Reviser：通过自回归光标动作实现可修订的文本生成

# Reviser: Revision-Capable Text Generation via Autoregressive Cursor Actions
Source: [https://arxiv.org/html/2609.20830](https://arxiv.org/html/2609.20830)
###### Abstract

Revision\-capable generation is appealing because it can insert or revise earlier content, but many non\-autoregressive and edit\-based approaches obtain this flexibility through repeated sequence\-level computation\. We propose Reviser, a decoder\-only Transformer that generates a response as a sequence of cursor\-relative actions on a mutable canvas\. At each step, Reviser predicts exactly one action token:Insert\(token\),Move\(Δ\\Delta\), orStop, and is autoregressive over edit\-history actions rather than final text order\.

This design enables genuinely non\-monotonic generation while preserving a simple next\-action interface\. On a continuation benchmark, Reviser is strongly preferred to SEDD and MDLM in our arena evaluations, and trajectory statistics confirm that the model performs frequent backward moves and mid\-canvas insertions rather than merely emulating end\-append decoding\. Against size\-matched autoregressive baselines, Reviser is competitive at both the 100M and 300M scales\. Under our shared FLOPs convention, Reviser also requires substantially less inference compute than representative multi\-pass refinement and diffusion\-style baselines\.

## 1Introduction

Autoregressive Transformers dominate text generation, but they are structurally biased toward producing content in final left\-to\-right order: once a clause is emitted, correcting it typically requires generating additional text after it rather than directly revising earlier content\(Vaswaniet al\.,[2017](https://arxiv.org/html/2609.20830#bib.bib1); Brownet al\.,[2020](https://arxiv.org/html/2609.20830#bib.bib2)\)\. Revision\-capable and non\-autoregressive methods promise post\-hoc correction and increased parallelism, yet in practice they frequently incur large overhead in the forms of multiple full\-sequence refinement passes, scoring every insertion slot, or many\-step sampling procedures\(Ghazvininejadet al\.,[2019](https://arxiv.org/html/2609.20830#bib.bib5); Guet al\.,[2019](https://arxiv.org/html/2609.20830#bib.bib7); Liet al\.,[2022](https://arxiv.org/html/2609.20830#bib.bib12); Louet al\.,[2024](https://arxiv.org/html/2609.20830#bib.bib13); Sahooet al\.,[2024](https://arxiv.org/html/2609.20830#bib.bib14)\)\. This paper asks: can we get revision\-style generation while keeping total compute close to a standard AR Transformer?

We propose Reviser, which generates by executing a stream of simple cursor edits on a mutable canvas\. In the primary implementation, Reviser uses only insert and move actions \(plusStop\), where “revision” means non\-left\-to\-right insertion into earlier positions; although Reviser naturally supports richer edit operators \(e\.g\.,Delete/Replace/span edits\), we focus here on this minimal insert\+move \(\+Stop\) instantiation and leave destructive editing to future work\. The model is a standard decoder\-only transformer, but crucially, it is autoregressive over action tokens \(the edit history\), not over the final text token order\. Because the cursor can move and insert earlier content, Reviser is not constrained to left\-to\-right generation in the final text order, enabling revision\-like behavior while keeping each model call “normal\-sized\.”

Rather than outputting a distribution over all positions \(or all insertion slots\) at each step, Reviser outputs exactly one cursor\-relative action token per step\. Importantly, the transformer trunk attends only to the action\-history sequenceHtH\_\{t\}; it never attends to canvas tokens directly\. The canvas is implicit in the history of executed actions and is accessed only through validity masking\. This keeps each model call comparable to a standard AR step \(transformer trunk \+ one head\)\. The remaining overhead is the number of action steps, which can be close to the output length in an insert\-dominant regime\.

Beyond text continuation, the cursor\-action formulation also suggests applications to structured editing tasks such as code or document modification\. Modern agent systems often edit files by repeatedly proposing diffs or patches over entire sequences\(Yanget al\.,[2024](https://arxiv.org/html/2609.20830#bib.bib21); Gauthier,[2024](https://arxiv.org/html/2609.20830#bib.bib22)\), which can require multiple full\-sequence passes\. In contrast, Reviser operates through localized insert and move actions on a mutable canvas, which may offer a more natural interface for incremental editing\. We do not evaluate this setting in the current work, but view it as a promising direction for future research\.

A concrete example helps illustrate the behavior; we write the cursor as a vertical bar “\|” between tokens\. In one 300M Reviser generated trajectory \(300M Reviser Example 1 in[Appendix˜E](https://arxiv.org/html/2609.20830#A5)\):

> Before edit Information is deemed correct and is subject to change\. Real estate listings obtained from third party sources are for \| consumers’ personal purchasing decisions and should\.\.\. Actions \(steps 204\-209\) Move\(\-16\)\+Insert\(at the time of publishing\) After move Information is deemed correct at the time of publishing \| and is subject to change\. Real estate listings obtained from third party sources are for\.\.\.

This edit makes the statement more precise\.[Appendix˜E](https://arxiv.org/html/2609.20830#A5)provides full qualitative examples and trajectories\.

##### Contributions\.

1. 1\.We introduce Reviser, a cursor\-action generator that is autoregressive over edit\-history actions rather than final text order\.
2. 2\.We formalize the canvas state, cursor\-based edit operators, validity masking, and deterministic executor updates for the insert\+move\+Stopsetting\.
3. 3\.We describe an obfuscation–restoration supervision scheme for training next\-action predictors on edit trajectories\.
4. 4\.We show empirically that Reviser produces genuinely non\-monotonic trajectories, with frequent backward moves and mid\-canvas insertions\.
5. 5\.We evaluate Reviser on continuation against diffusion and autoregressive baselines, and analyze quality, length behavior, and trajectory statistics\.
6. 6\.We provide an analytic FLOPs\-based comparison showing that Reviser is substantially cheaper than representative multi\-pass refinement and diffusion\-style baselines under a shared convention\.

[Section˜2](https://arxiv.org/html/2609.20830#S2)states the problem setup and design goals, and[Section˜3](https://arxiv.org/html/2609.20830#S3)motivates the compute tradeoffs behind our design\.[Section˜4](https://arxiv.org/html/2609.20830#S4)situates Reviser in prior work\. Section[5](https://arxiv.org/html/2609.20830#S5)–Section[6](https://arxiv.org/html/2609.20830#S6)formalize Reviser and the decoding procedure, and[Section˜7](https://arxiv.org/html/2609.20830#S7)describes supervision via obfuscation–restoration trajectories\.[Section˜8](https://arxiv.org/html/2609.20830#S8)reports empirical results, while[Section˜9](https://arxiv.org/html/2609.20830#S9)–[Section˜11](https://arxiv.org/html/2609.20830#S11)discuss limitations, future directions, and conclusions\. The Appendix provides additional variants, full FLOPs/accounting derivations, qualitative examples, and reproducibility details\.

## 2Problem Setup and Design Goals

Reviser supports prompt\-conditioned generation in general; in this work, we instantiate it as a prefix\-seeding text continuation model: given an input prefixx=\(x1,…,xm\)x=\(x\_\{1\},\\dots,x\_\{m\}\), the goal is to generate the continuation sequence\.

To make the prefix visible to the history\-only model, we write it into both the canvas and the action history via a deterministic insert\-only prefix\-seeding action sequence:

Apref​\(x\)=\(Insert​\(x1\),Insert​\(x2\),…,Insert​\(xm\)\)\.A^\{\\text\{pref\}\}\(x\)\\;=\\;\\bigl\(\\text\{\{Insert\}\}\(x\_\{1\}\),\\,\\text\{\{Insert\}\}\(x\_\{2\}\),\\,\\dots,\\,\\text\{\{Insert\}\}\(x\_\{m\}\)\\bigr\)\.ExecutingApref​\(x\)A^\{\\text\{pref\}\}\(x\)from a blank canvas places each prefix token on the canvas in order, sets the cursor at positionmm, and makes the full prefix content visible to the transformer through its action\-history inputHtH\_\{t\}\. Continuation decoding then begins from this seeded state, with a validity mask that prevents edits to the prefix region\.

Our design goal is to support revision\-capable generation, the ability to insert or modify earlier content during decoding, while keeping the compute profile close to a standard AR transformer\.

We aim to avoid common sources of overhead in prior NAR approaches: \(i\) repeated full\-sequence refinement passes, \(ii\) per\-step scoring over all positions/slots, \(iii\) large per\-position action heads, and \(iv\) sampling procedures requiring many denoiser steps\. Reviser instead makes a single cursor\-relative decision per step using a standard transformer trunk and a single action head\.

We evaluate \(a\) generation quality \(evalPPL under GPT\-2 Large and arena pairwise win rates\), \(b\) compute \(FLOPs\), and \(c\) trajectory behavior \(steps/token, move fraction, cursor travel, insertion locations\)\.

Table 1:Notation used throughout the paper \(core variables\)\.
## 3Compute Tradeoffs in Existing NAR and Edit\-Based Transformers

Many non\-autoregressive and edit\-based Transformers obtain flexibility or parallelism by repeating expensive sequence\-level computation multiple times per response\(Leeet al\.,[2018](https://arxiv.org/html/2609.20830#bib.bib4); Ghazvininejadet al\.,[2019](https://arxiv.org/html/2609.20830#bib.bib5); Guet al\.,[2019](https://arxiv.org/html/2609.20830#bib.bib7); Liet al\.,[2022](https://arxiv.org/html/2609.20830#bib.bib12); Louet al\.,[2024](https://arxiv.org/html/2609.20830#bib.bib13); Sahooet al\.,[2024](https://arxiv.org/html/2609.20830#bib.bib14)\)\. Under a shared FLOPs convention, this often leads to substantially higher total inference compute than a standard autoregressive baseline\. Our goal in this section is not to claim that all such methods are inefficient in practice, but rather to highlight a common tradeoff: repeated full\-sequence prediction can raise total compute even when sequential dependence is reduced\.

In our FLOPs accounting \([Appendix˜B](https://arxiv.org/html/2609.20830#A2)\), an AR baseline produces a length\-nnresponse with one full\-sequence evaluation\. By contrast, most NAR families run multiple full\-sequence evaluations \(refinement iterations, insertion rounds, denoising steps, etc\.\), so they repeatedly pay the dominant Transformer trunk cost over allnnpositions\.

A single full\-sequence evaluation computes hidden states for allnnpositions and then applies a vocab projection, yieldingn×\|V\|n\\times\|V\|logits\. At modern scales, both terms matter: the full Transformer pass is expensive, and the vocab head is also large and non\-negligible \(e\.g\.,\|V\|≈50​k\|V\|\\approx 50\\text\{k\}\)\. Methods that performRRrefinement/denoising iterations therefore multiply both costs by roughlyRRper response, often with additional task\-specific heads, slot\-scoring loops, or auxiliary passes\. In several families,RRis large: for example, CMLM commonly uses aroundR=10R=10refinement passes, while diffusion\-style decoders often useR=Tdec∈\[200,2000\]R=T\_\{\\text\{dec\}\}\\in\[200,2000\]reverse steps\. This repeated sequence\-level evaluation is highly inefficient at inference time, especially for long outputs or throughput\-limited deployment\.

For overall efficiency, especially at scale, the dominant quantity is often total FLOPs per response\. If a method is10×10\\timesmore compute\-intensive, modest systems\-level scheduling gains usually do not offset that gap\. Total compute is therefore the primary constraint for training cost, energy, and throughput\-limited deployments\. We report a compute multiplier

Iinferℳ≜FinferℳFinferAR,I\_\{\\text\{infer\}\}^\{\\mathcal\{M\}\}\\;\\triangleq\\;\\frac\{F\_\{\\text\{infer\}\}^\{\\mathcal\{M\}\}\}\{F\_\{\\text\{infer\}\}^\{\\text\{AR\}\}\},whereFinferℳF\_\{\\text\{infer\}\}^\{\\mathcal\{M\}\}is the total FLOPs to generate a full length\-nnresponse under methodℳ\\mathcal\{M\}’s decoding procedure\. In this section and appendix, we focus onFinferℳF\_\{\\text\{infer\}\}^\{\\mathcal\{M\}\}andIinferℳI\_\{\\text\{infer\}\}^\{\\mathcal\{M\}\}as the primary compute indicators\.

[Table˜2](https://arxiv.org/html/2609.20830#S3.T2)summarizes our computed multipliers relative to the AR baseline \(derivations in the Appendix\)\. With few exceptions, popular NAR Transformers require significantly more total compute than AR, often by an order of magnitude or more\. The methods that appear closer to AR in compute typically rely on highly parallel, one\-/few\-shot predictions; in practice these variants struggle due to the parallel decoding issue \(below\), and are commonly augmented with iterative refinement, which reintroduces the repeated\-pass overhead\.

The most compute\-efficient NAR variants attempt to predict many \(or all\) output tokens simultaneously\. This creates a global coordination problem: each position must choose a token that is compatible with the \(unknown\) choices at other positions\. Formally, one\-shot NAR variants often behave like a product\-of\-marginals approximation\(Guet al\.,[2018](https://arxiv.org/html/2609.20830#bib.bib3)\),

p​\(y∣x\)≈∏i=1np​\(yi∣x\),p\(y\\mid x\)\\approx\\prod\_\{i=1\}^\{n\}p\(y\_\{i\}\\mid x\),which cannot reliably enforce inter\-token constraints without extra structure \(latents, constraints, or iterative refinement\)\. In practice, this manifests as agreement errors, repetition, missing required entities, and internal contradictions, motivating additional passes that raise compute\.

