026](https://arxiv.org/html/2607.28166#bib.bib35)\)’sFast\-dLLM,Weiet al\.\([2026](https://arxiv.org/html/2607.28166#bib.bib37)\)’sSlowFast Sampling, andKimet al\.\([2025](https://arxiv.org/html/2607.28166#bib.bib18)\)’sKLASSchange how quickly positions are committed while decoding continues, whereas generation\-time*early\-exit*rules such asLiet al\.\([2026](https://arxiv.org/html/2607.28166#bib.bib32)\)’sProphetdecide when the whole sequence may stop\. A sampling commit fixes one position; termination freezes every remaining position at once, the answer included\. The two axes therefore demand different evidence, and existing methods fail precisely where one axis’s evidence settles the other’s\.

The termination axis carries the harder decision, trusting that a run has genuinely converged\. A natural proxy is decoding progress\. Under a matched protocol, however, short\-answer tasks meet an operational convergence criterion after roughly4%4\\%of decoding while multi\-step tasks do not until the final4%4\\%, so elapsed progress is a poor surrogate for convergence\. Existing early\-exit gates substitute an aggregate position\-level signal instead, evidence of sampling grade for a sequence\-scope decision\. Prophet’s fixed monitoring region can look stable even while the underlying candidate keeps changing, so its threshold fires and fills*every*remaining masked position in one shot, with no chance to revisit it, andSchED\(Mohamedet al\.,[2026b](https://arxiv.org/html/2607.28166#bib.bib19)\)inherits the same trigger in smoothed form \(Section[3](https://arxiv.org/html/2607.28166#S3)formalizes both\)\. Evaluated under the same free\-form zero\-shot protocol across five long\-reasoning tasks and both models, these termination gates exceed our2\.02\.0\-pointaccuracy tolerance in every setting, by up to6969points; Prophet fails the same way under its own*suffix\-prompt*construction, confirming the gap lies in what counts as evidence, not in prior knowledge of the answer region\.

To address this, we introduceConfidence\-Verified Commit \(CVC\), which re\-extracts and relocates the candidate answer at every step and requires both confidence and sustained argmax stability over that specific span before allowing the sequence to terminate\. Because the verified quantity is the candidate itself, not a proxy for it, a transiently stable guess cannot satisfy the gate\.

CVC’s verification is deliberately conservative and governs only the sequence’s*global*fill\-and\-stop decision, not the pace of individual blocks\. Under block\-wise decoding, only the final block typically carries the answer, so non\-final blocks, usually intermediate reasoning, fall outside what CVC’s identity\-tracking machinery was designed to speed up\. Pace is exactly what the sampling axis addresses, and SlowFast and KLASS show a local confidence signal can drive it\. Applied buffer\-wide, however, the same cheap evidence also commits the answer span, and no sampler decides termination; SlowFast exceeds the accuracy tolerance on every long\-reasoning setting, while KLASS stays within it only on its calibration backbone, dropping55–5252points on Dream\. Even a safe sampler, moreover, still decodes every token a verified stop would skip\.

This motivates our second design,Block\-Wise Early Commit \(BWEC\), which adopts the sampling axis’s cheaper, locally evaluated confidence threshold but confines it to non\-final blocks, while leaving the final block and the global fill\-and\-stop decision entirely to CVC\.

Together,CVCandBWECformLATCH, one gate per axis; CVC verifies the identity and stability of the answer candidate itself before the sequence stops \(*when*\), and BWEC paces commitment under evidence whose reach never exceeds a single block \(*where*\)\. Both transfer to Dream from one LLaDA calibration; prior methods’ do not\.

![Refer to caption](https://arxiv.org/html/2607.28166v1/x1.png)Figure 1:Bounded\-accuracy acceleration\.LATCH matches full\-decoding accuracy using37%37\\%of the steps \(left\), while the remaining runtime concentrates in the CVC\-gated final block \(right\)\.Our contributions are:

- •We show that candidate stabilization is strongly task\-dependent, occurring either early or only near the decoding horizon \(e\.g\.,s0\.9s\_\{0\.9\}, the progress by which90%90\\%of trajectories have stabilized, ranges0\.040\.04–0\.960\.96across tasks\), which makes progress\-only early commitment unreliable \(Section[4\.1](https://arxiv.org/html/2607.28166#S4.SS1)\)\.
- •We proposeLATCH, a candidate\-aware framework with one gate per axis;Confidence\-Verified Commit \(CVC\)verifies the dynamically extracted candidate span before global termination, andBlock\-Wise Early Commit \(BWEC\)paces non\-final blocks through a cheaper local rule under CVC’s protection \(Sections[4\.2](https://arxiv.org/html/2607.28166#S4.SS2)and[4\.3](https://arxiv.org/html/2607.28166#S4.SS3)\)\.
- •We evaluate LATCH across1111tasks and two model families under one frozen CVC threshold tuple and a fixed BWEC threshold, never retuned per task or model, obtaining9\.39\.3–17\.8×17\.8\\timesspeedup on short\-answer tasks and2\.02\.0–3\.3×3\.3\\timeson long\-reasoning tasks while staying within2\.02\.0points of full\-decoding accuracy on every task under both models \(Section[5](https://arxiv.org/html/2607.28166#S5)\)\.

## 2Related Work

#### Diffusion language models\.

The diffusion framework traces toSohl\-Dicksteinet al\.\([2015](https://arxiv.org/html/2607.28166#bib.bib5)\), extended to discrete data byHoogeboomet al\.\([2021](https://arxiv.org/html/2607.28166#bib.bib6)\); Austinet al\.\([2021](https://arxiv.org/html/2607.28166#bib.bib7)\); Campbellet al\.\([2022](https://arxiv.org/html/2607.28166#bib.bib8)\), withLouet al\.\([2024](https://arxiv.org/html/2607.28166#bib.bib9)\)and the masked\-diffusion line\(Shiet al\.,[2024](https://arxiv.org/html/2607.28166#bib.bib10); Sahooet al\.,[2024](https://arxiv.org/html/2607.28166#bib.bib11); Ouet al\.,[2025](https://arxiv.org/html/2607.28166#bib.bib12); Zhenget al\.,[2025](https://arxiv.org/html/2607.28166#bib.bib13)\)establishing the parameterizations LLaDA and Dream build on; product\-level DLMs \(Mercury\(Inception Labset al\.,[2025](https://arxiv.org/html/2607.28166#bib.bib14)\), Gemini Diffusion\(Google DeepMind,[2025](https://arxiv.org/html/2607.28166#bib.bib15)\), Seed Diffusion\(Songet al\.,[2025](https://arxiv.org/html/2607.28166#bib.bib16)\)\) scale the same paradigm, underscoring the stakes of accelerating this decoding\. LLaDA\(Nieet al\.,[2025](https://arxiv.org/html/2607.28166#bib.bib33)\)and Dream\(Yeet al\.,[2025](https://arxiv.org/html/2607.28166#bib.bib34)\), the open\-weight DLMs we evaluate on, expose a revisable prediction at every masked position and admit an arbitrary step budget at inference; LATCH reduces that budget under block\-wise decoding without prematurely terminating the candidate answer\.

#### Early exit and sequence termination\.

Early exit has been studied at the layer, reasoning\-step, and token level\.Guet al\.\([2026](https://arxiv.org/html/2607.28166#bib.bib2)\)apply it to*depth*via hidden\-state stabilization\. Among autoregressive CoT methods, S\-GRPO\(Daiet al\.,[2025](https://arxiv.org/html/2607.28166#bib.bib3)\), DEER\(Yanget al\.,[2026](https://arxiv.org/html/2607.28166#bib.bib4)\), CORE\(Zhaiet al\.,[2026](https://arxiv.org/html/2607.28166#bib.bib50)\), and BMC\(Ruanet al\.,[2026](https://arxiv.org/html/2607.28166#bib.bib49)\)trigger early stopping via decaying reward, transition confidence, brittle\-token revision, and geometric reconstruction, respectively\. For DLMs, Prophet\(Liet al\.,[2026](https://arxiv.org/html/2607.28166#bib.bib32)\)terminates generation once an aggregate confidence gap over a fixed monitoring region clears a staged threshold, and SchED\(Mohamedet al\.,[2026b](https://arxiv.org/html/2607.28166#bib.bib19)\)smooths that trigger into a decay schedule \(Section[3](https://arxiv.org/html/2607.28166#S3)details both\); the decision that freezes the whole remaining sequence thus never inspects the candidate it freezes\. LATCH instead conditions global termination on candidate\-local convergence evidence, confidence and stability over a dynamically extracted candidate span, not answer correctness\.

#### Adaptive sampling for DLMs\.

A separate axis instead paces how many positions commit per step while decoding continues\. Fast\-dLLM\(Wuet al\.,[2026](https://arxiv.org/html/2607.28166#bib.bib35)\)commits every position whose confidence clears a threshold in parallel, SlowFast Sampling\(Weiet al\.,[2026](https://arxiv.org/html/2607.28166#bib.bib37)\)force\-commits high\-confidence positions across exploratory and accelerated phases, and KLASS\(Kimet al\.,[2025](https://arxiv.org/html/2607.28166#bib.bib18)\)unmasks per position once confidence and KL\-stability jointly clear a threshold\. Concurrent work refines the same per\-position evidence; LESS\(Mohamedet al\.,[2026a](https://arxiv.org/html/2607.28166#bib.bib20)\)applies a joint confidence\-and\-stability rule per masked position, STDec\(Chenet al\.,[2026b](https://arxiv.org/html/2607.28166#bib.bib57)\)adapts thresholds over spatial neighborhoods and relaxes them for temporally consistent tokens, TACG\(Wanget al\.,[2026](https://arxiv.org/html/2607.28166#bib.bib58)\)gates commits on EMA\-logit trajectories,R2R^\{2\}\-dLLM\(Duet al\.,[2026](https://arxiv.org/html/2607.28166#bib.bib59)\)finalizes stable tokens via spatio\-temporal redundancy while requiring fine\-tuning, andKimet al\.\([2026](https://arxiv.org/html/2607.28166#bib.bib1)\)attribute commitment instability to a proximity bias in the denoising order\. However refined, these samplers decide which positions to commit next, never whether the sequence is finished; a run they accelerate still decodes every remaining token, whereas a verified stop skips those tokens outright, so the two axes’ savings compose rather than compete\. BWEC adopts this axis’s evidence, following Fast\-dLLM’s parallel\-emission rule, but confines it to non\-final blocks, leaving termination to CVC\. Orthogonal training\-free work lowers per\-step cost through KV caching and suffix pruning\(Maet al\.,[2025](https://arxiv.org/html/2607.28166#bib.bib17); Liuet al\.,[2026](https://arxiv.org/html/2607.28166#bib.bib21); Huet al\.,[2026](https://arxiv.org/html/2607.28166#bib.bib22); Xiaoet al\.,[2026](https://arxiv.org/html/2607.28166#bib.bib27); Chenet al\.,[2026a](https://arxiv.org/html/2607.28166#bib.bib28)\), composing with both axes\.

## 3Preliminaries

#### DLM generation process\.

A DLM generates a sequencex0x\_\{0\}of lengthLLby learning to reverse a discrete corruption process that progressively masks a clean sequence over forward timeu∈\[0,1\]u\\in\[0,1\],

q​\(xu∣x0\)=∏i=1Lq​\(xui∣x0i\),q\(x\_\{u\}\\mid x\_\{0\}\)=\\textstyle\\prod\_\{i=1\}^\{L\}q\(x\_\{u\}^\{i\}\\mid x\_\{0\}^\{i\}\),\(1\)q​\(xui∣x0i\)=\{x0i,w\.p\.​1−u,\(a\) token kept\[MASK\],w\.p\.​u,\(b\) token maskedq\(x\_\{u\}^\{i\}\\mid x\_\{0\}^\{i\}\)=\\left\\\{\\begin\{array\}\[\]\{ll@\{\\quad\}l\}x\_\{0\}^\{i\},&\\text\{w\.p\. \}1\-u,&\\text\{\(a\) token kept\}\\\\ \\texttt\{\[MASK\]\},&\\text\{w\.p\. \}u,&\\text\{\(b\) token masked\}\\end\{array\}\\right\.\(2\)sox1x\_\{1\}is fully masked andx0x\_\{0\}is the original sequence\. The modelpθ​\(x0∣xu\)p\_\{\\theta\}\(x\_\{0\}\\mid x\_\{u\}\)learns to predictx0x\_\{0\}from any maskedxux\_\{u\}; generation reverses this overTTdiscrete*decoding steps*t∈\{1,…,T\}t\\in\\\{1,\\ldots,T\\\}, a separate, discrete index unrelated to forward timeuuand the one used throughout the rest of this paper\. Each step produces a full predictionx^\\hat\{x\}for every masked position, then a*remasking*rule commits some subset permanently and leaves the rest masked\. SinceTTis chosen at inference time, how many steps are used and what the remasking rule commits is the design space this paper targets\.