Method \(family / variant\)Decoding structureIinferℳI\_\{\\text\{infer\}\}^\{\\mathcal\{M\}\}Parallel decoding issue?AR \(baseline\)nnAR steps1\.001\.00NoReviser \(this work\)TrestT\_\{\\text\{rest\}\}AR\-style steps1\.251\.25–1\.501\.50†NoLevT \(iterative edit/refine\)R∈\{5,10\}R\\in\\\{5,10\\\}passes6\.916\.91–19\.4019\.40YesInsT \(balanced\-tree\)log2⁡n\\log\_\{2\}npasses2\.022\.02YesInsT \(serial\)nnpasses65\.0165\.01NoCMLM / Mask\-Predict \(Tmp=10T\_\{\\text\{mp\}\}\{=\}10\)10 passes11\.8611\.86YesDiffusion\-LM \(Tdec=200T\_\{\\text\{dec\}\}\{=\}200–20002000\)200–2000 passes140\.51140\.51–1,402\.361,402\.36NoOne\-shot NAT \(few\-pass\)1 enc \+ 1 dec pass1\.961\.96YesTable 2:Analytic inference\-compute summary under a shared FLOPs convention \(computed in the Appendix\)\.Iinferℳ≜Finferℳ/FinferARI\_\{\\text\{infer\}\}^\{\\mathcal\{M\}\}\\triangleq F\_\{\\text\{infer\}\}^\{\\mathcal\{M\}\}/F\_\{\\text\{infer\}\}^\{\\text\{AR\}\}is the total inference FLOPs multiplier of methodℳ\\mathcal\{M\}relative to AR; values are structural estimates, not measured wall\-clock latency\.†\\daggerRange shown forpmove∈\{0\.20,0\.28,0\.33\}p\_\{\\text\{move\}\}\\in\\\{0\.20,0\.28,0\.33\\\}atn=128n=128\(including observed move fractions from[Table˜10](https://arxiv.org/html/2609.20830#S8.T10)\); see[Section˜C\.1\.2](https://arxiv.org/html/2609.20830#A3.SS1.SSS2)\. For AR/Reviser, “steps” denotes KV\-cached next\-token/next\-action decoding; “passes” for other methods denotes repeated full\-sequence evaluations\. “Parallel decoding issue” marks families whose highly parallel variants often underperform due to global coordination constraints, commonly motivating additional refinement passes\. Further details of all calculations are provided in[Appendix˜B](https://arxiv.org/html/2609.20830#A2)\.Reviser avoids the parallel\-decoding coordination issue by predicting one cursor\-relative action token at a time, conditioned on the full prior edit history\. This keeps global coherence through autoregressive dependence while still allowing non\-monotonic canvas edits\. It also avoids repeated full\-sequence refinement: each step is a standard AR\-style next\-action pass, rather than repeated re\-evaluation over allnnoutput positions\. If the move fraction ispmovep\_\{\\text\{move\}\}, producingnnfinal tokens takes an expectedneff=n1−pmoven\_\{\\text\{eff\}\}=\\frac\{n\}\{1\-p\_\{\\text\{move\}\}\}action steps, so

IinferReviser​\(n\)≈FinferAR​\(neff\)FinferAR​\(n\)\.I\_\{\\text\{infer\}\}^\{\\text\{Reviser\}\}\(n\)\\approx\\frac\{F\_\{\\text\{infer\}\}^\{\\text\{AR\}\}\(n\_\{\\text\{eff\}\}\)\}\{F\_\{\\text\{infer\}\}^\{\\text\{AR\}\}\(n\)\}\.Forpmove∈\{0\.20,0\.28,0\.33\}p\_\{\\text\{move\}\}\\in\\\{0\.20,0\.28,0\.33\\\}andn=128n=128, this givesneff∈\{160,177\.78,191\.04\}n\_\{\\text\{eff\}\}\\in\\\{160,\\;177\.78,\\;191\.04\\\}andIinferReviser​\(128\)∈\{1\.25,1\.39,1\.50\}I\_\{\\text\{infer\}\}^\{\\text\{Reviser\}\}\(128\)\\in\\\{$1\.25$,\\;$1\.39$,\\;$1\.50$\\\}\.

## 4Related Work

Reviser is closest to non\-autoregressive and partially autoregressive generation that relaxes strict left\-to\-right decoding\. Early one\-shot NAT models improve parallelism but face multimodality and coordination issues\(Guet al\.,[2018](https://arxiv.org/html/2609.20830#bib.bib3)\); iterative variants such as deterministic refinement and Mask\-Predict improve quality by repeating full\-sequence passes\(Leeet al\.,[2018](https://arxiv.org/html/2609.20830#bib.bib4); Ghazvininejadet al\.,[2019](https://arxiv.org/html/2609.20830#bib.bib5)\)\. Reviser targets the same non\-monotonic capability, but keeps a one\-action interface per step instead of repeated sequence\-level prediction\.

Our approach is also related to insertion and edit\-based generation\. Insertion Transformer and Levenshtein Transformer show that insertion/deletion operations can realize flexible generation orders\(Sternet al\.,[2019](https://arxiv.org/html/2609.20830#bib.bib6); Guet al\.,[2019](https://arxiv.org/html/2609.20830#bib.bib7)\)\. Text\-edit tagging systems such as LaserTagger and FELIX frame generation as edit prediction over an existing sequence\(Malmiet al\.,[2019](https://arxiv.org/html/2609.20830#bib.bib8); Mallinsonet al\.,[2020](https://arxiv.org/html/2609.20830#bib.bib9)\)\. Many of these methods were introduced and evaluated primarily in sequence transduction settings \(especially machine translation and grammatical\-error\-correction style tasks\), rather than open\-ended continuation generation\. PIE\-style post\-editing formulations make a similar design choice by treating generation as targeted rewriting rather than pure left\-to\-right continuation\. Reviser is in the same family of ideas, but uses explicit cursor actions with deterministic executor semantics\.

Diffusion\-style LMs provide another route to non\-monotonic generation\. Diffusion\-LM, SEDD, and MDLM decouple final token order from AR factorization through denoising trajectories\(Liet al\.,[2022](https://arxiv.org/html/2609.20830#bib.bib12); Louet al\.,[2024](https://arxiv.org/html/2609.20830#bib.bib13); Sahooet al\.,[2024](https://arxiv.org/html/2609.20830#bib.bib14)\)\. More recent semi\-AR or block\-diffusion variants, including LLaDA, Dream, and SDLM \(analyzed in our Appendix FLOPs section\), further explore the quality and throughput tradeoff by mixing iterative denoising with partial autoregressive structure\.

Latent\-variable NAR models are also relevant\. Flow\-based sequence generators such as FlowSeq model conditional generation through invertible latent transformations instead of strict tokenwise AR decoding\(Maet al\.,[2019](https://arxiv.org/html/2609.20830#bib.bib10)\)\. This line is conceptually close in its goal of relaxing left\-to\-right constraints, though its modeling interface differs from explicit executable edit actions\.

Reviser also relates to work on non\-left\-to\-right autoregression\. XLNet demonstrates permutation\-based autoregressive objectives over factorization orders\(Yanget al\.,[2019](https://arxiv.org/html/2609.20830#bib.bib11)\), and insertion\-based AR models similarly depart from fixed final\-token order\(Sternet al\.,[2019](https://arxiv.org/html/2609.20830#bib.bib6)\)\. Reviser differs by making edit history itself the autoregressive object: one cursor\-relative action per step, executed immediately on a mutable canvas\.

Our positioning is therefore narrow: Reviser uses cursor\-relative actions over a mutable canvas, predicts exactly one next action token at a time, and applies edits through a deterministic executor\. This preserves revision capability while keeping the decoding interface close to standard next\-token prediction and, empirically, much closer to AR compute than multi\-pass refinement families\.

## 5Reviser Formalism: State, Actions, and Executor

Reviser maintains a mutable canvas and a cursor indicating the insertion boundary\. At each step, the model reads the history of past actions \(action tokens\), applies validity masking using\(Ct,ut\)\(C\_\{t\},u\_\{t\}\), and predicts one next action token \(Insert / Move / Stop\)\. An external executor applies the action to update the canvas and cursor\. In the prefix\-seeding setting, the canvas and action history are pre\-seeded withApref​\(x\)A^\{\\text\{pref\}\}\(x\)before continuation decoding begins\.[Figure˜1](https://arxiv.org/html/2609.20830#S5.F1)illustrates one decoding step\.

### 5\.1State and Canvas Representation

A generation state at stepttis

st=\(Ct,ut,Ht\),s\_\{t\}\\;=\\;\(C\_\{t\},u\_\{t\},H\_\{t\}\),where:

- •Ct=\(ct,1,…,ct,ℓt\)C\_\{t\}=\(c\_\{t,1\},\\dots,c\_\{t,\\ell\_\{t\}\}\)is the canvas token sequence at steptt, with canvas lengthℓt\\ell\_\{t\},
- •ut∈\{0,1,…,ℓt\}u\_\{t\}\\in\\\{0,1,\\dots,\\ell\_\{t\}\\\}is the cursor index between tokens \(0 means before the first token\),
- •HtH\_\{t\}is the edit history at continuation steptt\(the action sequence executed so far\)\. In the prefix\-seeding setting,H1=Apref​\(x\)H\_\{1\}=A^\{\\text\{pref\}\}\(x\)and, fort≥1t\\geq 1,Ht=\(Apref​\(x\),a1,…,at−1\)H\_\{t\}=\(A^\{\\text\{pref\}\}\(x\),a\_\{1\},\\dots,a\_\{t\-1\}\), whereaia\_\{i\}are continuation actions\.

Reviser uses a standard decoder\-only transformer that consumes the sequence of past action tokensHtH\_\{t\}and predicts the next action tokenata\_\{t\}\.

Current state at stepttDecoder\-only Transformerautoregressive overedit\-history actionsHtH\_\{t\}Apply validity maskfrom\(Ct,ut\)\(C\_\{t\},u\_\{t\}\)to logitsdisallow invalid moves / insertsNext\-actiondistributionInsert\(language\)Move\(\+2\)StopChosen actionat=a\_\{t\}=Insert\(language\)ExecutorApplyata\_\{t\}to updatecanvas, cursor, and historyUpdated state at stept\+1t\+1Canvas:The \| model can revise earlier text\.Cursor:utu\_\{t\}History:Ht=\(a1,…,at−1\)H\_\{t\}=\(a\_\{1\},\\dots,a\_\{t\-1\}\)Canvas:The language \| model can revise earlier text\.Cursor:ut\+1u\_\{t\+1\}History:Ht\+1=\(a1,…,at\)H\_\{t\+1\}=\(a\_\{1\},\\dots,a\_\{t\}\)

Figure 1:Reviser decoding at a single step\. The model is autoregressive over edit\-history actions rather than final text order\. At each step it predicts exactly one cursor\-relative action, applies a validity mask derived from the current canvas state, and then uses a deterministic executor to update the canvas, cursor, and history\.
### 5\.2Action Space \(Primary Implementation\)

The action vocabulary is

Va=Vc⏟Insert​\(token\)∪ℳ⏟Move​\(Δ\)∪\{Stop\}\.V\_\{a\}\\;=\\;\\underbrace\{V\_\{c\}\}\_\{\\text\{\{Insert\}\}\(\\text\{token\}\)\}\\;\\cup\\;\\underbrace\{\\mathcal\{M\}\}\_\{\\text\{\{Move\}\}\(\\Delta\)\}\\;\\cup\\;\\\{\\text\{\{Stop\}\}\\\}\.HereVcV\_\{c\}is the normal token vocabulary \(each token corresponds to anInsertaction\), andℳ\\mathcal\{M\}is a small discrete set of move actions \(e\.g\.,Δ∈\{±1,±2,±4,…\}\\Delta\\in\\\{\\pm 1,\\pm 2,\\pm 4,\\dots\\\}\)\.Stopends generation\.

### 5\.3Executor: Canvas Update Mathematics

LetCt=\(ct,1,…,ct,ℓt\)C\_\{t\}=\(c\_\{t,1\},\\dots,c\_\{t,\\ell\_\{t\}\}\)and cursorut∈\{0,…,ℓt\}u\_\{t\}\\in\\\{0,\\dots,\\ell\_\{t\}\\\}\.

For an insertion of tokenx∈Vcx\\in V\_\{c\}at cursor boundaryut∈\{0,…,ℓt\}u\_\{t\}\\in\\\{0,\\dots,\\ell\_\{t\}\\\},

Insert\(x\):Ct\+1=\(ct,1,…,ct,ut,x,ct,ut\+1,…,ct,ℓt\),ut\+1=ut\+1\.\\text\{\{Insert\}\}\(x\):\\quad C\_\{t\+1\}\\;=\\;\(c\_\{t,1\},\\dots,c\_\{t,u\_\{t\}\},x,c\_\{t,u\_\{t\}\+1\},\\dots,c\_\{t,\\ell\_\{t\}\}\),\\qquad u\_\{t\+1\}=u\_\{t\}\+1\.
For a displacementΔ∈ℤ\\Delta\\in\\mathbb\{Z\}chosen fromℳ\\mathcal\{M\},

Move\(Δ\):Ct\+1=Ct,ut\+1=ut\+Δ\.\\text\{\{Move\}\}\(\\Delta\):\\quad C\_\{t\+1\}=C\_\{t\},\\qquad u\_\{t\+1\}=u\_\{t\}\+\\Delta\.We enforce the post\-state constraintut\+1∈\{0,…,ℓt\+1\}u\_\{t\+1\}\\in\\\{0,\\dots,\\ell\_\{t\+1\}\\\}via validity masking \(forMove,ℓt\+1=ℓt\\ell\_\{t\+1\}=\\ell\_\{t\}\)\.

Stop:terminate and outputCt\.\\text\{\{Stop\}\}:\\quad\\text\{terminate and output \}C\_\{t\}\.

### 5\.4Validity Masking

At each step, Reviser constructs a valid\-action mask based on\(Ct,ut\)\(C\_\{t\},u\_\{t\}\), for example:

- •forbid movesMove​\(Δ\)\\text\{\{Move\}\}\(\\Delta\)such thatut\+Δ∉\{0,…,ℓt\+1\}u\_\{t\}\+\\Delta\\notin\\\{0,\\dots,\\ell\_\{t\+1\}\\\}\(equivalently\{0,…,ℓt\}\\\{0,\\dots,\\ell\_\{t\}\\\}forMove\),
- •forbid inserting ifℓt\\ell\_\{t\}has reached a maximum length,
- •optionally forbid inserting certain reserved tokens\.

Masking is applied to the action logits before sampling/argmax\.

## 6Model

### 6\.1Edit\-History Transformer

LetHtH\_\{t\}be the edit\-history action tokens at continuation steptt\. In prefix\-seeding decoding,Ht=\(Apref​\(x\),a1,…,at−1\)H\_\{t\}=\(A^\{\\text\{pref\}\}\(x\),a\_\{1\},\\dots,a\_\{t\-1\}\)\. We use a single shared embedding tableE∈ℝ\|Va\|×dE\\in\\mathbb\{R\}^\{\|V\_\{a\}\|\\times d\}for all action tokens \(including token\-valuedInsertactions,Moveactions, andStop\), and a positional embedding tableP\(H\)∈ℝTmax×dP^\{\(H\)\}\\in\\mathbb\{R\}^\{T\_\{\\max\}\\times d\}for edit\-history positions\. The history\-token embeddings are

eτ=E​\[aτ\]\+P\(H\)​\[τ\],τ=1,…,t−1\.e\_\{\\tau\}\\;=\\;E\[a\_\{\\tau\}\]\+P^\{\(H\)\}\[\\tau\],\\qquad\\tau=1,\\dots,t\-1\.A standard causal transformer processes\(e1,…,et−1\)\(e\_\{1\},\\dots,e\_\{t\-1\}\)and produces hidden states\(h1,…,ht−1\)\(h\_\{1\},\\dots,h\_\{t\-1\}\)\. The next\-action logits are

rt=Wout​ht−1\+bout,p​\(at∣Ht,Ct\)=softmax​\(rt\+mt\),r\_\{t\}\\;=\\;W\_\{\\text\{out\}\}\\,h\_\{t\-1\}\+b\_\{\\text\{out\}\},\\quad p\(a\_\{t\}\\mid H\_\{t\},C\_\{t\}\)\\;=\\;\\mathrm\{softmax\}\\\!\\big\(r\_\{t\}\+m\_\{t\}\\big\),wheremtm\_\{t\}applies the validity mask computed from\(Ct,ut\)\(C\_\{t\},u\_\{t\}\)\(invalid actions get−∞\-\\infty\)\. In our experiments, the trunk depends only onHtH\_\{t\}; the canvas enters through the executed action sequence \(which determines what the model has seen\) and through masking\. Optional designs that add an explicit canvas summaryμt\\mu\_\{t\}\(attention pooling\) or cross\-attention to canvas token representations are described in[Sections˜A\.2](https://arxiv.org/html/2609.20830#A1.SS2)and[A\.3](https://arxiv.org/html/2609.20830#A1.SS3)\.

In the prefix\-seeding setting, the prefixx=\(x1,…,xm\)x=\(x\_\{1\},\\dots,x\_\{m\}\)enters the model exclusively through the seeded action history: themmprefix\-seeding actionsApref​\(x\)=\(Insert​\(x1\),…,Insert​\(xm\)\)A^\{\\text\{pref\}\}\(x\)=\(\\text\{\{Insert\}\}\(x\_\{1\}\),\\dots,\\text\{\{Insert\}\}\(x\_\{m\}\)\)occupy the firstmmpositions ofHtH\_\{t\}, so the transformer’s self\-attention over edit\-history tokens directly attends to the full prefix content\. No separate encoder or prefix embedding is required; the prefix is fully visible through the standard action\-history input stream, and a validity mask applied during continuation decoding prevents the model from editing the prefix region of the canvas\.

### 6\.2Generation Algorithm

Algorithm 1Reviser decoding \(insert\+move primary implementation\)1:Input prefix

x=\(x1,…,xm\)x=\(x\_\{1\},\\dots,x\_\{m\}\)\(may be empty\), max steps

TmaxT\_\{\\max\}, max canvas length

LmaxL\_\{\\max\}
2:Phase 1: Prefix seeding

3:Initialize canvas

C←\(\)C\\leftarrow\(\), cursor

u←0u\\leftarrow 0, history

H←\(\)H\\leftarrow\(\)
4:for

i=1,…,mi=1,\\dots,mdo

5:Apply

Insert​\(xi\)\\text\{\{Insert\}\}\(x\_\{i\}\):

C←\(C,xi\)C\\leftarrow\(C,x\_\{i\}\),

u←u\+1u\\leftarrow u\+1,

H←\(H,Insert​\(xi\)\)H\\leftarrow\(H,\\text\{\{Insert\}\}\(x\_\{i\}\)\)
6:endfor

7:Set

C1←CC\_\{1\}\\\!\\leftarrow\\\!C,

u1←mu\_\{1\}\\\!\\leftarrow\\\!m,

H1←HH\_\{1\}\\\!\\leftarrow\\\!H⊳\\trianglerightH1=Apref​\(x\)H\_\{1\}=A^\{\\text\{pref\}\}\(x\); canvas=x=x; cursor atmm

8:Phase 2: Continuation decoding

9:for

t=1,2,…,Tmaxt=1,2,\\dots,T\_\{\\max\}do

10:Compute action logits

rt←fθ​\(Ht\)r\_\{t\}\\leftarrow f\_\{\\theta\}\(H\_\{t\}\)⊳\\trianglerightoptionally supply a canvas summary; see Appendix

11:Construct validity mask

mt←Mask​\(Ct,ut,Lmax,\|x\|\)m\_\{t\}\\leftarrow\\textsc\{Mask\}\(C\_\{t\},u\_\{t\},L\_\{\\max\},\|x\|\)⊳\\trianglerightdisallow edits to prompt\-prefix

12:Choose action

at∼softmax​\(rt\+mt\)a\_\{t\}\\sim\\mathrm\{softmax\}\(r\_\{t\}\+m\_\{t\}\)
13:if

at=Stopa\_\{t\}=\\text\{\{Stop\}\}then

14:return

CtC\_\{t\}
15:else

16:Apply executor update

\(Ct\+1,ut\+1\)←Exec​\(Ct,ut,at\)\(C\_\{t\+1\},u\_\{t\+1\}\)\\leftarrow\\textsc\{Exec\}\(C\_\{t\},u\_\{t\},a\_\{t\}\)
17:Append to history

Ht\+1←\(Ht,at\)H\_\{t\+1\}\\leftarrow\(H\_\{t\},a\_\{t\}\)
18:endif

19:endfor

20:return

CTmax\+1C\_\{T\_\{\\max\}\+1\}⊳\\trianglerightfallback if noStop

[Algorithm˜1](https://arxiv.org/html/2609.20830#alg1)gives the decoding loop\. The loop terminates whenStopis chosen \(or a maximum step budget is reached\)\. Algorithm[1](https://arxiv.org/html/2609.20830#alg1)has two phases\. Phase 1 \(prefix\-seeding\) is deterministic: it replays the prefix asmminsert actions, writingxxonto the canvas and buildingH1=Apref​\(x\)H\_\{1\}=A^\{\\text\{pref\}\}\(x\)in the action history\. No model call is made during Phase 1\. Phase 2 \(continuation decoding\) is autoregressive: the model conditions on the full seeded historyHtH\_\{t\}\(which begins withApref​\(x\)A^\{\\text\{pref\}\}\(x\)\) and samples continuation actions one at a time\. Because the prefix tokens appear as action\-history entries, the model’s self\-attention directly observes prefix content at every continuation step without any additional encoder\.

## 7Learning and Training

### 7\.1Worked Example: Edit History Trajectory

This section first shows a sample non\-monotonic trajectory in[Figure˜2](https://arxiv.org/html/2609.20830#S7.F2), then gives a separate worked obfuscation–restoration trajectory in[Table˜3](https://arxiv.org/html/2609.20830#S7.T3)\. We render the cursor as a vertical bar “\|\|” between tokens\.

Step 0\[The model revise earlier text \| \]Step 1Action:Insert\(efficiently\) \[The model revise earlier text efficiently \| \]Step 2Action:Move\(\-4\) \[The model \| revise earlier text efficiently \]Step 3Action:Insert\(can\) \[The model can \| revise earlier text efficiently \]Step 4Action:Move\(\+4\) \[The model can revise earlier text efficiently \| \]Step 5Action:Insert\(\.\) \[The model can revise earlier text efficiently\. \| \]Step 6Action:Stop Final output: The model can revise earlier text efficiently\.

Figure 2:Illustrative Reviser trajectory\. The model need not generate in final left\-to\-right order: it first appends a word to the end \(Step 1\), then moves the cursor backward \(Step 2\), inserts another word into the middle of the canvas \(Step 3\), returns to the end \(Step 4\), appends a period \(Step 5\), and stops \(Step 6\)\. This non\-monotonic pattern, backward moves followed by mid\-canvas insertions, is common in large\-scale trajectory statistics, not an edge case\.Obfuscation \(target→\\rightarrowblank\)Restoration \(blank→\\rightarrowtarget\)1\.Initial
\[Hi,\|how are you?\]2\.Delete
\[Hi\|how are you?\]3\.Delete
\[\|how are you?\]4\.Move​\(\+4\)\\text\{\{Move\}\}\(\+4\)
\[how are you?\|\]5\.Delete
\[how are you\|\]6\.Delete
\[how are\|\]7\.Delete
\[how\|\]8\.Delete
\[\|\]1\.Initial
\[\|\]2\.Insert\(how\)
\[how\|\]3\.Insert\(are\)
\[how are\|\]4\.Insert\(you\)
\[how are you\|\]5\.Insert\(?\)
\[how are you?\|\]6\.Move​\(−4\)\\text\{\{Move\}\}\(\-4\)
\[\|how are you?\]7\.Insert\(Hi\)
\[Hi\|how are you?\]8\.Insert\(,\)
\[Hi,\|how are you?\]9\.Stop
\[Hi,\|how are you?\]Table 3:Side\-by\-side obfuscation and restoration trajectory for a full continuation without a prefix\.Reviser is trained to predict the next action token under teacher forcing on action trajectories\. Training follows the same two\-phase structure as decoding: a deterministic prefix\-seeding phaseApref​\(x\)A^\{\\text\{pref\}\}\(x\)seeds the canvas and action history, followed by a learned restoration phaseArest​\(y\)A^\{\\text\{rest\}\}\(y\)over the continuation target; NLL is computed only overArest​\(y\)A^\{\\text\{rest\}\}\(y\)\. Given a restoration trajectoryArest=\(a1,…,aT\)A^\{\\text\{rest\}\}=\(a\_\{1\},\\dots,a\_\{T\}\), we minimize the standard negative log\-likelihood:

ℒ​\(θ\)=−∑t=1Tlog⁡pθ​\(at∣st\)\.\\mathcal\{L\}\(\\theta\)\\;=\\;\-\\sum\_\{t=1\}^\{T\}\\log p\_\{\\theta\}\(a\_\{t\}\\mid s\_\{t\}\)\.

### 7\.2Obfuscation–Restoration Supervision \(Main Training Procedure\)

Algorithm 2Obfuscation–restoration trajectory generation \(primary implementation\)1:Target tokens

y=\(y1,…,yn\)y=\(y\_\{1\},\\dots,y\_\{n\}\), move set

ℳ\\mathcal\{M\}, max steps

KmaxK\_\{\\max\}
2:Initialize canvas

C←yC\\leftarrow y; initialize cursor

u←Uniform​\(\{0,…,n\}\)u\\leftarrow\\textsc\{Uniform\}\(\\\{0,\\dots,n\\\}\)
3:Initialize empty obfuscation action list

B←\(\)B\\leftarrow\(\)and empty metadata list

𝒟←\(\)\\mathcal\{D\}\\leftarrow\(\)
4:for

k=1,2,…,Kmaxk=1,2,\\dots,K\_\{\\max\}do

5:if

\|C\|=0\|C\|=0thenbreak

6:endif

7:Sample an obfuscation action

bk∼πobf\(⋅∣C,u\)b\_\{k\}\\sim\\pi\_\{\\text\{obf\}\}\(\\cdot\\mid C,u\)fromDeleteor a move actionMove\(

Δ\\Delta\), using validity masking

8:if

bk=Deleteb\_\{k\}=\\text\{\{Delete\}\}then

9:Let

x←cux\\leftarrow c\_\{u\}be the token immediately left of the cursor boundary

10:Delete

xxfrom

CCand update cursor

u←u−1u\\leftarrow u\-1
11:Append

xxto

𝒟\\mathcal\{D\}
12:else

13:Apply cursor move

u←u\+Δu\\leftarrow u\+\\Delta
14:endif

15:Append

bkb\_\{k\}to

BB
16:endfor

17:Let

nobf←\|B\|n\_\{\\text\{obf\}\}\\leftarrow\|B\|
18:Construct restoration actions

A←\(\)A\\leftarrow\(\)by iterating

BBfrom last to first:

19:Treat

𝒟\\mathcal\{D\}as a LIFO stack for deleted\-token replay

20:for

k=nobf,nobf−1,…,1k=n\_\{\\text\{obf\}\},n\_\{\\text\{obf\}\}\-1,\\dots,1do

21:if

bk=Deleteb\_\{k\}=\\textsc\{Delete\}then

22:pop

xxfrom

𝒟\\mathcal\{D\}and append

Insert​\(x\)\\text\{\{Insert\}\}\(x\)to

AA
23:else

24:append

Move​\(−Δ\)\\text\{\{Move\}\}\(\-\\Delta\)to

AA
25:endif

26:endfor

27:AppendStopto

AA;returnobfuscated start state and restoration trajectory

AA

[Algorithm˜2](https://arxiv.org/html/2609.20830#alg2)specifies the offline trajectory\-construction procedure used for supervision\. It samples an obfuscation sequence over the continuation canvas, records deleted tokens, and then builds the restoration sequence by reversing and inverting the obfuscation actions, finally appendingStop\.

We construct training data using paired trajectories \(see[Table˜3](https://arxiv.org/html/2609.20830#S7.T3)for a concrete side\-by\-side example\): \(i\) an obfuscation trajectory that transforms a target sequence into a blank canvas state, and \(ii\) a restoration trajectoryArest​\(y\)A^\{\\text\{rest\}\}\(y\)that transforms the blank state back to the target\. The full supervised sequence for a document split into prefixxxand continuation targetyyis

A=\(Apref​\(x\),Arest​\(y\)\),A\\;=\\;\\bigl\(A^\{\\text\{pref\}\}\(x\),\\;A^\{\\text\{rest\}\}\(y\)\\bigr\),whereApref​\(x\)=\(Insert​\(x1\),…,Insert​\(xm\)\)A^\{\\text\{pref\}\}\(x\)=\(\\text\{\{Insert\}\}\(x\_\{1\}\),\\dots,\\text\{\{Insert\}\}\(x\_\{m\}\)\)is the deterministic prefix\-seeding phase andArest​\(y\)A^\{\\text\{rest\}\}\(y\)is the restoration trajectory over the continuation targety=\(y1,…,yn\)y=\(y\_\{1\},\\dots,y\_\{n\}\)\. In richer action spaces that include temporary obfuscation\-only insertions later removed by restoration deletes, those transient insertions are excluded from the loss because they are often random/noise tokens introduced only to create states that include delete actions, not meaningful target\-response content\. In our primary experiments \(insert\+move\+Stopaction set at training and test time\), obfuscation/restoration is applied only toyy\(the prompt prefixxxis not edited\), and we construct obfuscations using only deletions and moves, with restoration defined as the inverse mapping \(each obfuscation deletion becomes an insertion of the deleted token, and each obfuscation move becomes the opposite move\)\.

We generate an obfuscation trajectory by initializing the editable canvas to the continuation target and inserting the cursor at a uniformly random editable boundary, i\.e\.,C←yC\\leftarrow yandu∼Uniform​\(\{0,…,\|y\|\}\)u\\sim\\mathrm\{Uniform\}\(\\\{0,\\dots,\|y\|\\\}\)\. At each obfuscation step, we sample an action from a simple state\-dependent random policy with validity masking: with probability0\.80\.8we applyDelete, which deletes the token immediately to the left of the cursor; with probability0\.20\.2we apply a move actionMove\(Δ\\Delta\), whereΔ\\Deltais sampled uniformly from the set of valid moves \(i\.e\., those satisfyingu\+Δ∈\{0,…,ℓ\}u\+\\Delta\\in\\\{0,\\dots,\\ell\\\}\)\. We store the resulting obfuscation action sequence asB=\(b1,…,bnobf\)B=\(b\_\{1\},\\dots,b\_\{n\_\{\\text\{obf\}\}\}\), wherenobfn\_\{\\text\{obf\}\}is the number of obfuscation steps until termination\. For each deletion step, we additionally record the identity of the deleted token in temporal order in an aligned side list𝒟=\(d1,…,dndel\)\\mathcal\{D\}=\(d\_\{1\},\\dots,d\_\{n\_\{\\text\{del\}\}\}\), wherendeln\_\{\\text\{del\}\}is the number of deletions inBB\.

We represent cursor moves using a finite discrete set of displacementsℳ\\mathcal\{M\}\. In our implementation we use powers\-of\-two jumps up to a maximum displacement:

ℳ=\{±2k∣k∈ℤ≥0,2k≤max\_move\}\.\\mathcal\{M\}\\;=\\;\\\{\\,\\pm 2^\{k\}\\mid k\\in\\mathbb\{Z\}\_\{\\geq 0\},\\;2^\{k\}\\leq\\text\{max\\\_move\}\\,\\\}\.At each step, we form the state\-dependent valid subsetℳ​\(Ct,ut\)=\{Δ∈ℳ:ut\+Δ∈\{0,…,ℓt\}\}\\mathcal\{M\}\(C\_\{t\},u\_\{t\}\)=\\\{\\Delta\\in\\mathcal\{M\}:u\_\{t\}\+\\Delta\\in\\\{0,\\dots,\\ell\_\{t\}\\\}\\\}and sampleΔ\\Deltauniformly fromℳ​\(Ct,ut\)\\mathcal\{M\}\(C\_\{t\},u\_\{t\}\)\.