#### LLaDA’s block\-wise schedule\.

We use LLaDA\-8B\-Instruct\(Nieet al\.,[2025](https://arxiv.org/html/2607.28166#bib.bib33)\)as the reference decoder because its fixed per\-block budget and explicit commitment schedule expose the two control points LATCH modifies, block advancement through BWEC and sequence termination through CVC\. This choice is not model\-specific; we apply the same gates to Dream\-7B\-Instruct\. LLaDA partitions the generation region intoNNequal contiguous blocksB0,…,BN−1B\_\{0\},\\ldots,B\_\{N\-1\}, processed from left to right, with each block denoised forS=T/NS=T/Nsteps via*low\-confidence remasking*\(ttresets within each block\)\. Letci\(t\)c\_\{i\}^\{\(t\)\}denote the model’s softmax confidence in its top\-1 predictionx^i\(t\)\\hat\{x\}\_\{i\}^\{\(t\)\}for currently masked positionii, and letmmbe the block’s initial mask count\. Writingq=⌊m/S⌋q=\\lfloor m/S\\rfloorandr=mmodSr=m\\bmod S, stepttcommits thekt=q\+𝟏​\[t≤r\]k\_\{t\}=q\+\\mathbf\{1\}\[t\\leq r\]highest\-confidence masked positions\. This rank\-based quota is determined solely bymmandSS, independent of the confidence values themselves, and guarantees that the block is fully committed by stepSS\.

#### Early\-termination gates\.

Prophet\(Liet al\.,[2026](https://arxiv.org/html/2607.28166#bib.bib32)\)and SchED\(Mohamedet al\.,[2026b](https://arxiv.org/html/2607.28166#bib.bib19)\)modify this fixed schedule on the termination axis, deciding when the whole sequence may stop and fill; the adaptive samplers of Section[2](https://arxiv.org/html/2607.28166#S2)instead pace how quickly positions commit and never make that decision\. Prophet averages the top\-1/top\-2 logit gap over a monitored regionℛ\\mathcal\{R\},

g¯t=1\|ℛ\|​∑i∈ℛ\(ℓi\(t\),1−ℓi\(t\),2\),\\bar\{g\}\_\{t\}=\\tfrac\{1\}\{\|\\mathcal\{R\}\|\}\\textstyle\\sum\_\{i\\in\\mathcal\{R\}\}\\left\(\\ell\_\{i\}^\{\(t\),1\}\-\\ell\_\{i\}^\{\(t\),2\}\\right\),\(3\)whereℓi\(t\),1,ℓi\(t\),2\\ell\_\{i\}^\{\(t\),1\},\\ell\_\{i\}^\{\(t\),2\}are the two largest logits at positioniiand steptt\. Here,ℛ\\mathcal\{R\}is a task\-format\-specific monitoring region whose definition is held fixed across our free\-form evaluation and Prophet’s suffix\-prompt setting \(Appendices[A\.2](https://arxiv.org/html/2607.28166#A1.SS2)and[E](https://arxiv.org/html/2607.28166#A5)\)\. Prophet fills all remaining masked positions in a single step onceg¯t\\bar\{g\}\_\{t\}crosses its published three\-stage, progress\-dependent threshold; SchED smooths this into a decay curve with a stability guard, still firing as one global fill\. Both gates aggregate position\-level signals into one sequence\-wide trigger, never the identity and stability of the dynamically extracted candidate span, so a position can look converged while its predicted token keeps changing\.

## 4Candidate\-Aware Decoding

Section[1](https://arxiv.org/html/2607.28166#S1)motivates one gate per acceleration axis, CVC for*when*to stop and BWEC for*where*to accelerate \(Figure[2](https://arxiv.org/html/2607.28166#S4.F2)\); this section develops both in full\. Section[4\.1](https://arxiv.org/html/2607.28166#S4.SS1)motivates CVC’s gate, Section[4\.2](https://arxiv.org/html/2607.28166#S4.SS2)develops it, and Section[4\.3](https://arxiv.org/html/2607.28166#S4.SS3)develops BWEC\.

![Refer to caption](https://arxiv.org/html/2607.28166v1/x2.png)Figure 2:LATCH combines global answer\-level stopping with local block\-wise acceleration\.CVC provides verified global stopping, while BWEC accelerates non\-final blocksB0,…,BN−2B\_\{0\},\\ldots,B\_\{N\-2\}; the final blockBN−1B\_\{N\-1\}retains baseline top\-kkdecoding under CVC\.The figure’s CVC track makes this concrete; the candidate is re\-extracted and relocated every step, so the candidate value and its temporal stability are tracked, not merely a fixed position’s confidence\. On the GSM8K trajectory shown, the extractor searches the fixed trailing region specified by the task format \(Appendix[A\.2](https://arxiv.org/html/2607.28166#A1.SS2)\); within the final blockBN−1B\_\{N\-1\}, the candidate itself flickers \(538→540538\\\!\\to\\\!540\) beforerunt\\mathrm\{run\}\_\{t\}accumulates enough successive valid observations to satisfy the joint confidence\-and\-stability criterion in Eq\.[4](https://arxiv.org/html/2607.28166#S4.E4); commitment is therefore not based on an instantaneous check\.

### 4\.1Task\-Dependent Candidate Stabilization

#### The stabilization\-timing gap\.

We collect full \(non\-early\-exited\) trajectories for LLaDA\-8B\-Instruct on120120zero\-shot questions \(4040each from MMLU, GSM8K, and MATH\), under a free\-form prompt with no suffix\-prompt anchor, and check when each trajectory’s extracted candidate*persistently*matches its own full\-decoding outputajfulla\_\{j\}^\{\\mathrm\{full\}\}: letsj=min⁡\{s:aj,u=ajfull​∀u≥s\}s\_\{j\}=\\min\\\{s:a\_\{j,u\}=a\_\{j\}^\{\\mathrm\{full\}\}\\ \\forall u\\geq s\\\}be the earliest progress after which the candidate never again changes, a stabilization diagnostic, not correctness \(accuracy is separate, Table[1](https://arxiv.org/html/2607.28166#S5.T1)\); CVC never has ground\-truth access while decoding\. For a cohort, definesps\_\{p\}as the earliest progress by which a fractionppof trajectories satisfysj≤ss\_\{j\}\\leq s\. Crediting a trajectory only oncesjs\_\{j\}is reached, not at the first mere touch, this stricter test confirms a sharp timing gap; short\-answer trajectories reachs0\.9=0\.04s\_\{0\.9\}=0\.04versus long\-reasoning’ss0\.9=0\.96s\_\{0\.9\}=0\.96, the same split Figure[3](https://arxiv.org/html/2607.28166#S4.F3)shows in the gate’s own replayed evidence\. This split reappearing under a stricter criterion makes it a property of the trajectories, not the threshold drawing the boundary\.

#### Why position\-level gates trigger prematurely\.

Prophet’s trigger ignores whether the candidate stays unchanged across steps \(Section[3](https://arxiv.org/html/2607.28166#S3)\)\. On GSM8K/MATH, it fires at7676–77%77\\%progress, near its most permissive stage, before most candidates stabilize\. Without a suffix anchor, its fixed region only proxies the candidate span\. Figure[4](https://arxiv.org/html/2607.28166#S5.F4)confirms this; Prophet is premature on73/9373/93GSM8K and81/9381/93MATH trajectories, CVC on4/934/93each\.

### 4\.2Confidence\-Verified Commit: Deciding When to Stop

![Refer to caption](https://arxiv.org/html/2607.28166v1/x3.png)Figure 3:Commit timing on diagnostic examples held out from CVC’s own calibration\(n=60n\{=\}60, disjoint from its120120\-trajectory calibration pool; same protocol as Table[1](https://arxiv.org/html/2607.28166#S5.T1)\), confirming the pattern generalizes beyond calibration data\. Prophet’s confidence gap often fires before the answer stabilizes on GSM8K/MATH, forcing a premature fill; CVC commits early on MMLU but waits on long\-reasoning trajectories\. Entropy corroborates this: near22bits at Prophet’s trigger, near0at CVC’s \(n=12n\{=\}12, MMLU\)\. Shaded bands: bootstrap5050/8080/95%95\\%confidence intervals\.#### A joint convergence criterion\.

A task\-agnostic earliest\-commit threshold is the wrong proxy \(Section[4\.1](https://arxiv.org/html/2607.28166#S4.SS1)\); LLaDA force\-commits a fixed quota regardless of confidence \(Section[3](https://arxiv.org/html/2607.28166#S3)\), so run\-length alone cannot separate refinement from scheduling accident, and confidence alone has no notion of temporal stability\. Jointly, they give a stronger convergence proxy\. At steptt, letata\_\{t\}be the extracted answer,runt\\mathrm\{run\}\_\{t\}the stability counter across successive same\-value extractions \(pausing, not resetting, absent a candidate; Appendix[A\.3](https://arxiv.org/html/2607.28166#A1.SS3)\),changest\\mathrm\{changes\}\_\{t\}the flip count, andct∈\[0,1\]c\_\{t\}\\in\[0,1\]the mean confidence overata\_\{t\}’s span\. The gate commits at the firstttsatisfying

ct\\displaystyle c\_\{t\}≥τCVC\\displaystyle\\geq\\tau\_\{\\text\{CVC\}\}\(a\) confidence gaterunt\\displaystyle\\mathrm\{run\}\_\{t\}≥max⁡\(pmin,⌈γ⋅changest⌉\)\\displaystyle\\geq\\max\\big\(p\_\{\\min\},\\,\\lceil\\gamma\\cdot\\mathrm\{changes\}\_\{t\}\\rceil\\big\)\(b\) stability gate\(4\)Both must hold*jointly*: confidence alone cannot rule out a lucky, unstable guess, and stability alone cannot rule out a low\-confidence answer that has not changed yet;pminp\_\{\\min\}prevents immediate commitment before any change occurs, whileγ\\gammasets how many further stable steps each additional flip demands\. All three hyperparameters \(τCVC,γ,pmin\\tau\_\{\\text\{CVC\}\},\\gamma,p\_\{\\min\}\) are calibrated once and then frozen \(next paragraph\), unlike Prophet’s own published thresholds, which differ by task family even in its released defaults \(Appendix[A\.1](https://arxiv.org/html/2607.28166#A1.SS1)\)\. Appendix[F\.1](https://arxiv.org/html/2607.28166#A6.SS1)ablates each condition: dropping either is safe on MMLU but fails on at least one long\-reasoning task\.

#### Extractor, missing candidates, and confidence\.

Both conditions read from the same underlying signals:ata\_\{t\}is the extractor’s own normalized output, not a raw token span, so formatting differences alone never register as a change; a step with no extractable candidate leavesrunt,changest\\mathrm\{run\}\_\{t\},\\mathrm\{changes\}\_\{t\}unchanged and fails the confidence gate automatically\.ctc\_\{t\}is the plain mean of per\-token softmax confidence over the span, recomputed fresh each step regardless of mask status; it reflects operational agreement rather than epistemic certainty at the point of commitment \(Appendix[A\.3](https://arxiv.org/html/2607.28166#A1.SS3)\)\.

#### One frozen setting, stronger evidence\.

Both model families use the same numerical tuple\(τCVC,γ,pmin\)\(\\tau\_\{\\text\{CVC\}\},\\gamma,p\_\{\\min\}\), calibrated once on LLaDA across the three development tasks and never retuned per task or per model; we also restrict the answer\-search region on reasoning tasks to the buffer’s trailing portion, suppressing most mid\-reasoning arithmetic as a candidate at the source rather than tolerating it downstream\. CVC resolves*when*to stop; we next ask*where*full verification is unnecessary\.

### 4\.3Block\-Wise Early Commit: Deciding Where to Accelerate

#### Separating block\-local advancement from global stopping\.

Non\-final blocks often contain intermediate reasoning rather than the final answer, especially on long\-reasoning tasks where the candidate stabilizes only near the decoding horizon \(Section[4\.1](https://arxiv.org/html/2607.28166#S4.SS1)\), motivating a cheaper local rule of the kind the adaptive samplers in Section[2](https://arxiv.org/html/2607.28166#S2)supply\. BWEC applies this rule only to non\-final blocks, while the final block retains the baseline schedule and global termination remains under CVC\.

#### Confidence and scheduled top\-kk, jointly\.

CVC does not gate individual non\-final\-block commits; it monitors the extracted candidate answer over a configured trailing search region of the buffer, wherever it lies within that region, and withholds only the decision to fill and stop the*entire*generation\.*Non\-final*blocks are allowed aggressive emission, via a pure confidence\-threshold rule with no answer semantics\. For blockn<N−1n<N\-1at steptt, every*currently masked*positioni∈Bni\\in B\_\{n\}\(i\.e\.xi\(t\)=\[MASK\]x\_\{i\}^\{\(t\)\}=\\texttt\{\[MASK\]\}; already\-committed positions are untouched by this rule\) updates as

xi\(t\+1\)=\{x^i\(t\),ci\(t\)≥τBWEC,\(a\) confidence commitx^i\(t\),i∈𝒦\(t\),\(b\) scheduled top\-​k​commitxi\(t\),otherwise,\(c\) stays maskedx\_\{i\}^\{\(t\+1\)\}=\\left\\\{\\begin\{array\}\[\]\{ll@\{\\quad\}l\}\\hat\{x\}\_\{i\}^\{\(t\)\},&c\_\{i\}^\{\(t\)\}\\geq\\tau\_\{\\text\{BWEC\}\},&\\text\{\(a\) confidence commit\}\\\\ \\hat\{x\}\_\{i\}^\{\(t\)\},&i\\in\\mathcal\{K\}^\{\(t\)\},&\\text\{\(b\) scheduled top\-\}k\\text\{ commit\}\\\\ x\_\{i\}^\{\(t\)\},&\\text\{otherwise\},&\\text\{\(c\) stays masked\}\\end\{array\}\\right\.\(5\)where𝒦\(t\)\\mathcal\{K\}^\{\(t\)\}is the scheduled top\-kkset among blocknn’s currently masked positions \(Section[3](https://arxiv.org/html/2607.28166#S3)\)\. Scheduled top\-kkguarantees progress even when no position clears the threshold on a given step; it always commits thekkhighest\-confidence still\-masked positions, by rank, so a block finishes on schedule regardless\. The confidence branch opportunistically commits*additional*positions the moment the model resolves them ahead of schedule, by value \(ci\(t\)≥τBWECc\_\{i\}^\{\(t\)\}\\geq\\tau\_\{\\text\{BWEC\}\}, following Fast\-dLLM\(Wuet al\.,[2026](https://arxiv.org/html/2607.28166#bib.bib35)\)\) rather than rank; a position commits if either rule would have\. Once every position in a block has committed this way, that whole block is done early: we define the block\-ready predicate on buffer statexx,Rn​\(x\)=⋀i∈Bn\[xi≠\[MASK\]\]R\_\{n\}\(x\)=\\bigwedge\_\{i\\in B\_\{n\}\}\\big\[x\_\{i\}\\neq\\texttt\{\[MASK\]\}\\big\], checked againstx\(t\+1\)x^\{\(t\+1\)\}right after Eq\.[5](https://arxiv.org/html/2607.28166#S4.E5)’s update; onceRn​\(x\(t\+1\)\)R\_\{n\}\(x^\{\(t\+1\)\}\)holds, blocknn’s remaining scheduled steps are skipped and decoding advances straight to blockn\+1n\+1, a genuine*block\-wise early exit*; the decision to skip a block’s remaining budget rests entirely on that block’s own evidence, never on a sequence\-wide average some other, unrelated block could dominate, which is exactly the failure mode Prophet exhibits \(Section[4\.1](https://arxiv.org/html/2607.28166#S4.SS1)\)\.

The*final*blockBN−1B\_\{N\-1\}is excluded from Eq\.[5](https://arxiv.org/html/2607.28166#S4.E5); it follows the baseline top\-kkschedule alone \(case \(b\) only, never the confidence commit\), while CVC independently determines whether the*entire*sequence \(final block included\) may be filled and terminated early \(Section[4\.2](https://arxiv.org/html/2607.28166#S4.SS2)\)\. Scope and caveats on this final\-block scoping are deferred to Appendix[F](https://arxiv.org/html/2607.28166#A6)\.

## 5Experiments

Datasets and setup\.We evaluate LLaDA\-8B\-Instruct\(Nieet al\.,[2025](https://arxiv.org/html/2607.28166#bib.bib33)\)and Dream\-7B\-Instruct\(Yeet al\.,[2025](https://arxiv.org/html/2607.28166#bib.bib34)\), bfloat16 \(bf16\), greedy decoding, zero\-shot, on a single NVIDIA A100\-SXM4\-40GB GPU, across1111tasks, six*short\-answer*tasks \(MMLU\(Hendryckset al\.,[2021a](https://arxiv.org/html/2607.28166#bib.bib39)\), ARC\-Challenge\(Clarket al\.,[2018](https://arxiv.org/html/2607.28166#bib.bib41)\), HellaSwag\(Zellerset al\.,[2019](https://arxiv.org/html/2607.28166#bib.bib42)\), WinoGrande\(Sakaguchiet al\.,[2021](https://arxiv.org/html/2607.28166#bib.bib43)\), PIQA\(Bisket al\.,[2020](https://arxiv.org/html/2607.28166#bib.bib44)\), TruthfulQA\-MC1\(Linet al\.,[2022](https://arxiv.org/html/2607.28166#bib.bib45)\)\) and five*long\-reasoning*tasks \(GSM8K\(Cobbeet al\.,[2021](https://arxiv.org/html/2607.28166#bib.bib38)\), MATH\(Hendryckset al\.,[2021b](https://arxiv.org/html/2607.28166#bib.bib40)\), SVAMP\(Patelet al\.,[2021](https://arxiv.org/html/2607.28166#bib.bib46)\), ASDiv\(Miaoet al\.,[2020](https://arxiv.org/html/2607.28166#bib.bib47)\), GSM\-Hard\(Gaoet al\.,[2023](https://arxiv.org/html/2607.28166#bib.bib48)\)\)\. CVC’s tuple \(γ=2\.0,τCVC=0\.7,pmin=3\\gamma\{=\}2\.0,\\tau\_\{\\text\{CVC\}\}\{=\}0\.7,p\_\{\\min\}\{=\}3\), SchED’s decay schedule, and KLASS’sτ/ϵKL\\tau/\\epsilon\_\{\\text\{KL\}\}\(Appendix[A\.1](https://arxiv.org/html/2607.28166#A1.SS1)\) are each calibrated once, offline, on LLaDA \(n=120n\{=\}120cached trajectories for CVC,4040each from MMLU, GSM8K, MATH, the same pool SchED and KLASS also reuse\) and reused unchanged for Dream and the other eight tasks, ensuring a fair cross\-backbone comparison; only Prophet’s staged thresholds instead come from its own published defaults\.τBWEC=0\.9\\tau\_\{\\text\{BWEC\}\}\{=\}0\.9is instead fixed a priori, since BWEC’s schedule changes which future steps execute and so cannot be calibrated by offline replay the way CVC is; we instead check its sensitivity end\-to\-end on the same held\-out examples as Table[1](https://arxiv.org/html/2607.28166#S5.T1)\(Appendix[G](https://arxiv.org/html/2607.28166#A7)\), but never optimize against it\.

Evaluation metrics and protocol fairness\.Accuracy and Step follow Prophet’s own evaluation convention, exact match after task\-specific answer extraction \(Appendix[A\.3](https://arxiv.org/html/2607.28166#A1.SS3)\) and the number of decoding steps, respectively; Speedup is the ratio of method tokens per second \(TPS\) to baseline TPS, measured end\-to\-end on a dedicated GPU \(Appendix[B](https://arxiv.org/html/2607.28166#A2)\)\. Paired McNemar tests and bootstrap confidence intervals find no statistically significant accuracy difference between LATCH and Baseline in any cell \(Appendix[C](https://arxiv.org/html/2607.28166#A3)\)\. We also replicate Prophet’s own suffix\-prompt setup \(Appendix[E](https://arxiv.org/html/2607.28166#A5)\), applied identically to*Baseline*, Prophet, and*LATCH*; Prophet’s drop persists even once the answer region no longer needs to be found, while LATCH shows none\.

### 5\.1Main Results

Table 1:Zero\-shot evaluation under free\-form generation\.LATCHis faster than Prophet, SlowFast, and KLASS on all six short\-answer tasks, and keeps accuracy degradation within the2\.02\.0\-point tolerance on all five long\-reasoning tasks without a suffix prompt, with hyperparameters frozen across backbones\.Redmarks accuracy drops beyond that tolerance; the termination gates \(Prophet, SchED\) and SlowFast exceed it on every long\-reasoning setting, while KLASS stays within it only on LLaDA, its calibration backbone\. Appendix[G\.1](https://arxiv.org/html/2607.28166#A7.SS1)gives two faster tiers \(τBWEC=0\.7,0\.8\\tau\_\{\\text\{BWEC\}\}\{=\}0\.7,0\.8\) trading some margin for extra speedup\.We evaluate LATCH by running complete zero\-shot decoding on examples not used for calibration, across all1111tasks and both models \(LLaDA\-8B\-Instruct\(Nieet al\.,[2025](https://arxiv.org/html/2607.28166#bib.bib33)\), Dream\-7B\-Instruct\(Yeet al\.,[2025](https://arxiv.org/html/2607.28166#bib.bib34)\)\); results are reported in Table[1](https://arxiv.org/html/2607.28166#S5.T1)\. Since every variant shown is already faster than baseline, what separates the outcomes below is whether the accuracy drop stays negligible, judged by the bar applied throughout this paper, accuracy within2\.02\.0points of*Baseline*’s with average Step strictly lower\.*LATCH*is always the full deployed configuration, CVC plus BWEC \(Section[4\.3](https://arxiv.org/html/2607.28166#S4.SS3)\), not the final\-block gate alone \(Table[2](https://arxiv.org/html/2607.28166#S5.T2)\)\.

Task groups and headline result\.Section[4\.1](https://arxiv.org/html/2607.28166#S4.SS1)’s stabilization\-timing contrast carries into the end\-to\-end results, split by axis\. The termination gates fire prematurely on late\-stabilizing tasks; Prophet and SchED exceed the2\.02\.0\-point tolerance on all ten long\-reasoning evaluations\. The samplers fail differently; SlowFast also exceeds it on all ten, and KLASS holds tolerance only on LLaDA, its calibration backbone, dropping55–5252points on Dream\. Neither reaches the short\-answer speedups a verified stop\-and\-fill provides\. Figure[4](https://arxiv.org/html/2607.28166#S5.F4)visualizes the premature\-termination failure across all held\-out trajectories, plotting when each trajectory’s candidate stabilizes against when each gate commits places Prophet below the diagonal \(premature commitment\) on73/9373/93GSM8K and81/9381/93MATH trajectories, while CVC does so on only4/934/93each; on MMLU both gates commit at or after stabilization on nearly every trajectory\.

### 5\.2Efficiency Decomposition and Component Ablation

The two axes dominate in different regimes\.The component ablation reveals a regime\-dependent division of labor; CVC, the termination gate, contributes most of the gain on the two short\-answer tasks shown here, whereas BWEC, the sampling gate, contributes most on the two long\-reasoning tasks \(Table[2](https://arxiv.org/html/2607.28166#S5.T2)\), consistent with LATCH’s speedup split across the full evaluation \(Table[1](https://arxiv.org/html/2607.28166#S5.T1)\)\. The full configuration exceeds either component alone in every row, the two axes’ savings composing rather than competing; the2\.00×2\.00\\timesresult on MATH/LLaDA reflects the protected final block, not bookkeeping overhead\. Scoping the global commit’s eligibility to the final block is load\-bearing; making it eligible from any block drops held\-out GSM8K and MATH by4\.04\.0points each, failing exactly like Prophet \(Appendix[F](https://arxiv.org/html/2607.28166#A6)\)\.

LLaDA\-8B\-InstructDream\-7B\-InstructTaskVariantAcc \(%\)StepTPSSpeedupAcc \(%\)StepTPSSpeedupGeneral / short\-answer tasksMMLUBaseline64\.064\.029\.41\.00×\\times71\.564\.033\.01\.00×\\times\(n=200, sequence length=64\)\+ CVC64\.07\.0358\.312\.20×\\times69\.58\.0130\.03\.94×\\times\(block=16, 4 blocks\)\+ BWEC64\.032\.856\.91\.94×\\times71\.024\.888\.72\.69×\\times\+ CVC \+ BWEC \(Full LATCH\)64\.05\.1446\.615\.20×\\times70\.05\.0469\.314\.21×\\timesHellaSwagBaseline75\.564\.023\.91\.00×\\times75\.564\.024\.71\.00×\\times\(n=200, sequence length=64\)\+ CVC76\.56\.3223\.09\.34×\\times75\.011\.377\.43\.13×\\times\(block=16, 4 blocks\)\+ BWEC76\.526\.259\.62\.50×\\times75\.024\.230\.51\.23×\\times\+ CVC \+ BWEC \(Full LATCH\)75\.54\.2320\.913\.44×\\times75\.56\.5229\.69\.29×\\timesLong\-reasoning tasks \(multi\-step CoT\)GSM8KBaseline66\.0256\.022\.21\.00×\\times85\.0256\.023\.11\.00×\\times\(n=100, sequence length=256\)\+ CVC66\.0250\.022\.41\.01×\\times85\.0256\.010\.80\.47×\\times\(block=32, 8 blocks\)\+ BWEC67\.099\.454\.42\.45×\\times85\.091\.330\.91\.34×\\times\+ CVC \+ BWEC \(Full LATCH\)67\.094\.055\.72\.51×\\times85\.090\.866\.32\.86×\\timesMATHBaseline31\.0256\.020\.91\.00×\\times41\.0256\.021\.81\.00×\\times\(n=100, sequence length=256\)\+ CVC31\.0252\.720\.91\.00×\\times41\.0255\.210\.00\.46×\\times\(block=32, 8 blocks\)\+ BWEC32\.0128\.541\.71\.99×\\times42\.0121\.120\.30\.93×\\times\+ CVC \+ BWEC \(Full LATCH\)31\.0124\.641\.92\.00×\\times41\.0120\.345\.12\.07×\\times

Table 2:Component ablation study\.CVC drives short\-answer speedup, BWEC drives long\-reasoning speedup\. On Dream, CVC\-only’s GSM8K/MATH rows run at0\.460\.46–0\.47×0\.47\\timesdespite near\-full steps since Dream rarely leaves an extractable candidate late; CVC\+BWEC recovers full speedup via BWEC’s savings\.Both of CVC’s own conditions are load\-bearing\.Table[2](https://arxiv.org/html/2607.28166#S5.T2)treats CVC as one unit; Table[9](https://arxiv.org/html/2607.28166#A6.T9)replays three ablated variants of Eq\.[4](https://arxiv.org/html/2607.28166#S4.E4)against the same held\-out trajectories behind Figure[3](https://arxiv.org/html/2607.28166#S4.F3)and shows neither of its two conditions is safe alone; Appendix[F\.1](https://arxiv.org/html/2607.28166#A6.SS1)gives the full analysis, together with a candidate\-free control gate showing no position\-level stability threshold is both safe and useful \(Table[10](https://arxiv.org/html/2607.28166#A6.T10)\)\.