We terminate obfuscation when the editable canvas is empty \(i\.e\.,ℓ=0\\ell=0, leaving only the cursor boundary\)\. If an obfuscation trajectory fails to reachℓ=0\\ell=0within a maximum step budgetKmaxK\_\{\\max\}, we discard the sample and resample a new trajectory\.

Given an obfuscation trajectoryB=\(b1,…,bnobf\)B=\(b\_\{1\},\\dots,b\_\{n\_\{\\text\{obf\}\}\}\)and deleted\-token metadata𝒟=\(d1,…,dndel\)\\mathcal\{D\}=\(d\_\{1\},\\dots,d\_\{n\_\{\\text\{del\}\}\}\), we construct a restoration trajectoryA=\(a1,…,aT\)A=\(a\_\{1\},\\dots,a\_\{T\}\)by scanningBBfrom last to first and replacing each obfuscation action with its inverse restoration action\. We treat𝒟\\mathcal\{D\}as a stack in temporal order and, whenever the reversed scan encounters aDelete, we pop the most recently deleted token from𝒟\\mathcal\{D\}\(LIFO order\)\. For eachk=nobf,nobf−1,…,1k=n\_\{\\text\{obf\}\},n\_\{\\text\{obf\}\}\-1,\\dots,1, we emit a restoration action

a←\{Insert​\(x\)​where​x=pop​\(𝒟\)if​bk=Delete,Move​\(−Δ\)if​bk=Move​\(Δ\),a\\;\\leftarrow\\;\\begin\{cases\}\\text\{\{Insert\}\}\(x\)\\text\{ where \}x=\\mathrm\{pop\}\(\\mathcal\{D\}\)&\\text\{if \}b\_\{k\}=\\textsc\{Delete\},\\\\ \\textsc\{Move\}\(\-\\Delta\)&\\text\{if \}b\_\{k\}=\\textsc\{Move\}\(\\Delta\),\\end\{cases\}and append these emitted actions in the scan order to formAA\. Finally, we appendStopafter the last restorative edit\. In this strict\-inverse construction, we produce one restoration action per obfuscation action, henceTrest=nobf\+1T\_\{\\text\{rest\}\}=n\_\{\\text\{obf\}\}\+1\. ExecutingAAfrom a blank canvas state deterministically reconstructs the target sequence and cursor position\.

This reverse\-inverse construction is a simple but effective supervision source\. Reversing the obfuscation trajectory yields restoration actions that are guaranteed to be state\-consistent with the executor dynamics, so each training target is a valid next edit for the current canvas/cursor state rather than a synthetic label detached from state\. In practice, this generates dense edit\-history data that teaches the model to repair a corrupted canvas into a coherent sequence using the same action interface used at inference, which we find produces strong generation quality and robust non\-monotonic editing behavior\.

Instead of strict inverse mapping, restoration trajectories can be constructed by \(i\) an oracle policy, \(ii\) alignment/diff procedures, \(iii\) dynamic programming, or \(iv\) constrained search; and one can also use human text\-edit traces, aggregate trajectories under the learned policy \(DAgger\), or fine\-tune with RL\. We discuss these variants in the Appendix \([Sections˜A\.4](https://arxiv.org/html/2609.20830#A1.SS4)and[A\.5](https://arxiv.org/html/2609.20830#A1.SS5)\)\.

Because the model’s actions affect future states, naive supervised learning can suffer from compounding error\. We consider two standard remedies: \(i\) dataset aggregation \(DAgger\-style\), where we roll out the learned policy and label visited states with an oracle action\(Rosset al\.,[2011](https://arxiv.org/html/2609.20830#bib.bib16)\), and \(ii\) reinforcement learning fine\-tuning \(e\.g\., PPO\-style\), where rewards are defined over completed trajectories\(Schulmanet al\.,[2017](https://arxiv.org/html/2609.20830#bib.bib17)\)\. In the reported experiments, we use supervised learning only \(teacher forcing on restoration trajectories\), without DAgger or RL fine\-tuning \(see Appendix[Sections˜A\.4](https://arxiv.org/html/2609.20830#A1.SS4)and[A\.5](https://arxiv.org/html/2609.20830#A1.SS5)\)\.

##### Limitations of synthetic restoration trajectories\.

Our training data is constructed by applying random obfuscation trajectories and training the model to invert them\. While this provides a simple and scalable source of supervision, these trajectories do not reflect the structure of humanlike editing behavior\. In particular, human edits are typically purposeful and context\-dependent, involving targeted insertions, deletions, and refinements rather than random perturbations\. As a result, the learned editing policies may differ from those that would arise from training on naturally occurring edit sequences\. We expect that training on datasets of real edits, such as document revision histories or code editing traces, could yield more efficient and semantically meaningful editing strategies\.

## 8Experiments

### 8\.1Setup

We evaluate Reviser on a C4 continuation benchmark built from the English validation split ofallenai/c4\(Raffelet al\.,[2020](https://arxiv.org/html/2609.20830#bib.bib25)\), comparing against autoregressive baselines at matched scales and non\-autoregressive diffusion baselines\. We pre\-filter examples to total GPT\-2 token length 144 to 216, use a 35\-token prefix, and evaluate continuation quality toward a 180\-token total sequence target\.

We report results for two Reviser checkpoints: 100M and 300M\. For the SEDD/MDLM comparison, we evaluate three seeds \(123,124,125\) with 1000 prompts per seed \(3000 total per model\)\. All main\-text results use decoding with a maximum of 256 actions\. For the diffusion baselines, both SEDD and MDLM are decoded with 128 diffusion steps\. For models we train ourselves, we use matched 30B\-token budgets: the trained AR baselines are trained on 30B text tokens, and Reviser models are trained on 30B edit\-history tokens \(includingMovetokens\)\. Because about 20% of Reviser training actions areMoveactions, Reviser is exposed to fewer word tokens than the AR models under this matched token\-budget accounting\.

We report two metric families\. First, we run pairwise 1v1 with\-input arenas where the judge sees the prompt and both candidate continuations and selects a winner\. For each arena example, we randomize candidate order \(which model is shown as A vs\. B\) before constructing the judge input\. We use Skywork\-Critic\-8B\(Skywork AI Alignment Team,[2024](https://arxiv.org/html/2609.20830#bib.bib20)\)as the judge throughout all arena comparisons\. Second, evalPPL is computed on continuation tokens \(lower is better\), using two evaluator backbones: an autoregressive evaluator \(GPT\-2 Large;Radfordet al\.,[2019](https://arxiv.org/html/2609.20830#bib.bib27)\) and a diffusion\-style evaluator \(Dream\-7B;Yeet al\.,[2025](https://arxiv.org/html/2609.20830#bib.bib28)\)\. Reporting both reduces evaluator\-family bias for Reviser’s nonstandard edit\-action generation interface\. We do not report regular teacher\-forced PPL over Reviser action sequences because restoration trajectories are randomized and non\-unique for a given final continuation, so trajectory\-level likelihood is not a canonical, directly comparable quantity\. Unless otherwise noted, all benchmark and arena results in this section are computed on 3000 samples\. For reproducibility, code/configs/results are available athttps://github\.com/Sean\-Diab/Reviser, and released Reviser checkpoints are available athttps://huggingface\.co/sean\-diab/reviser\-checkpoints\.

### 8\.2Reviser vs\. AR Baseline \(100M and 300M\)

We compare Reviser against autoregressive transformers of identical architecture trained on FineWeb data\(Penedoet al\.,[2024](https://arxiv.org/html/2609.20830#bib.bib26)\)\(the same distribution used to train Reviser\) at both 100M and 300M scales\. Throughout this section, we refer to these models as the AR baseline at each scale\. This is a challenging setting: the AR model is on its home data and optimises the exact objective that evalPPL measures\. Results are shown in[Table˜4](https://arxiv.org/html/2609.20830#S8.T4)\. The judge prefers Reviser at both scales:61\.361\.3% vs\.38\.738\.7% at 100M, and54\.454\.4% vs\.45\.645\.6% at 300M\.

Table 4:Reviser vs\. AR baseline at 100M and 300M: arena win rates\.Table 5:Reviser vs\. AR baseline at 100M and 300M: evalPPL results \(C4 decoding\)\. Lower is better\.Although Reviser has higher evalPPL than the AR baseline in[Table˜5](https://arxiv.org/html/2609.20830#S8.T5), its arena results remain strong \([Table˜4](https://arxiv.org/html/2609.20830#S8.T4)\)\. A likely reason is metric mismatch across generation paradigms: evalPPL is computed with an autoregressive scorer, while Reviser decodes via edit actions\. The very high evalPPL values observed for SEDD/MDLM in[Table˜8](https://arxiv.org/html/2609.20830#S8.T8)are consistent with this effect\.

### 8\.3Reviser vs\. AR Baselines

We evaluate Reviser in direct 1v1 arena matchups against a range of publicly available autoregressive models at roughly size\-matched scales\. All pairwise arena matchups in this subsection use 3000 samples per comparison\.

Table 6:Reviser vs\. AR baselines at 100M and 300M scales: arena win rates under Skywork\-Critic\-8B\.At 100M scale, Reviser is preferred to all four AR baselines in this comparison, with especially large margins against Cerebras\-GPT\-111M\(Deyet al\.,[2023](https://arxiv.org/html/2609.20830#bib.bib24)\)and Pythia\-160M\(Bidermanet al\.,[2023](https://arxiv.org/html/2609.20830#bib.bib29)\)\. At 300M scale, Reviser remains competitive: it strongly outperforms Cerebras\-GPT\-256M and is approximately tied with Pythia\-410M, GPT\-2 Medium\(Radfordet al\.,[2019](https://arxiv.org/html/2609.20830#bib.bib27)\), and OPT\-350M\(Zhanget al\.,[2022](https://arxiv.org/html/2609.20830#bib.bib30)\)\. Overall, these AR comparisons indicate a robust and promising profile\.

### 8\.4Results: Reviser vs\. SEDD and MDLM

[Table˜7](https://arxiv.org/html/2609.20830#S8.T7)reports arena win rates against both diffusion baselines and shows that Reviser wins all three matchups, with its largest margin against SEDD Small 169M \(85\.9385\.93% vs\.14\.0714\.07%\), followed by MDLM 170M \(78\.3378\.33% vs\.21\.6721\.67%\), and SEDD Absorb 353M \(68\.4768\.47% vs\.31\.5331\.53%\)\.[Table˜8](https://arxiv.org/html/2609.20830#S8.T8)reports the corresponding evalPPL values and shows the same qualitative pattern: Reviser is much lower than SEDD/MDLM under both evaluators at both available scales\. MDLM does not have a comparable 300M checkpoint in our setup, so we omit MDLM\-300M comparisons\.

Table 7:Reviser vs\. SEDD and MDLM: arena win rates\.Table 8:Reviser vs\. SEDD and MDLM: evalPPL results \(C4 decoding\)\. Lower is better\. MDLM 300M is omitted because no comparable checkpoint is available in this setup\.
### 8\.5MAUVE

We also report MAUVE\(Pillutlaet al\.,[2021](https://arxiv.org/html/2609.20830#bib.bib31)\)under a shared\-3k protocol \([Table˜9](https://arxiv.org/html/2609.20830#S8.T9)\): 3000 shared C4 examples, with references and model outputs truncated to 100 tokens, and BERT pseudo\-loglikelihood features used for MAUVE computation\. MAUVE measures distributional overlap between model outputs and references, with higher values indicating closer distributional match\.

Table 9:Combined MAUVE results on the shared 3000\-example C4 subset, using BERT pseudo\-loglikelihood features and 100\-token truncation for both references and model outputs\. Higher is better\.[Table˜9](https://arxiv.org/html/2609.20830#S8.T9)shows that Reviser 300M achieves the strongest MAUVE in this comparison, while diffusion baselines \(SEDD/MDLM\) are substantially lower, consistent with the arena and evalPPL trends\.

### 8\.6Trajectory Statistics

[Table˜10](https://arxiv.org/html/2609.20830#S8.T10)shows that Reviser uses the edit interface in a strongly non\-AR way\. Move actions are frequent, backward moves dominate, and almost all insertions are non\-end \(mid\-canvas\) insertions\. In every evaluated example, the trajectory contains at least one backward revision event, confirming that the model is not merely emulating a pure end\-append decoder\.

Statistic \(averaged across seeds\)100M300MActions per output token1\.511\.511\.401\.40Insert fraction67%72%Move fraction33%28%Mean\|Δ\|\|\\Delta\|move distance4\.924\.926\.056\.05Move\-distance mass on 1/2/4/8 moves \(%\)40\.5, 23\.3, 15\.8, 10\.037\.4, 22\.7, 15\.5, 11\.1Fraction backward moves65\.565\.5%64\.564\.5%Mean insertion relative position0\.410\.410\.420\.42Fraction end\-appends \(cursor at end\)3\.93\.9%3\.13\.1%Fraction non end\-appends96\.196\.1%96\.996\.9%Examples with≥1\\geq 1backward revision100%100%Table 10:Reviser trajectory diagnostics in decoding\. “Backward revision” means at least one backward move followed by subsequent insertion into an earlier canvas region\.

## 9Limitations

Reviser is sequential in action space, so decoding is not fully parallelizable over final\-token positions\. As a result, throughput is still constrained by step\-by\-step generation, even though the model can revise non\-monotonically\.

Quality also depends on the supervision trajectories\. Because training is based on synthetic obfuscation–restoration paths, performance can degrade under distribution shift and may exhibit compounding error when the model visits states that are weakly represented in training data\.

The primary insert\+move action set supports flexible revision, but some edits may require longer trajectories than richer operators \(e\.g\., delete/replace\)\. In addition, the history\-only trunk must maintain an implicit representation of the current canvas from the edit\-history stream\. In our reported runs, we did not observe this as a practical bottleneck, even for long trajectories, which is consistent with model capacity at 100M/300M\. If needed, explicit state\-conditioning mechanisms such as pooled canvas embeddings or cross\-attention to canvas representations \([Sections˜A\.2](https://arxiv.org/html/2609.20830#A1.SS2)and[A\.3](https://arxiv.org/html/2609.20830#A1.SS3)\) provide direct mitigation\.

## 10Future Work

The current results suggest several clear directions for improving Reviser\. The main opportunities are to expand the action space beyond insert\+move, strengthen state conditioning beyond the current history\-only trunk, and move beyond fixed synthetic restoration trajectories toward training procedures that better reflect the model’s own inference\-time distribution\. More broadly, we view the present system as a proof of concept for autoregression over edit actions, and expect future variants to improve both output quality and editing efficiency while preserving the lightweight one\-action decoding interface\.

##### Learning beyond supervised trajectories\.

While we train Reviser using supervised restoration trajectories, an important next step is to move from synthetic trajectories to real edit supervision, e\.g\., human editing traces where people iteratively revise drafts, document revision histories, or code editing logs\. The action\-based interface is also compatible with more flexible training paradigms such as reinforcement learning or dataset aggregation \(DAgger; see Appendix[Sections˜A\.4](https://arxiv.org/html/2609.20830#A1.SS4)and[A\.5](https://arxiv.org/html/2609.20830#A1.SS5)\)\. In principle, any editing idea that can be represented as a token \(or short token sequence\) can be emitted by the transformer as an executable edit action, opening a broad and creative design space for richer supervision and editing behavior\. Together, these approaches could allow the model to learn editing strategies under its own distribution, rather than following fixed trajectories\. We leave empirical investigation of these directions to future work\.