![Refer to caption](https://arxiv.org/html/2607.28166v1/x4.png)Figure 4:Commit\-stabilization phase diagram on held\-out LLaDA\-8B\-Instruct trajectories\.Each point pairs Prophet \(triangle\) and CVC \(circle\) for one trajectory, connected by a faint line; marker fill/outline and per\-panel premature\-commitment counts are annotated directly in each panel\. Panels include only trajectories with a defined stabilization time \(198/200198/200MMLU,93/10093/100GSM8K,93/10093/100MATH\); the rest lack an extractable candidate\.Cheap to calibrate, cheap to transfer, but not equally reliable\.Table[4](https://arxiv.org/html/2607.28166#A1.T4)times each method’s own hyperparameter search, and the split again follows the axes\. A termination gate leaves what the model conditions on untouched until it fires, so SchED and CVC calibrate offline by replaying cached trajectories \(CVC’s own search takes3939seconds of CPU time\); sampling rules decide what actually executes at later steps, so BWEC and KLASS each demand a fresh GPU decode per setting, and BWEC’s sweep dominates LATCH’s33h4343m total\. Reusing thresholds on Dream is equally cheap for every method, but only CVC’s transfer holds accuracy; SchED, SlowFast, KLASS, and Prophet all fail there \(Table[1](https://arxiv.org/html/2607.28166#S5.T1)\)\.

The per\-block view explains why\.Figure[5](https://arxiv.org/html/2607.28166#S5.F5)shows why long\-reasoning speedups plateau; BWEC shortens non\-final blocks by committing tokens once they clear the confidence threshold, while the protected final block stays near its full budget under CVC and becomes the bottleneck, an asymmetry Step alone cannot show\. Short\-answer tasks like MMLU and HellaSwag often terminate within one or two blocks, yielding a higher speedup ceiling than tasks occupying all eight, a pattern no prior gate reproduces, since each applies one undifferentiated rule across the whole buffer\. Step is nonetheless only a proxy for wall\-clock speed; under continuousτBWEC\\tau\_\{\\text\{BWEC\}\}sweeps it can stay flat while TPS\-ratio swings2\.22\.2–2\.8×2\.8\\times, and GSM8K accuracy can collapse with no Step warning at all \(Appendix[G\.3](https://arxiv.org/html/2607.28166#A7.SS3)\)\.

![Refer to caption](https://arxiv.org/html/2607.28166v1/x5.png)Figure 5:Per\-block step usage comparison\.Mean steps used \(% of per\-block budget\) by block, LLaDA\-8B\-Instruct\. KLASS reduces steps gradually, with no final\-block protection, while LATCH’s non\-final savings shrink asτBWEC\\tau\_\{\\text\{BWEC\}\}tightens and the final block stays near90%90\\%\. Appendix[G\.2](https://arxiv.org/html/2607.28166#A7.SS2)repeats this across all1111tasks and both models\.

## 6Conclusion

Training\-free DLM acceleration separates into two axes; adaptive sampling decides how quickly positions commit while decoding continues, and generation\-time early exit decides when the whole sequence may stop\. LATCH keeps the axes apart and gives each a gate whose evidence matches its scope,*Block\-Wise Early Commit \(BWEC\)*pacing non\-final blocks through a local confidence rule and*Confidence\-Verified Commit \(CVC\)*governing termination by re\-extracting and relocating the candidate answer at every step before committing\. What separates LATCH from ever\-finer per\-position stability rules is the object being verified, not the signal; even if every position individually stabilized, no position\-level rule could certify that the answer the task asks for exists and has stopped changing, a question only candidate extraction can pose\. A sampler, however refined, also still decodes every remaining token, so verified termination adds a saving that per\-position acceleration cannot reach\. LATCH stays within2\.02\.0points of full\-decoding accuracy everywhere under one frozen hyperparameter set, reaching9\.39\.3–17\.8×17\.8\\timesspeedup on short\-answer tasks and2\.02\.0–3\.3×3\.3\\timeson long\-reasoning tasks, transferring cross\-backbone untuned; Appendix[H](https://arxiv.org/html/2607.28166#A8)discusses where the underlying answer\-span assumption breaks down\.

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## Appendix Overview

Grouped by theme, reproducibility, protocol, and statistical validation \(Appendices[A](https://arxiv.org/html/2607.28166#A1)–[C](https://arxiv.org/html/2607.28166#A3)\), mechanistic evidence and fairness \(Appendices[D](https://arxiv.org/html/2607.28166#A4)–[E](https://arxiv.org/html/2607.28166#A5)\), structural ablation and sensitivity \(Appendices[F](https://arxiv.org/html/2607.28166#A6)–[G](https://arxiv.org/html/2607.28166#A7)\), and scope extension plus limitations \(Appendices[H](https://arxiv.org/html/2607.28166#A8)\)\.

- •[A](https://arxiv.org/html/2607.28166#A1)Hyperparameters Underlying Table[1](https://arxiv.org/html/2607.28166#S5.T1), the one deployed configuration, harness details, and answer\-search\-region \(search\_mode\) convention\.
- •[B](https://arxiv.org/html/2607.28166#A2)Timing Protocol, direct end\-to\-end TPS/Speedup measurement, dedicated GPU, batch size11\.
- •[C](https://arxiv.org/html/2607.28166#A3)Is the Negligible Accuracy Drop Real, or Noise? Paired significance and output\-identical rate\.
- •[D](https://arxiv.org/html/2607.28166#A4)Mechanistic Failure Case, Prophet vs\. LATCH on real GSM8K/SVAMP/PIQA trajectories, signal traces and literal decoded text\.
- •[E](https://arxiv.org/html/2607.28166#A5)Answer\-Region Determination, LATCH vs\. Prophet’s own suffix\-prompt structure, tested head\-to\-head, plus why short\-answer tasks search differently from long\-reasoning ones \(search\_mode\)\.
- •[G](https://arxiv.org/html/2607.28166#A7)Sensitivity, continuousτBWEC\\tau\_\{\\text\{BWEC\}\}sweep, all1111tasks and both models\.
- •[H](https://arxiv.org/html/2607.28166#A8)Limitations\.

## Appendix AHyperparameters Underlying Table[1](https://arxiv.org/html/2607.28166#S5.T1)

### A\.1Harness Details and the Deployed Configuration

#### Harness details deferred from Section[5](https://arxiv.org/html/2607.28166#S5)\.

Zero\-shot means a bare question plus, for reasoning tasks, a one\-line “Let’s think step by step” CoT cue, with no exemplars and no answer\-format scaffolding beyond that\. Dream\-7B\-Instruct retains a causal\-LM next\-token indexing convention; our harness applies its own official one\-position logit shift, otherwise decoding matches LLaDA\. The Prophet peer row ports the official gate \(unchanged published defaults\) into this same harness, monitoring our own answer region, rather than citing numbers from Prophet’s own repo, which uses a different prompt template\.

Table[1](https://arxiv.org/html/2607.28166#S5.T1)’s central claim is that*LATCH*needs exactly one*numerical*hyperparameter set,τCVC=0\.7\\tau\_\{\\text\{CVC\}\}\{=\}0\.7,γ=2\.0\\gamma\{=\}2\.0,pmin=3p\_\{\\min\}\{=\}3\(Eq\.[4](https://arxiv.org/html/2607.28166#S4.E4)\),τBWEC=0\.9\\tau\_\{\\text\{BWEC\}\}\{=\}0\.9\(Eq\.[5](https://arxiv.org/html/2607.28166#S4.E5)\),tail\_frac=0\.3\\texttt\{tail\\\_frac\}\{=\}0\.3\(Section[4](https://arxiv.org/html/2607.28166#S4)\), identical across all1111tasks and both models, with no per\-task or per\-model retuning \(the deterministic extractor and search region follow each task’s own output format,search\_modebelow, but neither is tuned\)\. Table[3](https://arxiv.org/html/2607.28166#A1.T3)makes this explicit alongside the one setting that*does*vary by task, Prophet’s own staged confidence\-gap thresholds, which vary by task family \(Section[5](https://arxiv.org/html/2607.28166#S5)\)\. That is exactly the per\-task tuning*LATCH*is designed to avoid needing\.

Table 3:Per\-task settings underlying Table[1](https://arxiv.org/html/2607.28166#S5.T1)\.nnis the held\-out sample size; len is generation length; Steps is the full decode budget; Block is the block\-diffusion block size \(Section[4](https://arxiv.org/html/2607.28166#S4)\); Batch is11throughout \(Appendix[B](https://arxiv.org/html/2607.28166#A2)\)\.search\_mode\(explained below\) is fixed by answer format, never tuned\. Prophet’s staged thresholds are taken unchanged from its own paper/repo, not tuned by us\. LATCH’s five hyperparameters are identical on every row \(listed above\)\. SchED’s mode/patience are its calibrated decay\-curve shape and stability\-guard patience \(τhigh/τlow\\tau\_\{\\text\{high\}\}/\\tau\_\{\\text\{low\}\}reuse Prophet’s values above\); KLASS’sτ/ϵKL\\tau/\\epsilon\_\{\\text\{KL\}\}are its two frozen\-per\-family calibrated values\. Other hyperparameters \(both\) are fixed and not shown per row\.Table 4:Calibration wall\-clock time\(discussed in Section[5\.2](https://arxiv.org/html/2607.28166#S5.SS2)\)\. “–” denotes no separate calibration \(hyperparameters are published or inherited\)\. GPU\-free:✓\\checkmarkoffline,×\\timesneeds GPU\. Transfers to Dream:✓\\checkmarkholds,×\\timesfails\.

### A\.2Whatsearch\_modeControls

search\_modefixes, per task family, which region of the buffer the extractor reads and where the gate relocates the answer span \(never tuned; details in Appendix[E\.1](https://arxiv.org/html/2607.28166#A5.SS1)\)\."last"\(GSM8K, MATH, SVAMP, ASDiv, GSM\-Hard\) restricts both to the trailingtail\_frac=0\.3\\texttt\{tail\\\_frac\}\{=\}0\.3fraction;"first5"\(MMLU, ARC\-C, HellaSwag, WinoGrande, PIQA, TruthfulQA\) reads the whole buffer but restricts the search to the first55positions\.

### A\.3Extractor Normalization, Missing Candidates, and Confidence Aggregation

The change\-tracking comparison in Eq\.[4](https://arxiv.org/html/2607.28166#S4.E4)uses the extractor’s own normalized output, never a raw token span\. Numeric answers have currency symbols and punctuation stripped, boxed math answers haveLaTeXspacing/macros canonicalized, so formatting changes and span movement never register as a change; only the normalized value is compared\.

runt\\mathrm\{run\}\_\{t\}is an implementation\-maintained stability counter, not a step count; it increments across successive valid extractions with the same value and pauses, rather than resets, when no candidate is extractable \(changest\\mathrm\{changes\}\_\{t\}likewise holds;ctc\_\{t\}is undefined, failing the gate automatically\)\. Across120120calibration trajectories,30%30\\%show such a gap and21%21\\%show the counter resuming through it; a strict\-restart\-at\-one counterfactual reproduces the same commit outcome everywhere, so resumption is common but never decision\-changing\.

Confidencectc\_\{t\}is the model’s per\-step softmax mean over the span, recomputed each step regardless of mask status, so it may partly reflect self\-reconstruction rather than genuine uncertainty; we treat it as an operational agreement score, not an epistemic estimate\. We use the plain mean rather than a minimum or geometric mean to avoid penalizing longer answers, thoughrunt\\mathrm\{run\}\_\{t\}’s joint requirement limits how much one lucky token can do alone\.

## Appendix BTiming Protocol

Every TPS/Speedup number in this paper is timeddirectly, end\-to\-end, not extrapolated from a shared per\-step constant\. For every cell we wrap one complete call to the decode loop \(full step\-by\-step decoding, CVC/BWEC gate bookkeeping including the per\-step answer\-stability extractor, and the final\-fill commit when the gate stops early\) intorch\.cuda\.synchronize\(\)immediately before/after, timed on the host withtime\.time\(\)\(wall clock, not a CUDA event timer\)\. This applies uniformly to*Baseline*,*Prophet*,*LATCH*,*SlowFast Sampling*\(Weiet al\.,[2026](https://arxiv.org/html/2607.28166#bib.bib37)\),*SchED*\(Mohamedet al\.,[2026b](https://arxiv.org/html/2607.28166#bib.bib19)\), and*KLASS*\(Kimet al\.,[2025](https://arxiv.org/html/2607.28166#bib.bib18)\)in Table[1](https://arxiv.org/html/2607.28166#S5.T1), and the*Aggressive*/*Normal*τBWEC\\tau\_\{\\text\{BWEC\}\}tiers \(Table[11](https://arxiv.org/html/2607.28166#A7.T11)\)\.

#### Protocol\.

Every cell uses the identical, fixedn=20n\{=\}20subsample \(the first2020of the same held\-out examples Table[1](https://arxiv.org/html/2607.28166#S5.T1)uses,seed=0\\texttt\{seed\}\{=\}0,skip=40\\texttt\{skip\}\{=\}40\) for all timing within that cell\.22warmup examples \(a disjoint, immediately\-following slice\) are decoded and discarded first to absorb first\-call overhead \(CUDA context/kernel warmup\), then33timed passes run back to back over the same2020examples; we report the mean of the33pass\-level means, plus their coefficient of variation \(CV%\), so no cell’s number rests on a single run\. Every cell runs on a GPU with no other job co\-resident \(verified before launch, Table[5](https://arxiv.org/html/2607.28166#A2.T5)\), batch size11\(matching*Prophet*’s and*SlowFast Sampling*’s own released protocols, Section[5](https://arxiv.org/html/2607.28166#S5);*SchED*and*KLASS*run under this same fixed batch size for a controlled comparison, since neither paper specifies its own\),bf16, greedy decoding\.

Table 5:Direct end\-to\-end TPS measurement protocol\.Shared by every table/figure in Appendix[B](https://arxiv.org/html/2607.28166#A2)’s scope\. CV% is the coefficient of variation across each cell’s33timed passes; every cell lands under2\.6%2\.6\\%, evidence the33\-pass mean is stable, not noise\-dominated\.

## Appendix CIs the Negligible Accuracy Drop Real, or Noise? Paired Significance and Output\-Identical Rate

Table[1](https://arxiv.org/html/2607.28166#S5.T1)reports point estimates, and the±2\.0\\pm 2\.0\-point threshold is a prespecified practical tolerance rather than a confidence interval\.*Baseline*and*LATCH*are not independent samples, however; every example is decoded from the identical prompt, model, and seed, so the right comparison is*paired*, and paired uncertainty is tighter than a naive independent\-sample CI would be \(e\.g\.≈±6\\approx\\\!\\pm 6–77pt at GSM8K/MATH’sn=100n\{=\}100under a binomial approximation\)\. Because*Baseline*and*LATCH*decode the same examples, this appendix assesses uncertainty using paired McNemar tests and paired bootstrap intervals; no cell shows a statistically detectable accuracy difference, although these intervals are not equivalence tests for the±2\.0\\pm 2\.0\-point margin: some reach\[−5\.0,\+0\.0\]\[\-5\.0,\+0\.0\]or\[−3\.0,\+3\.0\]\[\-3\.0,\+3\.0\]\(Table[6](https://arxiv.org/html/2607.28166#A3.T6)\), wide enough that they do not themselves certify the margin holds\. We report three paired statistics per task, both models, on the same held\-out sample as Table[1](https://arxiv.org/html/2607.28166#S5.T1),output\-identical rate\(the fraction of examples where LATCH’s extracted answer exactly matches the full\-budget baseline’s, the direct evidence that early\-commit did not*change*the answer, independent of whether that answer happens to be correct\),McNemar’s exact teston the examples where the two disagree \(bb= baseline\-only\-correct,cc= LATCH\-only\-correct; a symmetric split is consistent with equal accuracy, an asymmetric one is not\), and apaired bootstrap95%95\\%CI onΔ​acc\\Delta\\text\{acc\}\(resampling example indices, not independent baseline/LATCH draws\)\. Table[6](https://arxiv.org/html/2607.28166#A3.T6)reports the full per\-task breakdown\.

Table 6:Paired statistics for the accuracy difference in Table[1](https://arxiv.org/html/2607.28166#S5.T1)\.For each task and model,bbandccdenote*Baseline*\-only\-correct and*LATCH*\-only\-correct examples in McNemar’s exact test;Δ\\Deltaacc reports the paired bootstrap point estimate and95%95\\%CI; Ident\.\(%\) is the output\-identical rate\. No cell reaches conventional significance, and every CI stays near zero\.Output\-identical rate is8888–100%100\\%on every task; LATCH’s early commitment overwhelmingly reproduces the exact same answer the full\-budget decode would have reached, not merely a similarly\-accurate different one\.bb\(baseline\-only\-correct\) andcc\(LATCH\-only\-correct\) are small enough everywhere \(≤3\\leq\\\!3out of100100–200200examples per task\) that McNemar’s exact test has essentially no power to reject anything at this sample size, itself informative; the two variants disagree on at most a handful of examples per task, and no task reaches conventional significance \(the smallestpp\-value is0\.250\.25, Dream/MMLU\)\. The paired bootstrap95%95\\%CI behind eachΔ\\Deltaacc is substantially narrower than the naive independent\-sample binomial SE \(≈4\.7\\approx\\\!4\.7pt at GSM8K’sn=100n\{=\}100/acc≈0\.66\\approx\\\!0\.66\) and centered at or near0on every task\. On this evidence, the±2\.0\\pm 2\.0pt tolerance used throughout this paper is not quietly measuring noise\.

#### Reading the disagreements\.

bbandccare the*counts*of examples where the two variants land on opposite sides of correct/incorrect; the underlying per\-example diffs show these are exactly the kind of noise any two similarly\-accurate decodes would produce, not a systematic direction\. GSM\-Hard/LLaDA’s lowest identical rate \(consistent with that task’s own long floating\-point\-noisy targets\) is still mostly both\-wrong on different wrong numbers, not LATCH converting a right answer to a wrong one\. Dream/MMLU is the one cell with a one\-sided split worth naming \(b=3b\{=\}3,c=0c\{=\}0\), still far short of significance \(p=0\.25p\{=\}0\.25\) at this sample size, and the paired bootstrap CI’s upper bound still touches0\.00\.0, so it is not evidence that the drop turns severe, but it is the single most CVC\-unfavorable cell in the whole sweep\.

## Appendix DMechanistic Failure Case: Prophet vs\. LATCH on Real Trajectories

![Refer to caption](https://arxiv.org/html/2607.28166v1/x6.png)Figure 6:Prophet vs\. CVC on representative trajectories\.Why Prophet fails and how Confidence\-Verified Commit fixes it, on one representative real GSM8K trajectory \(Figure[3](https://arxiv.org/html/2607.28166#S4.F3)in Section[4](https://arxiv.org/html/2607.28166#S4)poolsn=40n\{=\}40such trajectories with bootstrap CIs, so this single example is not the paper’s evidence by itself\)\. Columns 1 and 3 replay the identical trajectory \(gt=21=21\): Prophet commits at54%54\\%progress to a garbled non\-answer \(100%100\\%of its window still masked\); ours withholds until70%70\\%and gets it right\. Column 2 \(MMLU\) succeeds after one false start\.Columns 1 and 3 replay the*same*GSM8K decode, so every intermediate output is identical and the two gates’ decisions are directly comparable, one model run, two gate outcomes\. All three columns replay the exact deployed hyperparameters \(τCVC=0\.7\\tau\_\{\\text\{CVC\}\}\{=\}0\.7,γ=2\.0\\gamma\{=\}2\.0,pmin=3p\_\{\\min\}\{=\}3\)\. Every column shares the same four\-panel structure \(candidate answer identity, the model’s own verification signal, the evidence behind the eventual commit decision, and the answer\-region predictive entropyHtH\_\{t\}against decoding progress\), so the contrast is legible panel\-for\-panel\.

#### Prophet \(column 1\): the correct answer surfaces repeatedly, but nothing locks it in\.

The candidate hits the correct value, 21, twice in passing before the gate fires at step 139 of 256; Prophet’s own top1\-top2 logit gap simply has no mechanism to distinguish a passing correct guess from any other transient one\. The gap panel shows why the gate fires*anyway*\. The gap itself never rises appreciably; it is Prophet’s own staged threshold, tuned for this task family \(Appendix[A\.1](https://arxiv.org/html/2607.28166#A1.SS1)\), that decays until the noisy gap crosses it\. At that exact moment the tail window monitored by the gate is100%100\\%masked \(row 3\); every token in it is force\-filled from a single, unrefined forward pass in one shot, and the entropy panel \(row 4\) shows why that is dangerous;Ht≈0\.48H\_\{t\}\{\\approx\}0\.48bits of real uncertainty remain in that same window at the instant of commit, not the near\-zero value a genuine convergence would show\. The one\-shot fill lands on a truncated, garbled continuation with no extractable number at all \(graded wrong by construction\), the same failure mode, corrupted trailing text rather than a clean wrong digit, as the gt=288=288case in Appendix[E](https://arxiv.org/html/2607.28166#A5)\(Figures[11](https://arxiv.org/html/2607.28166#A5.F11)and[12](https://arxiv.org/html/2607.28166#A5.F12)\)\. This is the mechanism behind the1212–6969point collapses in Table[1](https://arxiv.org/html/2607.28166#S5.T1), not a badly\-tuned threshold, but a gate with no way to tell a transient guess from a verified one\.

#### LATCH \(columns 2–3\): the same two mechanisms \(confidence and run\-length\) rule out exactly this failure\.

On MMLU \(column 2\), the candidate is wrong \(D\) at step 1, flips to the correct answer \(A\) at step 2 with confidence jumping from0\.420\.42to0\.830\.83\(crossingτCVC\\tau\_\{\\text\{CVC\}\}in the same step as the flip, not gradually\), and the gate fires three steps later once the run\-length requirement is also satisfied, at step 5 of 64 \(8%8\\%of budget\); entropy over that same span has already collapsed to≈0\.5\{\\approx\}0\.5bits by the time it fires\.

GSM8K \(column 3\) shows the opposite regime and illustrates the late\-stabilization mechanism characterized in Section[4\.1](https://arxiv.org/html/2607.28166#S4.SS1), the identical trajectory Prophet fails on in column 1: the answer position is still under a fully\- or partially\-masked span for most of the trajectory, soctc\_\{t\}is undefined there \(dotted gray baseline, row 2\); there is nothing to verify a candidate against yet, unlike Prophet’s gap statistic, which stays defined \(and noisy\) even over pure mask tokens\. Once the span is populated the candidate genuinely oscillates across66distinct values before settling on the correct one, 21; the gate withholds commitment until step 178 of 256 \(70%70\\%of budget\), sincerunt\\mathrm\{run\}\_\{t\}’s required threshold has itself grown from the accumulated flip count \(changest=17\\mathrm\{changes\}\_\{t\}\{=\}17by the time it fires\); the same run\-length that would have looked sufficient on a stability\-only gate early in the trace is not sufficient here, because this trace has already shown itself to be unreliable\. On this exact same model output, Prophet commits3939steps earlier to a garbled non\-answer; our gate waits and gets it right\.

#### The literal decoded text, not just the signal traces above\.

Figure[7](https://arxiv.org/html/2607.28166#A4.F7)shows the actual decoded buffer underlying the GSM8K trace just discussed \(gt=21=21\) at each method’s own commit point \(step counts in each column header\), not a stylized transcript\.*Baseline*and*Prophet*share the exact same decode up to Prophet’s trigger step;*LATCH*is the same trajectory replayed under our own gate\. Baseline runs to completion and is correct; Prophet’s one\-shot fill lands on a truncated, garbled tail with no extractable number at all, while LATCH commits correctly with budget still unspent\. We observed the same mechanism on MATH, including cases where the reasoning remained correct throughout but Prophet’s one\-shot fill corrupted only the final\\boxed\{\}span itself, the one part of the derivation the whole answer depends on; Figures[8](https://arxiv.org/html/2607.28166#A4.F8)and[9](https://arxiv.org/html/2607.28166#A4.F9)repeat the same comparison on SVAMP and PIQA, showing the same one\-shot\-fill signature is not specific to this single GSM8K trajectory\.

![Refer to caption](https://arxiv.org/html/2607.28166v1/x7.png)Figure 7:Literal decoded text at each method’s own commit point\.Qualitative comparison for one real GSM8K trajectory \(gt=21=21\), the same trace as Figure[6](https://arxiv.org/html/2607.28166#A4.F6)\. Extracted final answer highlighted in blue \(correct\); Prophet’s one\-shot fill leaves no number to extract at all\.![Refer to caption](https://arxiv.org/html/2607.28166v1/x8.png)Figure 8:A third real trajectory \(SVAMP\)\.The same literal\-decoded\-text comparison as Figure[7](https://arxiv.org/html/2607.28166#A4.F7)\. CVC correctly declines to commit early when nothing in the trajectory clears its confidence bar, rather than forcing an early exit regardless\.![Refer to caption](https://arxiv.org/html/2607.28166v1/x9.png)Figure 9:A fourth real trajectory \(PIQA\)\.The same literal\-decoded\-text comparison as Figure[7](https://arxiv.org/html/2607.28166#A4.F7)\. Even where Prophet’s*extracted*letter is still correct, its one\-shot fill can leave the surrounding text measurably more garbled than either*Baseline*or*LATCH*, a formatting cost the accuracy metric alone does not capture\.

## Appendix EAnswer\-Region Determination: LATCH vs\. Prophet’s Suffix\-Prompt Structure

Section[4\.1](https://arxiv.org/html/2607.28166#S4.SS1)attributes Prophet’s long\-reasoning failure to*where*its one\-shot fill is allowed to land, not to its confidence statistic per se\. A closer read of Prophet’s own Appendix C\.1 \(Liet al\.,[2026](https://arxiv.org/html/2607.28166#bib.bib32)\) reveals a second, compounding gap;*how the answer region itself is located*differs structurally between the two setups, not just in threshold values\.