##### Flexible generation order as a potential advantage\.

A key property of Reviser is that it can build outputs in whatever order is useful for the task, rather than being constrained to final left\-to\-right token order\. This gives the model an explicit draft\-and\-revise mechanism during generation: it can insert provisional content, move backward, and refine earlier regions before stopping\. We hypothesize that, if learned reliably at scale, this flexibility may provide a meaningful quality advantage over strictly AR decoding, particularly in settings where iterative revision is important\.

##### Structured editing and agent\-based applications\.

Beyond text continuation, the cursor\-action formulation also suggests applications to structured editing tasks such as code or document modification\. Modern agent systems typically edit files by proposing diffs or patches over whole sequences\(Yanget al\.,[2024](https://arxiv.org/html/2609.20830#bib.bib21); Gauthier,[2024](https://arxiv.org/html/2609.20830#bib.bib22)\); this can be inference\-inefficient, since the model must spend tokens to emit a diff/patch command rather than directly editing the target content\. In contrast, Reviser operates through localized cursor actions on a mutable canvas, which may provide a more direct interface for incremental editing\. In such settings, richer edit operators such asDelete,Replace, or span\-level edits would likely make editing substantially more efficient by allowing the model to modify existing content directly rather than simulating corrections through longer insert\-and\-move trajectories\. This structural alignment suggests the potential for more efficient editing workflows\.

## 11Conclusion

Reviser shows that a simple autoregressive\-over\-edits decoder, seeded with a deterministic prefix\-seeding history and then decoding continuations via cursor actions, can produce genuinely non\-monotonic text generation with a lightweight next\-action interface\. Across our experiments, the model performs frequent backward moves and mid\-canvas insertions, is strongly preferred to the diffusion baselines we tested, and is competitive with roughly size\-matched AR baselines\. Overall, these results provide a strong example that edit\-history autoregression is a practical and scalable path to models that can actively revise and improve their responses during generation\.

## References

- J\. Austin, D\. D\. Johnson, J\. Ho, D\. Tarlow, and R\. van den Berg \(2021\)Structured denoising diffusion models in discrete state\-spaces\.Advances in Neural Information Processing Systems\.Cited by:[§C\.2\.3](https://arxiv.org/html/2609.20830#A3.SS2.SSS3.p1.1)\.
- S\. Biderman, H\. Schoelkopf, Q\. Anthony, H\. Bradley, K\. O’Brien, E\. Hallahan, M\. A\. Khan, S\. Purohit, U\. S\. Prashanth, E\. Raff, A\. Skowron, L\. Sutawika, and O\. van der Wal \(2023\)Pythia: a suite for analyzing large language models across training and scaling\.InInternational Conference on Machine Learning,Cited by:[§8\.3](https://arxiv.org/html/2609.20830#S8.SS3.p2.1)\.
- T\. B\. Brown, B\. Mann, N\. Ryder, M\. Subbiah, J\. D\. Kaplan, P\. Dhariwal, A\. Neelakantan, P\. Shyam, G\. Sastry, A\. Askell, A\. Herbert\-Voss, G\. Krueger, T\. Henighan, R\. Child, A\. Ramesh, D\. Ziegler, J\. Wu, C\. Winter, C\. Hesse, M\. Chen, E\. Sigler, M\. Litwin, S\. Gray, B\. Chess, J\. Clark, C\. Berner, S\. McCandlish, A\. Radford, I\. Sutskever, and D\. Amodei \(2020\)Language models are few\-shot learners\.InAdvances in Neural Information Processing Systems,Cited by:[§1](https://arxiv.org/html/2609.20830#S1.p1.1)\.
- N\. Dey, G\. Gosal, Z\. Khachane, W\. Marshall, R\. Pathria, M\. Tom, and J\. Hestness \(2023\)Cerebras\-GPT: open compute\-optimal language models trained on the Pile\.Technical reportCerebras Systems\.Note:arXiv preprint arXiv:2304\.03208Cited by:[§8\.3](https://arxiv.org/html/2609.20830#S8.SS3.p2.1)\.
- P\. Gauthier \(2024\)Aider: ai pair programming in your terminal\.Note:GitHub repository,[https://github\.com/Aider\-AI/aider](https://github.com/Aider-AI/aider)Cited by:[§1](https://arxiv.org/html/2609.20830#S1.p4.1),[§10](https://arxiv.org/html/2609.20830#S10.SS0.SSS0.Px3.p1.1)\.
- M\. Ghazvininejad, O\. Levy, Y\. Liu, and L\. Zettlemoyer \(2019\)Mask\-predict: parallel decoding of conditional masked language models\.InProceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing \(EMNLP\-IJCNLP\),Cited by:[§C\.4\.4](https://arxiv.org/html/2609.20830#A3.SS4.SSS4.p1.1),[§1](https://arxiv.org/html/2609.20830#S1.p1.1),[§3](https://arxiv.org/html/2609.20830#S3.p1.1),[§4](https://arxiv.org/html/2609.20830#S4.p1.1)\.
- J\. Gu, J\. Bradbury, C\. Xiong, V\. O\. K\. Li, and R\. Socher \(2018\)Non\-autoregressive neural machine translation\.InInternational Conference on Learning Representations,Cited by:[§C\.4\.3](https://arxiv.org/html/2609.20830#A3.SS4.SSS3.p1.1),[§3](https://arxiv.org/html/2609.20830#S3.p6.1),[§4](https://arxiv.org/html/2609.20830#S4.p1.1)\.
- J\. Gu, C\. Wang, and J\. Zhao \(2019\)Levenshtein transformer\.InAdvances in Neural Information Processing Systems,Cited by:[§C\.4\.1](https://arxiv.org/html/2609.20830#A3.SS4.SSS1.p1.7),[§1](https://arxiv.org/html/2609.20830#S1.p1.1),[§3](https://arxiv.org/html/2609.20830#S3.p1.1),[§4](https://arxiv.org/html/2609.20830#S4.p2.1)\.
- J\. Lee, E\. Mansimov, and K\. Cho \(2018\)Deterministic non\-autoregressive neural sequence modeling by iterative refinement\.InConference on Empirical Methods in Natural Language Processing,Cited by:[§3](https://arxiv.org/html/2609.20830#S3.p1.1),[§4](https://arxiv.org/html/2609.20830#S4.p1.1)\.
- X\. L\. Li, J\. Thickstun, I\. Gulrajani, P\. S\. Liang, and T\. B\. Hashimoto \(2022\)Diffusion\-lm improves controllable text generation\.Advances in Neural Information Processing Systems\.Cited by:[§C\.2\.4](https://arxiv.org/html/2609.20830#A3.SS2.SSS4.p1.2),[§1](https://arxiv.org/html/2609.20830#S1.p1.1),[§3](https://arxiv.org/html/2609.20830#S3.p1.1),[§4](https://arxiv.org/html/2609.20830#S4.p3.1)\.
- A\. Lou, C\. Meng, and S\. Ermon \(2024\)Discrete diffusion modeling by estimating the ratios of the data distribution\.InInternational Conference on Machine Learning,Cited by:[§C\.2\.1](https://arxiv.org/html/2609.20830#A3.SS2.SSS1.p1.1),[§1](https://arxiv.org/html/2609.20830#S1.p1.1),[§3](https://arxiv.org/html/2609.20830#S3.p1.1),[§4](https://arxiv.org/html/2609.20830#S4.p3.1)\.
- X\. Ma, C\. Zhou, X\. Li, G\. Neubig, and E\. Hovy \(2019\)FlowSeq: non\-autoregressive conditional sequence generation with generative flow\.InProceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing \(EMNLP\-IJCNLP\),Cited by:[§4](https://arxiv.org/html/2609.20830#S4.p4.1)\.
- J\. Mallinson, A\. Severyn, E\. Malmi, and G\. Garrido \(2020\)FELIX: flexible text editing through tagging and insertion\.InFindings of the Association for Computational Linguistics: EMNLP 2020,Cited by:[§4](https://arxiv.org/html/2609.20830#S4.p2.1)\.
- E\. Malmi, S\. Krause, S\. Rothe, D\. Mirylenka, and A\. Severyn \(2019\)Encode, tag, realize: high\-precision text editing\.InProceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing \(EMNLP\-IJCNLP\),Cited by:[§4](https://arxiv.org/html/2609.20830#S4.p2.1)\.
- G\. Penedo, H\. Kydlíček, L\. Ben Allal, A\. Lozhkov, M\. Mitchell, C\. Raffel, L\. Von Werra, and T\. Wolf \(2024\)The FineWeb datasets: decanting the web for the finest text data at scale\.InAdvances in Neural Information Processing Systems,Cited by:[§8\.2](https://arxiv.org/html/2609.20830#S8.SS2.p1.4)\.
- K\. Pillutla, S\. Swayamdipta, R\. Zellers, J\. Thickstun, S\. Welleck, Y\. Choi, and Z\. Harchaoui \(2021\)MAUVE: measuring the gap between neural text and human text using divergence frontiers\.InAdvances in Neural Information Processing Systems,Cited by:[§8\.5](https://arxiv.org/html/2609.20830#S8.SS5.p1.1)\.
- A\. Radford, J\. Wu, R\. Child, D\. Luan, D\. Amodei, and I\. Sutskever \(2019\)Language models are unsupervised multitask learners\.OpenAI technical report\.Cited by:[§8\.1](https://arxiv.org/html/2609.20830#S8.SS1.p3.1),[§8\.3](https://arxiv.org/html/2609.20830#S8.SS3.p2.1)\.
- C\. Raffel, N\. Shazeer, A\. Roberts, K\. Lee, S\. Narang, M\. Matena, Y\. Zhou, W\. Li, and P\. J\. Liu \(2020\)Exploring the limits of transfer learning with a unified text\-to\-text transformer\.Journal of Machine Learning Research21\(140\),pp\. 1–67\.Cited by:[§8\.1](https://arxiv.org/html/2609.20830#S8.SS1.p1.1)\.
- S\. Ross, G\. Gordon, and D\. Bagnell \(2011\)A reduction of imitation learning and structured prediction to no\-regret online learning\.InInternational Conference on Artificial Intelligence and Statistics,Cited by:[§A\.4](https://arxiv.org/html/2609.20830#A1.SS4.p1.1),[§7\.2](https://arxiv.org/html/2609.20830#S7.SS2.p9.1)\.
- S\. S\. Sahoo, M\. Arriola, A\. Gokaslan, E\. M\. Marroquin, A\. M\. Rush, Y\. Schiff, J\. T\. Chiu, and V\. Kuleshov \(2024\)Simple and effective masked diffusion language models\.InAdvances in Neural Information Processing Systems,Cited by:[§C\.2\.2](https://arxiv.org/html/2609.20830#A3.SS2.SSS2.p1.1),[§1](https://arxiv.org/html/2609.20830#S1.p1.1),[§3](https://arxiv.org/html/2609.20830#S3.p1.1),[§4](https://arxiv.org/html/2609.20830#S4.p3.1)\.
- J\. Schulman, F\. Wolski, P\. Dhariwal, A\. Radford, and O\. Klimov \(2017\)Proximal policy optimization algorithms\.arXiv preprint arXiv:1707\.06347\.Cited by:[§7\.2](https://arxiv.org/html/2609.20830#S7.SS2.p9.1)\.
- Skywork AI Alignment Team \(2024\)Skywork\-Critic\-Llama\-3\.1\-8B\.Note:Hugging Face model card,[https://huggingface\.co/Skywork/Skywork\-Critic\-Llama\-3\.1\-8B](https://huggingface.co/Skywork/Skywork-Critic-Llama-3.1-8B)Cited by:[§8\.1](https://arxiv.org/html/2609.20830#S8.SS1.p3.1)\.
- M\. Stern, W\. Chan, J\. Kiros, and J\. Uszkoreit \(2019\)Insertion transformer: flexible sequence generation via insertion operations\.InInternational Conference on Machine Learning,Cited by:[§C\.4\.2](https://arxiv.org/html/2609.20830#A3.SS4.SSS2.p1.2),[§4](https://arxiv.org/html/2609.20830#S4.p2.1),[§4](https://arxiv.org/html/2609.20830#S4.p5.1)\.
- A\. Vaswani, N\. Shazeer, N\. Parmar, J\. Uszkoreit, L\. Jones, A\. N\. Gomez, L\. Kaiser, and I\. Polosukhin \(2017\)Attention is all you need\.InAdvances in Neural Information Processing Systems,Cited by:[§1](https://arxiv.org/html/2609.20830#S1.p1.1)\.
- J\. Yang, C\. Jimenez, A\. Wettig, K\. Lieret, S\. Yao, K\. Pei, O\. Press, and K\. Narasimhan \(2024\)SWE\-agent: agent\-computer interfaces enable automated software engineering\.arXiv preprint arXiv:2405\.15793\.Cited by:[§1](https://arxiv.org/html/2609.20830#S1.p4.1),[§10](https://arxiv.org/html/2609.20830#S10.SS0.SSS0.Px3.p1.1)\.
- Z\. Yang, Z\. Dai, Y\. Yang, J\. Carbonell, R\. Salakhutdinov, and Q\. V\. Le \(2019\)XLNet: generalized autoregressive pretraining for language understanding\.InAdvances in Neural Information Processing Systems,Cited by:[§4](https://arxiv.org/html/2609.20830#S4.p5.1)\.
- J\. Ye, Z\. Xie, L\. Zheng, J\. Gao, Z\. Wu, X\. Jiang, Z\. Li, and L\. Kong \(2025\)Dream 7b: diffusion large language models\.arXiv preprint arXiv:2508\.15487\.Cited by:[§8\.1](https://arxiv.org/html/2609.20830#S8.SS1.p3.1)\.
- S\. Zhang, S\. Roller, N\. Goyal, M\. Artetxe, M\. Chen, S\. Chen, C\. Dewan, M\. Diab, X\. Li, X\. V\. Lin, T\. Mihaylov, M\. Ott, S\. Shleifer, K\. Shuster, D\. Simig, P\. S\. Koura, A\. Sridhar, T\. Wang, and L\. Zettlemoyer \(2022\)OPT: open pre\-trained transformer language models\.arXiv preprint arXiv:2205\.01068\.Cited by:[§8\.3](https://arxiv.org/html/2609.20830#S8.SS3.p2.1)\.