#### Prophet’s construction\.

Their Appendix C\.1 states the answer region is built into the prompt directly: “*The suffix prompt is inserted as a semantic anchor near the end of the generation window, followed by mask tokens reserved for the final answer\. The resulting sequence structure is: \[Question\] \[MASKs for Reasoning Chain\] The answer is \[MASKs for Final Result\]\.*” For mathematical reasoning specifically: “*The dataset provides a standard separator between the reasoning chain and the final result\. We define the answer region as the tokens following this separator\.*” Critically, this suffix construction is used for*both*Prophet and their full\-step baseline in Table 1 of their paper\. The answer region’s location is never searched for at inference time; it is a fixed, pre\-allocated span known before decoding starts\.

#### Our construction\.

Every prompt in this paper is a*free\-form prompt*\(Section[5](https://arxiv.org/html/2607.28166#S5),"Q: \{question\}\\nA: Let’s think step by step\.", no suffix prompt, no answer\-position cue\)\. The gate has no pre\-allocated location for the answer; at every step it must*search*the trailingtail\_fracwindow of whatever text has been generated so far, re\-extracting a provisional answer candidate and relocating its token span from scratch \(Section[4](https://arxiv.org/html/2607.28166#S4)\)\. This is a strictly harder problem; the model is free to place its final numeric answer anywhere, at any length, after any amount of intermediate arithmetic\.

#### Concrete example\.

Table[7](https://arxiv.org/html/2607.28166#A5.T7)shows one real GSM8K trajectory from our diagnostic cache \(ground truth350350\)\. Our tail\-window extractor encounters*five*distinct numeric candidates over the course of generation \(130130,100100,120120,220220, then finally350350\), each of which is briefly "the last number seen so far" and therefore a candidate the gate must evaluate and reject before the true final answer even appears\. Under Prophet’s suffix\-prompt construction, none of this search exists; the final\-answer mask span is at a known position from step0, so the model’s own output at that fixed span is the only thing ever monitored\.

\#Text excerpt \(free\-form prompt, in decode order\)Candidate’s fate1“…Total pesos Axel has:50\+80=𝟏𝟑𝟎50\+80=\\mathbf\{130\}…”superseded by \#22“…twice as many silver pesos as Axel:2×50=𝟏𝟎𝟎2\\times 50=\\mathbf\{100\}silver pesos …”superseded by \#33“…40 more gold pesos than Axel:80\+40=𝟏𝟐𝟎80\+40=\\mathbf\{120\}gold pesos …”superseded by \#44“…Total pesos Anna has:100\+120=𝟐𝟐𝟎100\+120=\\mathbf\{220\}…”superseded by \#55“…total pesos together:130\+220=𝟑𝟓𝟎130\+220=\\mathbf\{350\}\. So, the total …is𝟑𝟓𝟎\\mathbf\{350\}\.”FINAL, committedProphet’s construction \(Appendix C\.1\): answer region fixed by prompt design, not searched\[Question\] \[MASKs for Reasoning Chain\] The answer is \[MASKs\]\. Final span’s position is fixed and known before decoding starts; candidates \#1–\#4 never occupy it, by construction, so Prophet’s gate never has to distinguish them from \#5 in the first place\.Table 7:Five candidates rejected before the true answer\.Same GSM8K example \(gt=350=350\)\. Our tail\-window extractor encounters and must evaluate*five*numeric candidates in turn, four transient \(\#1–\#4, each briefly "the last number seen so far" until overwritten\) and one final \(\#5, the one that survives to the end of generation and gets committed\), versus Prophet’s structurally pre\-allocated span, which by construction only ever contains \#5 and never has to make this distinction at all\.This is precisely what CVC’s confidence\-and\-run\-length requirement \(Section[4](https://arxiv.org/html/2607.28166#S4)\) exists to survive without needing a suffix prompt; a candidate like130130or220220is briefly "the answer" and may even holdrun≥1\\mathrm\{run\}\\geq 1for a step or two, but it is competing against four later re\-writes, so it rarely accumulates the argmax stability and confidence needed to pass the gate, whereas Prophet’sg¯t\\bar\{g\}\_\{t\}has no equivalent protection, monitoring the same free\-form buffer with no positional anchor at all in our replication \(Appendix[A\.1](https://arxiv.org/html/2607.28166#A1.SS1)\)\.

#### Does Prophet’s own suffix\-prompt construction rescue it?

We reproduce this construction and test it directly\. The final block’s buffer is initialized with the literal token ids for" The answer is"pinned at fixed positions from step0\(never masked, never subject to any gate\), with the remaining positions of that block reserved purely for the numeric result, an exact reproduction of Appendix C\.1’s\[Question\] \[MASKs for Reasoning Chain\] The answer is \[MASKs for Final Result\]structure, applied identically to baseline, Prophet, and*LATCH*so the comparison isolates the gate itself\. Table[8](https://arxiv.org/html/2607.28166#A5.T8)reports the result onn=100n\{=\}100held\-out GSM8K and MATH examples, both models, Prophet under its own corrected per\-task thresholds \(Liet al\.,[2026](https://arxiv.org/html/2607.28166#bib.bib32)’s Table 6\)\. Even with the answer region’s location no longer something the model or the gate has to find \(Prophet’s own construction, at its own thresholds\), Prophet’s accuracy still collapses sharply on GSM8K \(LLaDA68\.0%→41\.0%68\.0\\%\\\!\\to\\\!41\.0\\%,−27\-27pt; Dream72\.0%→54\.0%72\.0\\%\\\!\\to\\\!54\.0\\%,−18\-18pt\) and degrades severely on MATH \(LLaDA31\.0%→24\.0%31\.0\\%\\\!\\to\\\!24\.0\\%,−7\-7pt; Dream43\.0%→28\.0%43\.0\\%\\\!\\to\\\!28\.0\\%,−15\-15pt\);*LATCH*keeps the drop negligible on both tasks, both models\. This refutes the hypothesis that the suffix\-prompt structure alone explains the negligible\-drop claim in Prophet’s own paper; the gap is in*what counts as evidence of convergence*, not merely in*where the answer region is*, and a hard structural anchor for the answer location does not prevent Prophet’s position\-level confidence\-gap trigger from firing before the candidate value stabilizes\.

Prophet’s suffix\-prompt construction, final block \(positions224224–255255of256256, GSM8K\): \[pos 224\]Theansis\[pos 255\] pinned to" The answer is"from step0, never maskedfree/masked, model fills

Our free\-form\-prompt protocol, same final block, no reservation at all: \[pos 224\]\[pos 255\] every position starts masked; the model decides where and how the answer surfaces, and our extractor locates it after the fact \(task\-format\-specific search region, Appendix[A\.2](https://arxiv.org/html/2607.28166#A1.SS2)\)

Figure 10:Prophet’s suffix\-prompt construction vs\. ours\.The suffix\-prompt construction \(top\) pins the literal tokens" The answer is"at fixed positions from step0, so the answer’s*location*is never in question; only the2929remaining positions are free\. Our free\-form\-prompt protocol \(bottom\) reserves nothing: every position in every block starts masked, identically to*Baseline*\.Table 8:Prophet remains vulnerable with a pinned answer region\.GSM8K/MATH, with Prophet’s own suffix\-prompt buffer construction \(Appendix C\.1\) applied identically to all three variants; the answer region’s position is fixed and known from step0, removing the search problem Table[7](https://arxiv.org/html/2607.28166#A5.T7)illustrates\.*LATCH*is essentially1\.00×1\.00\\timeshere since the suffix prompt leaves almost nothing for CVC to shorten\. Prophet’s accuracy still degrades severely on both tasks and both models;*LATCH*keeps the drop negligible throughout\.A separate, weaker probe \(pinning only a single"Answer:"anchor token, not the full suffix prompt\) shifted GSM8K’s early\-convergence distribution the direction Prophet’s Figure 1 predicts, but cost end\-task accuracy \(30/40→25/4030/40\\\!\\to\\\!25/40\) without Prophet’s accompanying concision instruction\. This reaches the same conclusion as above; locating the answer region alone is not what makes a gate safe\.

#### The literal text, under Prophet’s own suffix\-prompt construction\.

Figures[11](https://arxiv.org/html/2607.28166#A5.F11)and[12](https://arxiv.org/html/2607.28166#A5.F12)show two of the trajectories behind Table[8](https://arxiv.org/html/2607.28166#A5.T8)’s numbers as literal decoded text, not just accuracy; even with the answer region’s location pinned from step0and never masked, Prophet’s one\-shot fill still overwrites the reserved numeric span itself with a corrupted value on both examples, while*LATCH*runs to the same full budget as*Baseline*and reproduces it exactly\.

![Refer to caption](https://arxiv.org/html/2607.28166v1/x10.png)Figure 11:Literal text under Prophet’s own suffix\-prompt construction \(GSM8K, balloon example\)\.One of the trajectories behind Table[8](https://arxiv.org/html/2607.28166#A5.T8)’s numbers, Prophet’s own suffix\-prompt construction \(Appendix C\.1\) applied identically to all three variants\.*Baseline*and*LATCH*reach the same correct answer at the same full step budget; Prophet’s one\-shot fill overwrites the pinned answer span itself with a corrupted value unrelated to the correct one, confirming at the text level that pinning the answer region’s location does not by itself protect against a premature commit\.![Refer to caption](https://arxiv.org/html/2607.28166v1/x11.png)Figure 12:Literal text under Prophet’s own suffix\-prompt construction \(GSM8K, debts example\)\.A second trajectory behind Table[8](https://arxiv.org/html/2607.28166#A5.T8)’s numbers, same construction and variants as Figure[11](https://arxiv.org/html/2607.28166#A5.F11)\. Prophet’s one\-shot fill again overwrites the pinned answer span with a corrupted value;*Baseline*and*LATCH*reach the same correct answer\.
### E\.1Task\-Format\-Specific Answer Search

The implementation uses two fixed search regions, a trailing window for long\-form reasoning and the first five positions for short\-answer tasks \(search\_modein the reproduction config, Appendix[A\.2](https://arxiv.org/html/2607.28166#A1.SS2)\)\. Everything above is the*long\-reasoning*search setting \("last"\); the gate searches a trailing window because a CoT answer can appear anywhere, arbitrarily late\. Short\- answer/MC tasks \(MMLU, ARC\-C, HellaSwag, WinoGrande, PIQA, TruthfulQA\) use the other setting,"first5", and the reason is visible directly in the prompt template itself, not a separate design choice\.

Prompt template, long\-reasoning \(search mode last\)Q: \{question\}\\nA: Let’s think step by step\.

Prompt template, short\-answer/MC \(search mode first5\)\{question\}\\nA\. \{a\}\\nB\. \{b\}\\nC\. \{c\}\\nD\. \{d\}\\nAnswer:

The CoT template ends mid\-thought, on purpose; the model has to write its way to an answer, so the gate has nowhere fixed to look and must search\. The MC template ends on the literal word"Answer:", which is itself a positional anchor; an instruction\-tuned model’s very next tokens are the letter, not more reasoning\. This task\-format\-specific search is answer\-*aware*in exactly the sense Section[4](https://arxiv.org/html/2607.28166#S4)claims: it is not one global window, it is a per\-task encoding of*where the answer structurally has to live given the prompt that was used to elicit it*, and the two settings are read directly off the two templates above, not tuned separately\.

#### Concrete example\.

A real MMLU trajectory from our diagnostic cache \(ground truthA, held out from calibration\) generates:

Model output \(LLaDA\-8B\-Instruct, greedy, first 200 characters\)A\. Antidiuretic hormone\.\\n\\nAntidiuretic hormone, also known as vasopressin, is primarily responsible for fluid regulation\. It is produced by the posterior pituitary gland and helps regulate water balan\[…\]

The letter is already correct and fully formed at position0, before the model has written a single word of the \(unrequested, unrewarded\) elaboration that follows it\. Table[1](https://arxiv.org/html/2607.28166#S5.T1)’sτCVC\\tau\_\{\\text\{CVC\}\}/run\-length check only ever has to look at this first token:"first5"searches the leading55positions of the generation buffer for a match, finds"A"immediately, and the gate commits as soon asct≥τCVCc\_\{t\}\\geq\\tau\_\{\\text\{CVC\}\}holds forrunt≥pmin\\mathrm\{run\}\_\{t\}\\geq p\_\{\\min\}steps, typically within the first handful of denoising steps \(Table[2](https://arxiv.org/html/2607.28166#S5.T2): MMLU’s own*\+CVC*row commits at avg Step≈5\\approx\\\!5–99out of a6464\-step budget\)\."last"mode searches the tail window for CoT tasks; doing the same here instead would be actively wrong, since the elaboration after the answer is free\-running commentary the model was never asked for and the gate was never designed to grade, and nothing guarantees a second, tail\-window\-visible restatement of the letter exists to be found at all \(the example above never repeats"A"again in the visible window\)\. The two search settings are therefore not an implementation convenience; they encode, per task family, the one structural fact that makes either family’s early\-commit problem tractable at all,*where the prompt itself guarantees the answer will be written*\.