###### Contents

1. [1Introduction](https://arxiv.org/html/2609.20830#S1)
2. [2Problem Setup and Design Goals](https://arxiv.org/html/2609.20830#S2)
3. [3Compute Tradeoffs in Existing NAR and Edit\-Based Transformers](https://arxiv.org/html/2609.20830#S3)
4. [4Related Work](https://arxiv.org/html/2609.20830#S4)
5. [5Reviser Formalism: State, Actions, and Executor](https://arxiv.org/html/2609.20830#S5)1. [5\.1State and Canvas Representation](https://arxiv.org/html/2609.20830#S5.SS1) 2. [5\.2Action Space \(Primary Implementation\)](https://arxiv.org/html/2609.20830#S5.SS2) 3. [5\.3Executor: Canvas Update Mathematics](https://arxiv.org/html/2609.20830#S5.SS3) 4. [5\.4Validity Masking](https://arxiv.org/html/2609.20830#S5.SS4)
6. [6Model](https://arxiv.org/html/2609.20830#S6)1. [6\.1Edit\-History Transformer](https://arxiv.org/html/2609.20830#S6.SS1) 2. [6\.2Generation Algorithm](https://arxiv.org/html/2609.20830#S6.SS2)
7. [7Learning and Training](https://arxiv.org/html/2609.20830#S7)1. [7\.1Worked Example: Edit History Trajectory](https://arxiv.org/html/2609.20830#S7.SS1) 2. [7\.2Obfuscation–Restoration Supervision \(Main Training Procedure\)](https://arxiv.org/html/2609.20830#S7.SS2)
8. [8Experiments](https://arxiv.org/html/2609.20830#S8)1. [8\.1Setup](https://arxiv.org/html/2609.20830#S8.SS1) 2. [8\.2Reviser vs\. AR Baseline \(100M and 300M\)](https://arxiv.org/html/2609.20830#S8.SS2) 3. [8\.3Reviser vs\. AR Baselines](https://arxiv.org/html/2609.20830#S8.SS3) 4. [8\.4Results: Reviser vs\. SEDD and MDLM](https://arxiv.org/html/2609.20830#S8.SS4) 5. [8\.5MAUVE](https://arxiv.org/html/2609.20830#S8.SS5) 6. [8\.6Trajectory Statistics](https://arxiv.org/html/2609.20830#S8.SS6)
9. [9Limitations](https://arxiv.org/html/2609.20830#S9)
10. [10Future Work](https://arxiv.org/html/2609.20830#S10)
11. [11Conclusion](https://arxiv.org/html/2609.20830#S11)
12. [References](https://arxiv.org/html/2609.20830#bib)
13. [AAdditional Reviser Variants](https://arxiv.org/html/2609.20830#A1)1. [A\.1Other Edit Operators](https://arxiv.org/html/2609.20830#A1.SS1) 2. [A\.2Conditioning on the Canvas Representations via Pooled Canvas Embeddings](https://arxiv.org/html/2609.20830#A1.SS2) 3. [A\.3Cross\-Attention to Canvas Representations](https://arxiv.org/html/2609.20830#A1.SS3) 4. [A\.4DAgger with an Alignment\-Based Oracle](https://arxiv.org/html/2609.20830#A1.SS4) 5. [A\.5Reinforcement Learning Fine\-Tuning](https://arxiv.org/html/2609.20830#A1.SS5)
14. [BPrior Work Mechanisms and FLOPs\-Based Efficiency Accounting](https://arxiv.org/html/2609.20830#A2)1. [B\.1Goal and definitions \(FLOPs\-based, shared constants across models\)](https://arxiv.org/html/2609.20830#A2.SS1) 2. [B\.2Primitive FLOPs functions](https://arxiv.org/html/2609.20830#A2.SS2)
15. [CModel\-by\-model FLOPs accounting](https://arxiv.org/html/2609.20830#A3)1. [C\.1Group 1\. Anchors](https://arxiv.org/html/2609.20830#A3.SS1) 2. [C\.2Group 2\. Diffusion NAR LMs \(100M\)](https://arxiv.org/html/2609.20830#A3.SS2) 3. [C\.3Group 3: Large\-Scale Diffusion NAR LMs](https://arxiv.org/html/2609.20830#A3.SS3) 4. [C\.4Group 4\. Refinement NAR LMs \(MT\)](https://arxiv.org/html/2609.20830#A3.SS4)
16. [DMore Qualitative Examples](https://arxiv.org/html/2609.20830#A4)1. [D\.1Obfuscation–Restoration Trajectory Example](https://arxiv.org/html/2609.20830#A4.SS1)
17. [ESelected Ranked Responses and Restoration Trajectories](https://arxiv.org/html/2609.20830#A5)1. [E\.1100M Examples](https://arxiv.org/html/2609.20830#A5.SS1) 2. [E\.2300M Examples](https://arxiv.org/html/2609.20830#A5.SS2)
18. [FReproducibility Checklist](https://arxiv.org/html/2609.20830#A6)1. [F\.1Artifacts, data, and runtime](https://arxiv.org/html/2609.20830#A6.SS1) 2. [F\.2End\-to\-end code path](https://arxiv.org/html/2609.20830#A6.SS2) 3. [F\.3Model and training](https://arxiv.org/html/2609.20830#A6.SS3) 4. [F\.4Hardware and FLOPs accounting](https://arxiv.org/html/2609.20830#A6.SS4) 5. [F\.5Decoding and inference configuration](https://arxiv.org/html/2609.20830#A6.SS5) 6. [F\.6Evaluation protocol and reporting](https://arxiv.org/html/2609.20830#A6.SS6)

## Appendix AAdditional Reviser Variants

### A\.1Other Edit Operators

This appendix subsection lists additional edit operators that can be supported by the same deterministic executor and validity masking used forInsert/Move/Stop\. More generally, any editing idea that can be represented by a token can be implemented as an action token \(or a short composition of action tokens\) and emitted by the transformer, provided the executor semantics are defined and validity\-masked\.

Replace the token immediately to the left of the cursor boundary with a new tokenx∈VAx\\in V\_\{A\}:

Replace\(x\):Ct\+1=\(ct,1,…,ct,ut−1,x,ct,ut\+1,…,ct,ℓt\),ut\+1=ut\.\\text\{\{Replace\}\}\(x\):\\quad C\_\{t\+1\}\\;=\\;\(c\_\{t,1\},\\dots,c\_\{t,u\_\{t\}\-1\},x,c\_\{t,u\_\{t\}\+1\},\\dots,c\_\{t,\\ell\_\{t\}\}\),\\qquad u\_\{t\+1\}=u\_\{t\}\.Validity constraint:ut∈\{1,…,ℓt\}u\_\{t\}\\in\\\{1,\\dots,\\ell\_\{t\}\\\}\. \(Equivalently,Replace\(x\)\(x\)can be viewed asDeletefollowed byInsert\(x\)\(x\)at boundaryut−1u\_\{t\}\-1, but we include it as a single macro\-action\.\)

For a span lengthk∈\{1,…,ut\}k\\in\\\{1,\\dots,u\_\{t\}\\\}, delete the lastkktokens immediately to the left of the cursor boundary:

SpanDelete\(k\):Ct\+1=\(ct,1,…,ct,ut−k,ct,ut\+1,…,ct,ℓt\),ut\+1=ut−k\.\\text\{\{SpanDelete\}\}\(k\):\\quad C\_\{t\+1\}\\;=\\;\(c\_\{t,1\},\\dots,c\_\{t,u\_\{t\}\-k\},c\_\{t,u\_\{t\}\+1\},\\dots,c\_\{t,\\ell\_\{t\}\}\),\\qquad u\_\{t\+1\}=u\_\{t\}\-k\.Validity constraint:1≤k≤ut1\\leq k\\leq u\_\{t\}\.

Swap the last two tokens immediately to the left of the cursor boundary:

Swap:Ct\+1=\(ct,1,…,ct,ut−2,ct,ut,ct,ut−1,ct,ut\+1,…,ct,ℓt\),ut\+1=ut\.\\text\{\{Swap\}\}:\\quad C\_\{t\+1\}\\;=\\;\(c\_\{t,1\},\\dots,c\_\{t,u\_\{t\}\-2\},c\_\{t,u\_\{t\}\},c\_\{t,u\_\{t\}\-1\},c\_\{t,u\_\{t\}\+1\},\\dots,c\_\{t,\\ell\_\{t\}\}\),\\qquad u\_\{t\+1\}=u\_\{t\}\.Validity constraint:ut∈\{2,…,ℓt\}u\_\{t\}\\in\\\{2,\\dots,\\ell\_\{t\}\\\}\.

Move a contiguous span of lengthkkthat ends at the token immediately left of the cursor boundary \(i\.e\., indicesut−k\+1,…,utu\_\{t\}\-k\+1,\\dots,u\_\{t\}\) to a destination boundaryjjin the pre\-removal canvas:

SpanMove\(k,j\):Ct\+1=\\text\{\{SpanMove\}\}\(k,j\):\\quad C\_\{t\+1\}=\{\(ct,1,…,ct,j⏟left context,ct,ut−k\+1,…,ct,ut⏟moved span,ct,j\+1,…,ct,ut−k⏟boosted context,ct,ut\+1,…,ct,ℓt⏟right context\),if​1≤j≤ut−k,\(ct,1,…,ct,ut−k⏟left context,ct,ut\+1,…,ct,j⏟collapsed context,ct,ut−k\+1,…,ct,ut⏟moved span,ct,j\+1,…,ct,ℓt⏟right context\),if​ut≤j≤ℓt\.\\begin\{cases\}\(\\underbrace\{c\_\{t,1\},\\dots,c\_\{t,j\}\}\_\{\\text\{left context\}\},\\;\\underbrace\{c\_\{t,u\_\{t\}\-k\+1\},\\dots,c\_\{t,u\_\{t\}\}\}\_\{\\text\{moved span\}\},\\;\\underbrace\{c\_\{t,j\+1\},\\dots,c\_\{t,u\_\{t\}\-k\}\}\_\{\\text\{boosted context\}\},\\;\\underbrace\{c\_\{t,u\_\{t\}\+1\},\\dots,c\_\{t,\\ell\_\{t\}\}\}\_\{\\text\{right context\}\}\),&\\text\{if \}1\\leq j\\leq u\_\{t\}\-k,\\\\\[2\.84526pt\] \(\\underbrace\{c\_\{t,1\},\\dots,c\_\{t,u\_\{t\}\-k\}\}\_\{\\text\{left context\}\},\\;\\underbrace\{c\_\{t,u\_\{t\}\+1\},\\dots,c\_\{t,j\}\}\_\{\\text\{collapsed context\}\},\\;\\underbrace\{c\_\{t,u\_\{t\}\-k\+1\},\\dots,c\_\{t,u\_\{t\}\}\}\_\{\\text\{moved span\}\},\\;\\underbrace\{c\_\{t,j\+1\},\\dots,c\_\{t,\\ell\_\{t\}\}\}\_\{\\text\{right context\}\}\),&\\text\{if \}u\_\{t\}\\leq j\\leq\\ell\_\{t\}\.\\end\{cases\}ut\+1=\{ut,if​1≤j≤ut−k,j,if​ut≤j≤ℓt\.u\_\{t\+1\}=\\begin\{cases\}u\_\{t\},&\\text\{if \}1\\leq j\\leq u\_\{t\}\-k,\\\\ j,&\\text\{if \}u\_\{t\}\\leq j\\leq\\ell\_\{t\}\.\\end\{cases\}Validity constraints:1≤k≤ut1\\leq k\\leq u\_\{t\}andj∈\{1,…,ut−k\}∪\{ut,…,ℓt\}j\\in\\\{1,\\dots,u\_\{t\}\-k\\\}\\cup\\\{u\_\{t\},\\dots,\\ell\_\{t\}\\\}\(enforced by masking\)\. Underbraced segments may be empty\.

Copy \(without removing\) the length\-kkspan immediately left of the cursor boundary and insert it at boundaryj∈\{0,…,ℓt\}j\\in\\\{0,\\dots,\\ell\_\{t\}\\\}:

SpanCopy\(k,j\):Ct\+1=\(ct,1,…,ct,j⏟left context,ct,ut−k\+1,…,ct,ut⏟copied context,ct,j\+1,…,ct,ℓt⏟right context\),ut\+1=j\+k,\\text\{\{SpanCopy\}\}\(k,j\):\\quad C\_\{t\+1\}\\;=\\;\(\\underbrace\{c\_\{t,1\},\\dots,c\_\{t,j\}\}\_\{\\text\{left context\}\},\\;\\underbrace\{c\_\{t,u\_\{t\}\-k\+1\},\\dots,c\_\{t,u\_\{t\}\}\}\_\{\\text\{copied context\}\},\\;\\underbrace\{c\_\{t,j\+1\},\\dots,c\_\{t,\\ell\_\{t\}\}\}\_\{\\text\{right context\}\}\),\\qquad u\_\{t\+1\}=j\+k,with validity constraint1≤k≤ut1\\leq k\\leq u\_\{t\}\. For bothSpanCopyandSpanMove, one can analogously copy/move spans taken from the right side of the cursor; we omit that symmetric math here\.

All of the operators above admit straightforward supervised training using obfuscation restoration trajectories\. The key observation is that each edit operator has a natural inverse\. When temporary obfuscation\-only insertions are used and later deleted, those transient insertions are treated as latent noise and excluded from the training loss because they are often random artifacts rather than meaningful target\-response content\.

### A\.2Conditioning on the Canvas Representations via Pooled Canvas Embeddings

This subsection describes a variant in which action selection uses an explicit pooled summary of the current canvas\. The motivation is simple: in a history\-only trunk, canvas content is visible only indirectly through past actions and masking; adding a pooled canvas summary provides a direct channel for the model to “see” the current canvas state when choosing the next action\. Our reported experiments use a history\-only trunk without this module\.

Attention pooling is just one instantiation of a broader idea: collapse variable\-length canvas information into a fixed\-size per\-step vector \(or small set of vectors\) that can condition next\-action prediction\. There are many ways to perform this collapse \(e\.g\., learned pooling queries, mean/max pooling with projections, convolutional pooling, recurrent summarizers, sparse/selective pooling, or learned routers\)\. We use attention pooling here as a simple reference design\.

Embed canvas tokens with the same shared token embedding tableEEas action tokens and a dedicated canvas positional tableP\(C\)P^\{\(C\)\}\. For the current canvasCt=\(ct,1,…,ct,ℓt\)C\_\{t\}=\(c\_\{t,1\},\\dots,c\_\{t,\\ell\_\{t\}\}\), define

zi=E​\[ct,i\]\+P\(C\)​\[i\],i=1,…,ℓt\.z\_\{i\}\\;=\\;E\[c\_\{t,i\}\]\+P^\{\(C\)\}\[i\],\\qquad i=1,\\dots,\\ell\_\{t\}\.Letq∈ℝdq\\in\\mathbb\{R\}^\{d\}be a learned query vector\. Compute attention weights:

si=q⊤​zi,αi=exp⁡\(si\)∑j=1ℓtexp⁡\(sj\)\.s\_\{i\}\\;=\\;q^\{\\top\}z\_\{i\},\\qquad\\alpha\_\{i\}\\;=\\;\\frac\{\\exp\(s\_\{i\}\)\}\{\\sum\_\{j=1\}^\{\\ell\_\{t\}\}\\exp\(s\_\{j\}\)\}\.The pooled canvas embedding is:

μt=∑i=1ℓtαi​zi∈ℝd\.\\mu\_\{t\}\\;=\\;\\sum\_\{i=1\}^\{\\ell\_\{t\}\}\\alpha\_\{i\}z\_\{i\}\\;\\in\\;\\mathbb\{R\}^\{d\}\.
In this variant, one injects the pooled canvas summary as an additive conditioning term on history\-token inputs:

xτ=eτ\+μt,τ=1,…,t−1\.x\_\{\\tau\}\\;=\\;e\_\{\\tau\}\\;\+\\;\\mu\_\{t\},\\quad\\tau=1,\\dots,t\-1\.One may instead apply a learned linear projectionWm∈ℝd×dW\_\{m\}\\in\\mathbb\{R\}^\{d\\times d\}:

xτ=eτ\+Wm​μt,x\_\{\\tau\}\\;=\\;e\_\{\\tau\}\\;\+\\;W\_\{m\}\\,\\mu\_\{t\},including the identity \(no projection\) as the simplest choice\.