## Appendix FAblation Studies

### F\.1CVC Component Ablation: Which Signal Is Load\-Bearing?

Eq\.[4](https://arxiv.org/html/2607.28166#S4.E4)requires two conditions to jointly hold before CVC commits, confidence \(ct≥τCVCc\_\{t\}\\geq\\tau\_\{\\text\{CVC\}\}\) and adaptive stability \(runt≥max⁡\(pmin,⌈γ⋅changest⌉\)\\mathrm\{run\}\_\{t\}\\geq\\max\(p\_\{\\min\},\\lceil\\gamma\\cdot\\mathrm\{changes\}\_\{t\}\\rceil\)\)\. We isolate which condition is load\-bearing by replaying four gate variants against the exact same held\-out diagnostic pool used for Figure[3](https://arxiv.org/html/2607.28166#S4.F3)\(n=60n\{=\}60, disjoint from the120120trajectories used to calibrate CVC, MMLU/GSM8K/MATH, LLaDA\-8B\-Instruct\), namely*Full CVC*\(both conditions, deployed hyperparameters\);*Confidence only*\(the stability condition removed\);*Stability only*\(the confidence condition removed\); and*Fixed patience*\(confidence kept, but the adaptive run\-length bar replaced with a constantpminp\_\{\\min\}\)\. This replay is entirely offline against cached trajectories, since a full, non\-early\-exited decode already contains everything any of these gates would have seen \(Appendix[A\.1](https://arxiv.org/html/2607.28166#A1.SS1)\)\.

Table 9:CVC component ablation\.Each cell: accuracy change vs\.*Baseline*\(pt\), with average decoding steps used \(% of budget\) in parentheses; bold marks the best variant per row, and shading marks accuracy cost \(yellow: none; red: darker is worse\)\.Table[9](https://arxiv.org/html/2607.28166#A6.T9)shows that no single ablated variant is safe across all three tasks\.*Stability only*fails catastrophically on both long\-reasoning tasks \(−25\.0\-25\.0pt on GSM8K,−25\.0\-25\.0pt on MATH\); without a confidence check, a candidate that merely stops changing for a few steps is accepted regardless of how uncertain the model still is, exactly the low\-confidence\-plateau failure mode a stability\-only rule cannot distinguish from genuine convergence\.*Confidence only*is safe on GSM8K but fails just as severely on MATH \(−25\.0\-25\.0pt\); without a stability check, a momentarily confident candidate that has not stopped flipping is accepted, and which task this bites depends on how often the model revisits a wrong candidate late in decoding\.*Fixed patience*stays safe on GSM8K but degrades on MATH \(−10\.0\-10\.0pt, worse than*Full CVC*’s−5\.0\-5\.0pt on the same pool\); a flat patience floor is not conservative enough for trajectories whose candidate keeps flipping late, which is exactly what the adaptive term⌈γ⋅changest⌉\\lceil\\gamma\\cdot\\mathrm\{changes\}\_\{t\}\\rceilis designed to raise the bar against\.*Full CVC*is the only variant close to safe on all three tasks\. The−5\.0\-5\.0pt deviation on MATH corresponds to one example in thisn=20n\{=\}20diagnostic pool; then=100n\{=\}100CVC\-only result in Table[2](https://arxiv.org/html/2607.28166#S5.T2)shows no accuracy change\. MMLU stabilizes early enough \(66–8%8\\%of budget\) that all four variants are safe there, consistent with Section[4\.1](https://arxiv.org/html/2607.28166#S4.SS1)’s stabilization\-gap finding; ablating either condition only matters once a task’s answer takes long to settle\.

#### Same signal, wrong object\.

The ablation above removes CVC’s two conditions one at a time; a sharper question is whether those signals suffice*without the candidate*, since cross\-step argmax stability is exactly the per\-position evidence adaptive samplers track \(Section[2](https://arxiv.org/html/2607.28166#S2)\)\. We therefore replay a candidate\-free control gate against the full Table[1](https://arxiv.org/html/2607.28166#S5.T1)held\-out trajectories \(n=200/100/100n\{=\}200/100/100, LLaDA\), terminating with a one\-shot fill at the first step where every monitored position’s argmax has been unchanged forkkconsecutive steps, monitored either over the whole buffer or, more charitably, only over positions the block schedule has already reached \(predictions in unreached blocks are noise by construction\)\. Table[10](https://arxiv.org/html/2607.28166#A6.T10)sweepskkunder both scopes\. No frozen setting is both safe and useful\. The only settings within the2\.02\.0\-point tolerance on all three tasks \(whole\-buffer,k≥8k\\geq 8\) commit at56\.956\.9–74\.6%74\.6\\%of budget on MMLU, five to seven times later than deployed CVC’s10\.9%10\.9\\%, while saving nothing on GSM8K/MATH; every setting that matches CVC’s early MMLU commit point exceeds the tolerance on long\-reasoning tasks by up to5757points, and the charitable scope is the worse offender precisely because it fires earlier\. The gate cannot tell which regime it is in; position\-level evidence never identifies where the answer lives, which is exactly the information candidate extraction adds and Section[4\.1](https://arxiv.org/html/2607.28166#S4.SS1)’s stabilization\-timing gap demands\.

Table 10:Position\-stability termination control gate\.Each cell: accuracy change vs\.*Baseline*\(pt\) with average decoding steps used \(% of budget\) in parentheses, replayed on the Table[1](https://arxiv.org/html/2607.28166#S5.T1)held\-out split; the gate stops and fills once every monitored position’s argmax has been unchanged forkksteps\. The CVC row \(from Table[2](https://arxiv.org/html/2607.28166#S5.T2)\) is the candidate\-aware reference\. Shading as in Table[9](https://arxiv.org/html/2607.28166#A6.T9)\. The\+1\.0\+1\.0MATH cells sit above baseline because of a single grading\-boundary example \(the replayed full decode grades32\.032\.0against Table[1](https://arxiv.org/html/2607.28166#S5.T1)’s31\.031\.0\)\.

### F\.2Structural Ablation: BWEC Applied Uniformly

#### Scope and caveats\.

Final\-block protection should not be read as an assumption that the answer resides in the final block; answer locality varies substantially across tasks and backbones \(see below\)\. Its purpose is instead to separate actions with different failure costs\. BWEC advances only the current block, whereas CVC’s fill\-and\-stop action terminates the entire sequence and makes all remaining predictions irreversible\. LATCH therefore permits aggressive local commitment in non\-final blocks but reserves global termination for the final block, where it is conditioned on the candidate’s identity and temporal stability\. This asymmetry, not final\-answer locality itself, is the intended safety mechanism\.

A natural question about Eq\.[5](https://arxiv.org/html/2607.28166#S4.E5)’s scoping to non\-final blocks arises\. Is the final/non\-final distinction itself load\-bearing, or would BWEC’s threshold\-plus\-schedule rule be safe applied*everywhere*, making CVC’s separate final\-block gate a redundant safety margin? A related, narrower check confirms the confidence signal itself was never the problem\. Deployed CVC updates its candidate statistics at every step, but its global fill\-and\-stop action becomes eligible only after decoding enters the final block; we call the ablation that instead makes this same fill\-and\-stop action eligible from*any*block the*any\-block\-eligible CVC commit*; it removes the final\-block scoping from the*global*commit decision, not from BWEC’s local rule \(Section[4\.3](https://arxiv.org/html/2607.28166#S4.SS3)\)\. This drops a fresh held\-out GSM8K to62\.0%62\.0\\%and MATH to27\.0%27\.0\\%\(both−4\.0\-4\.0pt\); it fails exactly like Prophet does, because*where*an early, one\-shot commit is allowed to become eligible is what matters, not the statistic used to justify it\.

#### How often does the answer actually land in the final block?

Under LLaDA’s block\-wise schedule, the final answer lands in the last block on43\.643\.6–94\.7%94\.7\\%of held\-out examples across five long\-reasoning tasks \(lowest on SVAMP\), far lower and less predictive on Dream \(as low as2\.6%2\.6\\%on GSM8K, which nonetheless shows only a negligible accuracy drop\), a real, model\-dependent risk factor, never the sole argument for scoping the global commit decision to the final block\. SlowFast Sampling\(Weiet al\.,[2026](https://arxiv.org/html/2607.28166#bib.bib37)\)omits this distinction from the opposite direction \(no final/non\-final split\), leaving short\-answer speedup on the table while accuracy still degrades severely on long\-reasoning \(Section[5](https://arxiv.org/html/2607.28166#S5)\); one undifferentiated rule cannot be maximally aggressive*and*maximally cautious at once\.

## Appendix GSensitivity

### G\.1DiscreteτBWEC\\tau\_\{\\text\{BWEC\}\}Tiers

#### The two undeployedτBWEC\\tau\_\{\\text\{BWEC\}\}tiers: an accuracy/speedup trade, not a second safe default\.

Table[1](https://arxiv.org/html/2607.28166#S5.T1)reports only the deployed tier \(τBWEC=0\.9\\tau\_\{\\text\{BWEC\}\}\{=\}0\.9\), the conservative end of the range that keeps every cell within the paper’s own±2\.0\\pm 2\.0pt tolerance\. Table[11](https://arxiv.org/html/2607.28166#A7.T11)gives the same breakdown for two looser, non\-deployed tiers \(τBWEC=0\.7\\tau\_\{\\text\{BWEC\}\}\{=\}0\.7andτBWEC=0\.8\\tau\_\{\\text\{BWEC\}\}\{=\}0\.8\), which exist only to characterize how far the trade can be pushed, not as recommended alternatives, and require no query\-time selection sinceτBWEC=0\.9\\tau\_\{\\text\{BWEC\}\}\{=\}0\.9alone is what LATCH deploys;66of4444task×\\timesmodel×\\timestier combinations here exceed the same tolerance\. This is expected of the looser tiers by design, not a failure of the method; they trade safety margin for speed and should be read as a sensitivity sweep, not a second deployment\-ready configuration\.

LLaDA\-8B\-InstructDream\-7B\-InstructTaskTierAcc \(%\)Avg\. StepTPSSpeedupAcc \(%\)Avg\. StepTPSSpeedupGeneral / short\-answer tasks \(single\-token or short\-span answers\)MMLUAggressive63\.54\.6405\.913\.81×\\times70\.04\.2457\.713\.87×\\times\(n=200, sequence length=64, block=16\)Normal63\.55\.1399\.713\.60×\\times70\.54\.5520\.115\.76×\\timesARC\-CAggressive86\.03\.8581\.919\.02×\\times88\.53\.7554\.315\.57×\\times\(n=200, sequence length=64, block=16\)Normal86\.03\.8481\.715\.74×\\times87\.54\.1547\.215\.37×\\timesHellaSwagAggressive76\.04\.2353\.114\.78×\\times75\.55\.4323\.213\.08×\\times\(n=200, sequence length=64, block=16\)Normal76\.54\.3333\.413\.95×\\times75\.05\.9274\.111\.10×\\timesWinoGrandeAggressive75\.53\.3580\.518\.67×\\times71\.03\.8710\.418\.40×\\times\(n=200, sequence length=64, block=16\)Normal75\.53\.3575\.618\.51×\\times71\.04\.0682\.217\.67×\\timesPIQAAggressive81\.04\.0407\.313\.10×\\times84\.53\.5681\.018\.81×\\times\(n=200, sequence length=64, block=16\)Normal81\.53\.6455\.014\.63×\\times84\.03\.5681\.718\.83×\\timesTruthfulQAAggressive62\.04\.6489\.015\.72×\\times64\.04\.8328\.39\.38×\\times\(n=200, sequence length=64, block=16\)Normal63\.04\.4464\.314\.93×\\times63\.04\.9355\.610\.16×\\timesLong\-reasoning tasks \(multi\-step CoT\)GSM8KAggressive67\.069\.378\.53\.54×\\times77\.072\.781\.63\.53×\\times\(n=100, sequence length=256, block=32\)Normal69\.079\.365\.92\.97×\\times84\.080\.675\.53\.27×\\timesMATHAggressive32\.095\.055\.62\.66×\\times39\.092\.059\.62\.73×\\times\(n=100, sequence length=256, block=32\)Normal32\.0107\.649\.42\.36×\\times41\.0104\.053\.02\.43×\\timesSVAMPAggressive85\.063\.193\.74\.18×\\times78\.064\.490\.63\.86×\\times\(n=100, sequence length=256, block=32\)Normal85\.075\.177\.33\.45×\\times78\.070\.583\.63\.56×\\timesASDivAggressive63\.069\.085\.63\.79×\\times78\.067\.494\.84\.03×\\times\(n=100, sequence length=256, block=32\)Normal64\.078\.975\.23\.33×\\times79\.073\.486\.63\.68×\\timesGSM\-HardAggressive33\.072\.378\.33\.61×\\times40\.080\.073\.73\.20×\\times\(n=100, sequence length=256, block=32\)Normal33\.083\.368\.23\.14×\\times41\.090\.664\.52\.80×\\times

Table 11:The two undeployedτBWEC\\tau\_\{\\text\{BWEC\}\}tiers, all 11 tasks\.Aggressive \(τBWEC=0\.7\\tau\_\{\\text\{BWEC\}\}\{=\}0\.7\) and Normal \(τBWEC=0\.8\\tau\_\{\\text\{BWEC\}\}\{=\}0\.8\) tiers, all1111tasks, both models, same TPS\-ratio Speedup convention as Table[1](https://arxiv.org/html/2607.28166#S5.T1); the deployedτBWEC=0\.9\\tau\_\{\\text\{BWEC\}\}\{=\}0\.9tier is in Table[1](https://arxiv.org/html/2607.28166#S5.T1)\.
#### An a priori choice, swept only afterward\.

τBWEC=0\.9\\tau\_\{\\text\{BWEC\}\}=0\.9was not tuned on the held\-out examples reported here; we chose it a priori as a conservative confidence level above the final gate’s ownτCVC=0\.7\\tau\_\{\\text\{CVC\}\}=0\.7, and only afterward swept it on a disjoint held\-out sample \(n=50n\{=\}50, GSM8K and MATH\)\. GSM8K plateaus byτBWEC≥0\.85\\tau\_\{\\text\{BWEC\}\}\\geq 0\.85while MATH degrades smoothly as the threshold loosens;0\.90\.9sits just past GSM8K’s knee\.