### A\.3Cross\-Attention to Canvas Representations

Another optional design lets the history stream cross\-attend to the full canvas sequence \(often paired with or used instead of a single pooled canvas vector;[Section˜A\.2](https://arxiv.org/html/2609.20830#A1.SS2)\)\. LetHt∈ℝm×dH\_\{t\}\\in\\mathbb\{R\}^\{m\\times d\}denote the history\-stream hidden states at steptt\(the model’s input token stream\), and letμt∈ℝd\\mu\_\{t\}\\in\\mathbb\{R\}^\{d\}be the pooled canvas embedding from[Section˜A\.2](https://arxiv.org/html/2609.20830#A1.SS2)\. Define𝐌t∈ℝn×d\\mathbf\{M\}\_\{t\}\\in\\mathbb\{R\}^\{n\\times d\}as the pooled\-canvas matrix whose rows are all equal toμt⊤\\mu\_\{t\}^\{\\top\}\. In a cross\-attention block, we compute queries from the history and keys/values from this pooled\-canvas matrix:

Qt=Ht​WQ,Kt=𝐌t​WK,Vt=𝐌t​WV,Q\_\{t\}=H\_\{t\}W\_\{Q\},\\qquad K\_\{t\}=\\mathbf\{M\}\_\{t\}W\_\{K\},\\qquad V\_\{t\}=\\mathbf\{M\}\_\{t\}W\_\{V\},and add the resulting cross\-attention output as a residual update:

H~t=Ht\+Softmax​\(Qt​Kt⊤dk\+M\)​Vt\.\\widetilde\{H\}\_\{t\}=H\_\{t\}\+\\textsc\{Softmax\}\\\!\\Big\(\\frac\{Q\_\{t\}K\_\{t\}^\{\\top\}\}\{\\sqrt\{d\_\{k\}\}\}\+M\\Big\)V\_\{t\}\.
In our main implementation, cross\-attention is inserted after the history self\-attention \(and before the MLP\) in each transformer layer, though in practice it often suffices to apply it only in the lastLcaL\_\{\\text\{ca\}\}layers to reduce cost\. The cross\-attention update can also be gated:

H~t=Ht\+λca⋅Softmax​\(Qt​Kt⊤dk\+M\)​Vt,\\widetilde\{H\}\_\{t\}=H\_\{t\}\+\\lambda\_\{\\text\{ca\}\}\\cdot\\textsc\{Softmax\}\\\!\\Big\(\\frac\{Q\_\{t\}K\_\{t\}^\{\\top\}\}\{\\sqrt\{d\_\{k\}\}\}\+M\\Big\)V\_\{t\},with either a learned scalarλca\\lambda\_\{\\text\{ca\}\}per layer or a small gating MLP\. With this pooled\-canvas matrix, the block uses a compressed canvas memory derived fromμt\\mu\_\{t\}rather than per\-token canvas states; in practice one can setn=1n=1for minimal cost or use smallnnfor implementation convenience\.

### A\.4DAgger with an Alignment\-Based Oracle

Supervised training on fixed restoration trajectories can lead to distribution shift at inference time\. DAgger\(Rosset al\.,[2011](https://arxiv.org/html/2609.20830#bib.bib16)\)mitigates this by iterating between rolling out the current policy and retraining on oracle\-labeled states from those rollouts\.

Our oracle aligns the current canvasCtC\_\{t\}against the targetC⋆C^\{\\star\}via LCS\-style sequence alignment, labeling tokens as matched \(anchors\) or mismatched\. From this alignment it constructs a deterministic edit script: when the cursor is in a matched region, the oracle emitsMoveactions to route to mismatched regions; when the cursor is in a mismatched region, the oracle emits local content edits \(e\.g\.,Insertand, when available,Delete\)\. DAgger then aggregates oracle\-labeled states into the training set and re\-optimizes by teacher forcing:

minθ⁡𝔼\(s,a⋆\)∼𝒟​\[−log⁡pθ​\(a⋆∣s\)\]\.\\min\_\{\\theta\}~\\mathbb\{E\}\_\{\(s,a^\{\\star\}\)\\sim\\mathcal\{D\}\}\\big\[\-\\log p\_\{\\theta\}\(a^\{\\star\}\\mid s\)\\big\]\.A mixture policy that occasionally defers to the oracle prevents catastrophic divergence during early iterations, with the oracle mixing probability decayed over training so the policy gradually assumes full control\.

### A\.5Reinforcement Learning Fine\-Tuning

While supervised restoration provides strong local imitation signals, it does not directly optimize sequence\-level objectives such as holistic response quality, preference alignment, or length/compute trade\-offs\. RL fine\-tuning is a natural extension for optimizing such non\-decomposable rewards over complete edit trajectories\.

Editing is formalized as an episodic MDP: statessts\_\{t\}encode\(Ct,ut,Ht\)\(C\_\{t\},u\_\{t\},H\_\{t\}\)plus a validity mask; actions are the edit operators; transitions are deterministic via the executor\. Terminal rewards come from an LLM judge that ranksKKcandidate outputs and assigns a linearly decayed preference rewardRpref​\(A\(π​\(r\)\)\)=1−\(r−1\)/\(K−1\)R\_\{\\text\{pref\}\}\(A^\{\(\\pi\(r\)\)\}\)=1\-\(r\-1\)/\(K\-1\)\.

Policy optimization uses PPO\-style clipping with entropy regularization, an optional KL penalty to the supervised reference policy, and an optional action\-type regularizer:

ℒ​\(θ,ϕ\)=−ℒpolicy​\(θ\)\+cv​ℒvalue​\(ϕ\)−ce​ℒent​\(θ\)\+ckl​ℒkl​\(θ\)\+ctype​ℒtype​\(θ\)\.\\mathcal\{L\}\(\\theta,\\phi\)=\-\\mathcal\{L\}\_\{\\text\{policy\}\}\(\\theta\)\+c\_\{v\}\\,\\mathcal\{L\}\_\{\\text\{value\}\}\(\\phi\)\-c\_\{e\}\\,\\mathcal\{L\}\_\{\\text\{ent\}\}\(\\theta\)\+c\_\{\\text\{kl\}\}\\,\\mathcal\{L\}\_\{\\text\{kl\}\}\(\\theta\)\+c\_\{\\text\{type\}\}\\,\\mathcal\{L\}\_\{\\text\{type\}\}\(\\theta\)\.To reduce early\-rollout collapse, rollouts are warm\-started with a decaying prefix of oracle actions\. Extensions to RLHF\-style preference optimization or multi\-objective length/compute penalties are straightforward within this MDP formulation\.

## Appendix BPrior Work Mechanisms and FLOPs\-Based Efficiency Accounting

### B\.1Goal and definitions \(FLOPs\-based, shared constants across models\)

We quantify inefficiency by comparing inference FLOPs to produce a full length\-nnoutput under each method’s decoding procedure, relative to an autoregressive \(AR\) baseline\.

We fix the same backbone hyperparameters for every method \(so ratios are meaningful\):

n=128,\|Vc\|=50,000,d=dmodel=768,L=12,dff=4​d,Kmax=16\.n=128,\\quad\|V\_\{c\}\|=50\{,\}000,\\quad d=d\_\{\\text\{model\}\}=768,\\quad L=12,\\quad d\_\{\\text\{ff\}\}=4d,\\quad K\_\{\\max\}=16\.For Reviser, the action vocabulary size is\|Va\|=\|Vc\|\+\|ℳ\|\+1\|V\_\{a\}\|=\|V\_\{c\}\|\+\|\\mathcal\{M\}\|\+1; since\|ℳ\|≪\|Vc\|\|\\mathcal\{M\}\|\\ll\|V\_\{c\}\|, we often use\|Va\|≈\|Vc\|\|V\_\{a\}\|\\approx\|V\_\{c\}\|when it does not materially affect ratios\.

We count dominant matrix\-multiply compute and omit small terms \(biases, layernorm, activations, elementwise ops\)\. All FLOPs expressions in this appendix are built from primitives in[Section˜B\.2](https://arxiv.org/html/2609.20830#A2.SS2)\. We count one fused multiply\-accumulate \(MAC\) as one unit inFmult​\(a,b,c\)=a​b​cF\_\{\\text\{mult\}\}\(a,b,c\)=abc\. \(To convert to conventions where one MAC equals two FLOPs, multiply all reportedF​\(⋅\)F\(\\cdot\)values by22; ratios are unchanged\.\)

For each methodℳ\\mathcal\{M\}, defineFinferℳ​\(n\)F\_\{\\text\{infer\}\}^\{\\mathcal\{M\}\}\(n\)as the total FLOPs required to output an entire length\-nnsequence under that method’s inference procedure \(summing all model calls, scoring/rounding steps, termination checks, etc\.\)\. We define inefficiency asIinferℳ≜Finferℳ​\(n\)FinferAR​\(n\)I\_\{\\text\{infer\}\}^\{\\mathcal\{M\}\}\\triangleq\\frac\{F\_\{\\text\{infer\}\}^\{\\mathcal\{M\}\}\(n\)\}\{F\_\{\\text\{infer\}\}^\{\\text\{AR\}\}\(n\)\}\.

### B\.2Primitive FLOPs functions

LetA∈ℝa×bA\\in\\mathbb\{R\}^\{a\\times b\}andB∈ℝb×cB\\in\\mathbb\{R\}^\{b\\times c\}\. We defineFmult​\(a,b,c\)≜a​b​cF\_\{\\text\{mult\}\}\(a,b,c\)\\triangleq abc, i\.e\., one multiply\-accumulate \(MAC\) is one unit of compute\.

We count dominant matrix\-multiply compute and omit small terms \(biases, layernorm, activations, elementwise ops\)\. HereLLdenotes Transformer depth \(number of layers\), whilenndenotes sequence length\. Because attention structure differs across settings, we distinguish full \(bidirectional\) attention from causal \(lower\-triangular\) attention\.

DefineFtransformerfull​\(n\)F\_\{\\text\{transformer\}\}^\{\\text\{full\}\}\(n\)as the dominant FLOPs for one forward pass through anLL\-block Transformer on a length\-nnsequence with full self\-attention:

Ftransformerfull​\(n\)≜L​\(4​Fmult​\(n,d,d\)\+2​Fmult​\(n,n,d\)\+2​Fmult​\(n,d,dff\)\)\.F\_\{\\text\{transformer\}\}^\{\\text\{full\}\}\(n\)\\triangleq L\\Big\(4\\,F\_\{\\text\{mult\}\}\(n,d,d\)\\;\+\\;2\\,F\_\{\\text\{mult\}\}\(n,n,d\)\\;\+\\;2\\,F\_\{\\text\{mult\}\}\(n,d,d\_\{\\text\{ff\}\}\)\\Big\)\.Withdff=4​d:d\_\{\\text\{ff\}\}=4d:

Ftransformerfull​\(n\)=L​\(12​n​d2\+2​n2​d\)\.F\_\{\\text\{transformer\}\}^\{\\text\{full\}\}\(n\)=L\\left\(12nd^\{2\}\+2n^\{2\}d\\right\)\.
Causal self\-attention uses only then​\(n\+1\)/2n\(n\+1\)/2lower\-triangular query–key pairs\. We therefore model the attention\-score and attention\-apply matmuls by replacing the fulln2n^\{2\}pair count withn​\(n\+1\)/2n\(n\+1\)/2\. Define the dominant FLOPs for one forward pass with causal self\-attention as

Ftransformercausal​\(n\)≜L​\(4​Fmult​\(n,d,d\)\+n​\(n\+1\)​d\+2​Fmult​\(n,d,dff\)\),F\_\{\\text\{transformer\}\}^\{\\text\{causal\}\}\(n\)\\triangleq L\\Big\(4\\,F\_\{\\text\{mult\}\}\(n,d,d\)\\;\+\\;n\(n\+1\)\\,d\\;\+\\;2\\,F\_\{\\text\{mult\}\}\(n,d,d\_\{\\text\{ff\}\}\)\\Big\),wheren​\(n\+1\)​dn\(n\+1\)dcomes from summing the triangular costs ofQ​K⊤QK^\{\\top\}andAttn⋅V\\mathrm\{Attn\}\\cdot V, each equal ton​\(n\+1\)2​d\\frac\{n\(n\+1\)\}\{2\}d\. Withdff=4​d:d\_\{\\text\{ff\}\}=4d:

Ftransformercausal​\(n\)=L​\(12​n​d2\+n2​d\+n​d\)\.F\_\{\\text\{transformer\}\}^\{\\text\{causal\}\}\(n\)=L\\left\(12nd^\{2\}\+n^\{2\}d\+nd\\right\)\.
Under this triangular convention, a causal forward pass at lengthnn\(computed in parallel under a causal mask\) and KV\-cached autoregressive decoding up to tokennnhave the same dominant attention\-matmul count\.

Encoder self\-attention is bidirectional, so we use the full\-attention expressionFenc​\(n\)≜Ftransformerfull​\(n\)F\_\{\\text\{enc\}\}\(n\)\\triangleq F\_\{\\text\{transformer\}\}^\{\\text\{full\}\}\(n\)\.

We model one decoder cross\-attention layer \(dominant matmuls\) between a target length\-nnsequence and a source length\-nsrcn\_\{\\text\{src\}\}sequence as:

Fxattn,layer​\(n,nsrc\)≜Fmult​\(n,d,d\)⏟Q proj \(tgt\)\+2​Fmult​\(nsrc,d,d\)⏟K,V proj \(src\)\+Fmult​\(n,d,d\)⏟O proj \(tgt\)\+Fmult​\(n,d,nsrc\)⏟attn logits​\(Q​K⊤\)\+Fmult​\(n,nsrc,d\)⏟attn apply​\(Attn⋅V\)\.F\_\{\\text\{xattn,layer\}\}\(n,n\_\{\\text\{src\}\}\)\\triangleq\\underbrace\{F\_\{\\text\{mult\}\}\(n,d,d\)\}\_\{\\text\{Q proj \(tgt\)\}\}\+\\underbrace\{2F\_\{\\text\{mult\}\}\(n\_\{\\text\{src\}\},d,d\)\}\_\{\\text\{K,V proj \(src\)\}\}\+\\underbrace\{F\_\{\\text\{mult\}\}\(n,d,d\)\}\_\{\\text\{O proj \(tgt\)\}\}\+\\underbrace\{F\_\{\\text\{mult\}\}\(n,d,n\_\{\\text\{src\}\}\)\}\_\{\\text\{attn logits \}\(QK^\{\\top\}\)\}\+\\underbrace\{F\_\{\\text\{mult\}\}\(n,n\_\{\\text\{src\}\},d\)\}\_\{\\text\{attn apply \}\(\\mathrm\{Attn\}\\cdot V\)\}\.Stacking acrossLLdecoder layers givesFxattn​\(n,nsrc\)≜L​Fxattn,layer​\(n,nsrc\)F\_\{\\text\{xattn\}\}\(n,n\_\{\\text\{src\}\}\)\\triangleq L\\,F\_\{\\text\{xattn,layer\}\}\(n,n\_\{\\text\{src\}\}\)\.

We model a dense vocab projection overmmpositions asFvocab​\(m\)≜Fmult​\(m,d,\|Vc\|\)F\_\{\\text\{vocab\}\}\(m\)\\triangleq F\_\{\\text\{mult\}\}\(m,d,\|V\_\{c\}\|\)\.