### G\.2Per\-Block and Total\-Step Behavior, All Tasks

#### The same measurements, extended to all1111tasks, both models\.

Figure[5](https://arxiv.org/html/2607.28166#S5.F5)in the main text shows a44\-task/LLaDA\-only subset; Figures[13](https://arxiv.org/html/2607.28166#A7.F13)–[20](https://arxiv.org/html/2607.28166#A7.F20)repeat the identical protocol across the full1111\-task,22\-model matrix, confirming the same two patterns throughout\. The final block stays near full budget while non\-final blocks empty out \(Figure[14](https://arxiv.org/html/2607.28166#A7.F14)\), and accuracy stays flat on short\-answer tasks while long\-reasoning tasks show the same smooth collapse asτBWEC\\tau\_\{\\text\{BWEC\}\}loosens \(Figures[19](https://arxiv.org/html/2607.28166#A7.F19)–[20](https://arxiv.org/html/2607.28166#A7.F20)\), exactly the dichotomy Section[4\.1](https://arxiv.org/html/2607.28166#S4.SS1)characterizes\.

![Refer to caption](https://arxiv.org/html/2607.28166v1/x12.png)

![Refer to caption](https://arxiv.org/html/2607.28166v1/x13.png)

Figure 13:Per\-block step usage, all short\-answer tasks\.All six general/short\-answer tasks, both models \(same convention as Figure[5](https://arxiv.org/html/2607.28166#S5.F5); LLaDA\-8B\-Instruct top, Dream\-7B\-Instruct bottom\)\. Under LATCH, all six short\-answer tasks complete within one or two blocks for both models\.![Refer to caption](https://arxiv.org/html/2607.28166v1/x14.png)

![Refer to caption](https://arxiv.org/html/2607.28166v1/x15.png)

Figure 14:Per\-block step usage, all long\-reasoning tasks\.All five long\-reasoning tasks, both models \(same convention as Figure[5](https://arxiv.org/html/2607.28166#S5.F5); LLaDA\-8B\-Instruct top, Dream\-7B\-Instruct bottom\)\. The final\-block\-stays\-near\-full\-budget pattern holds throughout; BWEC’s non\-final savings grow block by block under*LATCH*where Prophet and SlowFast do not\.
#### The same per\-block usage, totaled into one bar per method\.

Figures[15](https://arxiv.org/html/2607.28166#A7.F15)and[16](https://arxiv.org/html/2607.28166#A7.F16)lay the same per\-block segments end to end into a single bar per method, with accuracy shown as a thinner bar beneath so step savings can be read against whether they cost accuracy\. At the deployedτBWEC=0\.9\\tau\_\{\\text\{BWEC\}\}\{=\}0\.9, LATCH’s accuracy bar stays within tolerance of*Baseline*’s on every short\-answer task regardless of step\-bar length, though looser tiers and peer methods can deviate more \(e\.g\. TruthfulQA/Dream SlowFast,−7\.5\-7\.5pt\), while on long\-reasoning tasks Prophet’s and SlowFast’s accuracy bars shrink visibly even where their step bars match LATCH’s, the same severe\-drop pattern Table[1](https://arxiv.org/html/2607.28166#S5.T1)reports as numbers\.

![Refer to caption](https://arxiv.org/html/2607.28166v1/x16.png)

![Refer to caption](https://arxiv.org/html/2607.28166v1/x17.png)

Figure 15:Total steps and accuracy, all short\-answer tasks\.Total steps used \(thick bars\) and accuracy \(thin bars beneath\), all six general/short\-answer tasks, both models \(LLaDA\-8B\-Instruct top, Dream\-7B\-Instruct bottom\); same per\-block data as Figure[13](https://arxiv.org/html/2607.28166#A7.F13), concatenated into one bar per method\. At the deployedτBWEC=0\.9\\tau\_\{\\text\{BWEC\}\}\{=\}0\.9, LATCH remains within tolerance throughout; looser tiers and peer methods can deviate\.![Refer to caption](https://arxiv.org/html/2607.28166v1/x18.png)

![Refer to caption](https://arxiv.org/html/2607.28166v1/x19.png)

Figure 16:Total steps and accuracy, all long\-reasoning tasks\.Total steps used \(thick bars\) and accuracy \(thin bars beneath\), all five long\-reasoning tasks, both models \(LLaDA\-8B\-Instruct top, Dream\-7B\-Instruct bottom\); same per\-block data as Figure[14](https://arxiv.org/html/2607.28166#A7.F14), concatenated into one bar per method\. Prophet’s and SlowFast’s accuracy bars shrink visibly relative to*Baseline*’s even where their step bars are comparable in length to LATCH’s\.
#### Per\-block wall\-clock share: which block is actually the bottleneck\.

Figures[17](https://arxiv.org/html/2607.28166#A7.F17)and[18](https://arxiv.org/html/2607.28166#A7.F18)break the same data down by*time*instead of step count; segment width is that block’s share of wall\-clock time, apportioned from the directly\-measured aggregate TPS by step\-count share \(Table[1](https://arxiv.org/html/2607.28166#S5.T1)\), not an independent per\-block measurement\. This makes “final filling” legible; on long\-reasoning tasks, the final block’s time share grows toward the full bar under*LATCH*simply because every other block has been cut so much its fixed cost now dominates\.

![Refer to caption](https://arxiv.org/html/2607.28166v1/x20.png)

![Refer to caption](https://arxiv.org/html/2607.28166v1/x21.png)

Figure 17:Per\-block wall\-clock share and estimated TPS, all short\-answer tasks\.Per\-block time share \(segment width\) and estimated per\-block TPS \(segment label\), all six general/short\-answer tasks, both models \(LLaDA\-8B\-Instruct top, Dream\-7B\-Instruct bottom\); final block outlined in black\. Segment\-level TPS is apportioned from the directly\-measured aggregate TPS \(bold, at bar end\) by step\-count share; see the paragraph above for the exact derivation and its uniform\-per\-step\-cost assumption\.![Refer to caption](https://arxiv.org/html/2607.28166v1/x22.png)

![Refer to caption](https://arxiv.org/html/2607.28166v1/x23.png)

Figure 18:Per\-block wall\-clock share and estimated TPS, all long\-reasoning tasks\.Per\-block time share \(segment width\) and estimated per\-block TPS \(segment label\), all five long\-reasoning tasks, both models \(LLaDA\-8B\-Instruct top, Dream\-7B\-Instruct bottom\); final block outlined in black, growing toward the entire bar under*LATCH*asτBWEC\\tau\_\{\\text\{BWEC\}\}tightens; see the paragraph above for why\.

### G\.3ContinuousτBWEC\\tau\_\{\\text\{BWEC\}\}Sweep

![Refer to caption](https://arxiv.org/html/2607.28166v1/x24.png)

![Refer to caption](https://arxiv.org/html/2607.28166v1/x25.png)

Figure 19:ContinuousτBWEC\\tau\_\{\\text\{BWEC\}\}sweep, all short\-answer tasks\.All six general/short\-answer tasks, both models \(LLaDA\-8B\-Instruct top, Dream\-7B\-Instruct bottom\)\. Solid curves show accuracy \(left axis, Wilson\-score95%95\\%CI\); dashed curves show average Step; dash\-dot curves show TPS\-ratio Speedup relative to each panel’s ownτBWEC=0\.9\\tau\_\{\\text\{BWEC\}\}\{=\}0\.9value, measured independently at eachτBWEC\\tau\_\{\\text\{BWEC\}\}\(Appendix[B](https://arxiv.org/html/2607.28166#A2)\)\. Accuracy is generally stable near the deployed range, whereas more aggressive thresholds degrade several tasks\.![Refer to caption](https://arxiv.org/html/2607.28166v1/x26.png)

![Refer to caption](https://arxiv.org/html/2607.28166v1/x27.png)

Figure 20:ContinuousτBWEC\\tau\_\{\\text\{BWEC\}\}sweep, all long\-reasoning tasks\.All five long\-reasoning tasks, both models \(LLaDA\-8B\-Instruct top, Dream\-7B\-Instruct bottom\)\. Solid curves show accuracy \(left axis, Wilson\-score95%95\\%CI\); dashed curves show average Step; dash\-dot curves show TPS\-ratio Speedup relative to each panel’s ownτBWEC=0\.9\\tau\_\{\\text\{BWEC\}\}\{=\}0\.9value, measured independently at eachτBWEC\\tau\_\{\\text\{BWEC\}\}\(Appendix[B](https://arxiv.org/html/2607.28166#A2)\)\. Across tasks, looseningτBWEC\\tau\_\{\\text\{BWEC\}\}eventually causes substantial accuracy degradation, while Step and TPS\-ratio provide no reliable advance warning\.#### LooseningτBWEC\\tau\_\{\\text\{BWEC\}\}too far can cost speed, not just accuracy\.

BWEC’s force\-commit rule reads as monotonic in isolation; loweringτBWEC\\tau\_\{\\text\{BWEC\}\}should only make commits easier, never require*more*steps\. The three\-tier comparison in Tables[1](https://arxiv.org/html/2607.28166#S5.T1)and[11](https://arxiv.org/html/2607.28166#A7.T11)shows this holds on most tasks under both models, but not all; Figures[19](https://arxiv.org/html/2607.28166#A7.F19)–[20](https://arxiv.org/html/2607.28166#A7.F20)trace the mechanism continuously \(Section[5\.2](https://arxiv.org/html/2607.28166#S5.SS2), a premature commitment corrupts the context later blocks condition on, causing them to consume more steps\)\. On HellaSwag/LLaDA, Step is U\-shaped for exactly this reason, yet TPS\-ratio peaks elsewhere; on HellaSwag/Dream, Step stays flat while TPS\-ratio swings2\.22\.2–2\.8×2\.8\\times\. On GSM8K, accuracy can fall sharply with no corresponding warning in Step at all \(67%→3%67\\%\\\!\\to\\\!3\\%LLaDA,85%→5%85\\%\\\!\\to\\\!5\\%Dream\), the more dangerous failure shape, since nothing in the step count or TPS alone would flag it, which is exactly why threshold choice cannot be made on efficiency metrics alone\. Both are the same confidence\-is\-not\-convergence failure \(Section[4\.2](https://arxiv.org/html/2607.28166#S4.SS2)\) recurring at block scope, and are whyτBWEC\\tau\_\{\\text\{BWEC\}\}’s a priori conservatism \(Section[4](https://arxiv.org/html/2607.28166#S4)\) is not a one\-sided bet against accuracy: on long\-reasoning tasks the downside is not even visible in the metric an aggressive choice is trying to improve\.

## Appendix HLimitations

- •Requires a localizable answer\.CVC needs a*localizable*answer, a short span the task’s own extractor can pull out of the buffer and relocate every step\. Locating that span means searching a task\-specific side of the buffer for a task\-specific value type, a structural prior CVC’s design requires rather than a hyperparameter tuned per task \(Appendix[A\.2](https://arxiv.org/html/2607.28166#A1.SS2)\)\. This holds for every task family evaluated here \(a number, a letter, a boxed expression\), but breaks for tasks with no single extractable answer span at all, code generation being the clearest case; the entire generated program*is*the output, so there is no sub\-span for CVC to track separately from the rest of the buffer, and no extractor generalizes to it\. BWEC alone still applies to non\-final blocks of a multi\-block generation there, but the answer\-verification half of the gate has no defined target, so LATCH’s termination guarantee does not extend to such tasks\.
- •Commits are monotonic\.All of LATCH’s commits are also monotonic; once a position clears BWEC’s threshold or scheduled top\-kkquota, it is never revisited, even if a later step’s now\-richer context would predict it differently\. CVC’s joint gate protects only the final answer span this way; an intermediate reasoning token committed under BWEC’s cheaper, non\-final\-block rule has no equivalent safety net\. A mask\-and\-reconstruct verification pass, checking whether the model’s own updated context would reconstruct the same candidate before committing, could provide an additional safety check, but would require an extra forward pass per candidate, directly competing with the speedup this paper targets; evaluating this trade\-off, and whether the cost is better reinvested to justify a lower, more aggressiveτBWEC\\tau\_\{\\text\{BWEC\}\}, is left to future work\.
- •Extending beyond single localizable answers\.CVC’s verification currently targets one identity\-tracked answer span per example\. Long\-form generation has no single span playing that role, and falling back to whole\-buffer distributional stability would collapse into the same aggregate\-confidence failure mode Section[4\.1](https://arxiv.org/html/2607.28166#S4.SS1)identifies in Prophet, not a genuine extension of CVC’s own logic\. A more promising route decomposes the output into candidate units, each sub\-answer of a multi\-hop response or each function of a generated program, and applies CVC’s identity\-and\-stability test per unit; BWEC’s final\-block asymmetry would also need a different structural prior once no block is privileged this way\. Pursuing this decomposition, and adding distribution\-free risk control\(Xieet al\.,[2026](https://arxiv.org/html/2607.28166#bib.bib53); Wynnet al\.,[2026](https://arxiv.org/html/2607.28166#bib.bib54)\)on top of the empirical tolerance used throughout this paper, are natural next steps\.