## Appendix CModel\-by\-model FLOPs accounting

### C\.1Group 1\. Anchors

#### C\.1\.1Autoregressive Transformer \(AR baseline\)

We model the total dominant matmul compute of KV\-cached AR decoding up to lengthnnusing the causal \(triangular\) attention convention\. Acrossnndecoding steps, the vocab head is applied once per generated token \(totalnnapplications\), yielding:

FinferAR​\(n\)≜Ftransformercausal​\(n\)\+Fvocab​\(n\)\.F\_\{\\text\{infer\}\}^\{\\text\{AR\}\}\(n\)\\;\\triangleq\\;F\_\{\\text\{transformer\}\}^\{\\text\{causal\}\}\(n\)\+F\_\{\\text\{vocab\}\}\(n\)\.
Usingn=128n=128,\|Vc\|=50,000\|V\_\{c\}\|=50\{,\}000,d=768d=768,L=12L=12, anddff=4​dd\_\{\\text\{ff\}\}=4d:

Ftransformercausal​\(128\)≈11\.023,8​G,Fvocab​\(128\)≈4\.915,2​G,F\_\{\\text\{transformer\}\}^\{\\text\{causal\}\}\(128\)\\approx$11\.023,8$\\,\\mathrm\{G\},\\qquad F\_\{\\text\{vocab\}\}\(128\)\\approx$4\.915,2$\\,\\mathrm\{G\},so

FinferAR​\(128\)≈15\.939​G\.F\_\{\\text\{infer\}\}^\{\\text\{AR\}\}\(128\)\\approx$15\.939$\\,\\mathrm\{G\}\.
By definition,IinferAR=1I\_\{\\text\{infer\}\}^\{\\text\{AR\}\}=1\.

#### C\.1\.2Cursor\-style Edit Generation: Reviser \(this work\)

Reviser treats text generation as an editing process over a cursor position\. At each step it predicts exactly one action \(e\.g\.,Insert\(token\), orMove\(Δ\)\)\\textsc\{Move\}\(\\Delta\)\), applies that edit to the current sequence, and continues iterating until termination\. Unlike prior edit transformers that emit large per\-position edit heads, Reviser emits a single action per step with a normal\-sized token vocabulary head \(plus a small set of edit actions\), and it is trained with standard supervised learning \(teacher forcing\) in the same way as a typical Transformer\.

Letpmovep\_\{\\text\{move\}\}be the fraction of actions that are cursor\-moves\. To producenninserted tokens, the expected number of action steps isneff=n1−pmoven\_\{\\text\{eff\}\}=\\frac\{n\}\{1\-p\_\{\\text\{move\}\}\}\. Forn=128n=128, we report three settings:pmove∈\{0\.20,0\.28,0\.33\}p\_\{\\text\{move\}\}\\in\\\{0\.20,0\.28,0\.33\\\}, givingneff∈\{160,177\.78,191\.04\}n\_\{\\text\{eff\}\}\\in\\\{160,\\;177\.78,\\;191\.04\\\}\.

We approximate Reviser’s total decoding compute by evaluating the AR causal proxy at the effective length:

FinferReviser​\(n\)≜Ftransformercausal​\(neff\)\+Fvocab​\(neff\)\.F\_\{\\text\{infer\}\}^\{\\text\{Reviser\}\}\(n\)\\triangleq F\_\{\\text\{transformer\}\}^\{\\text\{causal\}\}\(n\_\{\\text\{eff\}\}\)\+F\_\{\\text\{vocab\}\}\(n\_\{\\text\{eff\}\}\)\.
IinferReviser​\(n\)≜FinferReviser​\(n\)FinferAR​\(n\)\.I\_\{\\text\{infer\}\}^\{\\text\{Reviser\}\}\(n\)\\triangleq\\frac\{F\_\{\\text\{infer\}\}^\{\\text\{Reviser\}\}\(n\)\}\{F\_\{\\text\{infer\}\}^\{\\text\{AR\}\}\(n\)\}\.
UsingFinferAR​\(128\)≈15\.939​GF\_\{\\text\{infer\}\}^\{\\text\{AR\}\}\(128\)\\approx$15\.939$\\,\\mathrm\{G\}, we obtain:

pmove=0\.20:\\displaystyle p\_\{\\text\{move\}\}=20:Ftransformercausal​\(160\)≈13\.826,9​G,Fvocab​\(160\)≈6\.144​G,\\displaystyle F\_\{\\text\{transformer\}\}^\{\\text\{causal\}\}\(60\)\\approx\\,\\mathrm\{G\},\\;F\_\{\\text\{vocab\}\}\(60\)\\approx\\,\\mathrm\{G\},FinferReviser​\(128\)≈19\.970,9​G,IinferReviser≈1\.253\.\\displaystyle F\_\{\\text\{infer\}\}^\{\\text\{Reviser\}\}\(28\)\\approx\\,\\mathrm\{G\},\\;I\_\{\\text\{infer\}\}^\{\\text\{Reviser\}\}\\approx\.pmove=0\.28:\\displaystyle p\_\{\\text\{move\}\}=28:Ftransformercausal​\(177\.78\)≈15\.392,4​G,Fvocab​\(177\.78\)≈6\.826,7​G,\\displaystyle F\_\{\\text\{transformer\}\}^\{\\text\{causal\}\}\(7778\)\\approx\\,\\mathrm\{G\},\\;F\_\{\\text\{vocab\}\}\(7778\)\\approx\\,\\mathrm\{G\},FinferReviser​\(128\)≈22\.219,1​G,IinferReviser≈1\.394\.\\displaystyle F\_\{\\text\{infer\}\}^\{\\text\{Reviser\}\}\(28\)\\approx\\,\\mathrm\{G\},\\;I\_\{\\text\{infer\}\}^\{\\text\{Reviser\}\}\\approx\.pmove=0\.33:\\displaystyle p\_\{\\text\{move\}\}=33:Ftransformercausal​\(191\.04\)≈16\.564,4​G,Fvocab​\(191\.04\)≈7\.336,1​G,\\displaystyle F\_\{\\text\{transformer\}\}^\{\\text\{causal\}\}\(9104\)\\approx\\,\\mathrm\{G\},\\;F\_\{\\text\{vocab\}\}\(9104\)\\approx\\,\\mathrm\{G\},FinferReviser​\(128\)≈23\.900,6​G,IinferReviser≈1\.499,5\.\\displaystyle F\_\{\\text\{infer\}\}^\{\\text\{Reviser\}\}\(28\)\\approx\\,\\mathrm\{G\},\\;I\_\{\\text\{infer\}\}^\{\\text\{Reviser\}\}\\approx\.

### C\.2Group 2\. Diffusion NAR LMs \(100M\)

Many diffusion\-style language models perform generation asTdecT\_\{\\text\{dec\}\}repeated full\-sequence Transformer forward passes, each followed by a vocabulary projection\. For methods with this structure, we define the generation FLOPs as

Fdiffusionℳdiff​\(n,Tdec\)≜Tdec​\(Ftransformerfull​\(n\)\+Fvocab​\(n\)\)\.F\_\{\\text\{diffusion\}\}^\{\\mathcal\{M\}\_\{\\text\{diff\}\}\}\(n,T\_\{\\text\{dec\}\}\)\\triangleq T\_\{\\text\{dec\}\}\\left\(F\_\{\\text\{transformer\}\}^\{\\text\{full\}\}\(n\)\+F\_\{\\text\{vocab\}\}\(n\)\\right\)\.
#### C\.2\.1SEDD

Louet al\.\([2024](https://arxiv.org/html/2609.20830#bib.bib13)\)parameterize SEDD, a reverse discrete diffusion process, and generate by running a fixed numberTdecT\_\{\\text\{dec\}\}of “network evaluations” \(function evaluations\) of Transformer conditioned on time and noise\.

A conservative matmul proxy is that each step computes full\-sequence hidden states \(full attention\) and produces categorical scores for allnnpositions:

FinferSEDD​\(n,Tdec\)≜FdiffusionSEDD​\(n,Tdec\)F\_\{\\text\{infer\}\}^\{\\text\{SEDD\}\}\(n,T\_\{\\text\{dec\}\}\)\\triangleq F\_\{\\text\{diffusion\}\}^\{\\text\{SEDD\}\}\(n,T\_\{\\text\{dec\}\}\)
We report two representative step counts:

Tdec=32:FinferSEDD\(128,32\)≈514\.842,4G,IinferSEDD=32\.300,8\.T\_\{\\text\{dec\}\}=32:\\quad F\_\{\\text\{infer\}\}^\{\\text\{SEDD\}\}\(128,32\)\\approx$514\.842,4$\\,\\mathrm\{G\},\\quad I\_\{\\text\{infer\}\}^\{\\text\{SEDD\}\}=$32\.300,8$\.Tdec=2048:FinferSEDD\(128,2048\)≈32,949\.915,4G,IinferSEDD=2,067\.249,7\.T\_\{\\text\{dec\}\}=2048:\\quad F\_\{\\text\{infer\}\}^\{\\text\{SEDD\}\}\(128,2048\)\\approx$32,949\.915,4$\\,\\mathrm\{G\},\\quad I\_\{\\text\{infer\}\}^\{\\text\{SEDD\}\}=$2,067\.249,7$\.

#### C\.2\.2MDLM

Sahooet al\.\([2024](https://arxiv.org/html/2609.20830#bib.bib14)\)introduce MDLM, a masked discrete diffusion language model\. Sampling starts from an all\-\[MASK\]sequence and runs a discretized reverse diffusion withTdecT\_\{\\text\{dec\}\}steps; at each step, the model predicts token distributions conditioned on the current partially denoised sequence\.

Using the same conservative “full logits per step” proxy:

FinferMDLM​\(n,Tdec\)≜FdiffusionMDLM​\(n,Tdec\)F\_\{\\text\{infer\}\}^\{\\text\{MDLM\}\}\(n,T\_\{\\text\{dec\}\}\)\\triangleq F\_\{\\text\{diffusion\}\}^\{\\text\{MDLM\}\}\(n,T\_\{\\text\{dec\}\}\)
FinferMDLM​\(128,1000\)≈16,088\.825,9​G,IinferMDLM=1,009\.399,3\.F\_\{\\text\{infer\}\}^\{\\text\{MDLM\}\}\(128,1000\)\\approx$16,088\.825,9$\\,\\mathrm\{G\},\\quad I\_\{\\text\{infer\}\}^\{\\text\{MDLM\}\}=$1,009\.399,3$\.

#### C\.2\.3D3PM

Austinet al\.\([2021](https://arxiv.org/html/2609.20830#bib.bib15)\)introduce D3PM, a general discrete denoising diffusion probabilistic model\. In the text setting, it corresponds to a time\-conditioned denoiser run forTdecT\_\{\\text\{dec\}\}discrete reverse steps to transform a highly corrupted sequence into a clean sample\.

FinferD3PM​\(n,Tdec\)≜FdiffusionD3PM​\(n,Tdec\)F\_\{\\text\{infer\}\}^\{\\text\{D3PM\}\}\(n,T\_\{\\text\{dec\}\}\)\\triangleq F\_\{\\text\{diffusion\}\}^\{\\text\{D3PM\}\}\(n,T\_\{\\text\{dec\}\}\)
FinferD3PM​\(128,1000\)≈16,088\.825,9​G,IinferD3PM=1,009\.399,3\.F\_\{\\text\{infer\}\}^\{\\text\{D3PM\}\}\(128,1000\)\\approx$16,088\.825,9$\\,\\mathrm\{G\},\\quad I\_\{\\text\{infer\}\}^\{\\text\{D3PM\}\}=$1,009\.399,3$\.

#### C\.2\.4Diffusion\-LM

Liet al\.\([2022](https://arxiv.org/html/2609.20830#bib.bib12)\)propose Diffusion\-LM, which performs continuous diffusion over a length\-nnsequence of vectors and runs a \(bidirectional\) Transformer denoiser forTdecT\_\{\\text\{dec\}\}reverse steps\. To convert continuous vectors to discrete tokens, we upper\-bound discretization/rounding by a dense vocab scoring matmul\.

Let\|V\|\|V\|denote the \(discrete\) output vocabulary size for this model\. We define

Fround​\(n\)≜Fmult​\(n,d,\|V\|\),F\_\{\\text\{round\}\}\(n\)\\triangleq F\_\{\\text\{mult\}\}\(n,d,\|V\|\),\(which equalsFvocab​\(n\)F\_\{\\text\{vocab\}\}\(n\)under our shared 100M configuration where\|V\|=\|Vc\|\|V\|=\|V\_\{c\}\|\)\.

Each reverse step runs the denoiser once over the full length\-nnsequence \(full attention\):

Fdenoise​\(n\)≜Ftransformerfull​\(n\)\.F\_\{\\text\{denoise\}\}\(n\)\\triangleq F\_\{\\text\{transformer\}\}^\{\\text\{full\}\}\(n\)\.
The clamping trick optionally applies rounding to the predictedx0x\_\{0\}on a subset of the non\-final reverse steps\. Letγclamp∈\[0,1\]\\gamma\_\{\\text\{clamp\}\}\\in\[0,1\]denote the fraction of the firstTdec−1T\_\{\\text\{dec\}\}\-1steps on which clamping \(rounding\) is applied\.

We payTdecT\_\{\\text\{dec\}\}denoiser evaluations, plus rounding once at the end, plus clamping\-rounding onγclamp​\(Tdec−1\)\\gamma\_\{\\text\{clamp\}\}\(T\_\{\\text\{dec\}\}\-1\)non\-final steps:

FinferDiffLM​\(n\)≜Tdec​Fdenoise​\(n\)\+\(1\+γclamp​\(Tdec−1\)\)​Fround​\(n\)\.F\_\{\\text\{infer\}\}^\{\\text\{DiffLM\}\}\(n\)\\triangleq T\_\{\\text\{dec\}\}\\,F\_\{\\text\{denoise\}\}\(n\)\+\\Big\(1\+\\gamma\_\{\\text\{clamp\}\}\(T\_\{\\text\{dec\}\}\-1\)\\Big\)\\,F\_\{\\text\{round\}\}\(n\)\.
UsingFtransformerfull​\(128\)≈11\.173,6​GF\_\{\\text\{transformer\}\}^\{\\text\{full\}\}\(128\)\\approx$11\.173,6$\\,\\mathrm\{G\}andFround​\(128\)=Fmult​\(128,768,50000\)≈4\.915,2​GF\_\{\\text\{round\}\}\(128\)=F\_\{\\text\{mult\}\}\(128,768,50000\)\\approx$4\.915,2$\\,\\mathrm\{G\}, we obtain:

Tdec=200,γclamp=0:FinferDiffLM\(128\)≈2,239\.640,4G,IinferDiffLM=140\.513,1\.T\_\{\\text\{dec\}\}=200,\\;\\gamma\_\{\\text\{clamp\}\}=0:\\quad F\_\{\\text\{infer\}\}^\{\\text\{DiffLM\}\}\(128\)\\approx$2,239\.640,4$\\,\\mathrm\{G\},\\quad I\_\{\\text\{infer\}\}^\{\\text\{DiffLM\}\}=$140\.513,1$\.Tdec=200,γclamp=1:FinferDiffLM\(128\)≈3,217\.765,2G,IinferDiffLM=201\.879,9\.T\_\{\\text\{dec\}\}=200,\\;\\gamma\_\{\\text\{clamp\}\}=1:\\quad F\_\{\\text\{infer\}\}^\{\\text\{DiffLM\}\}\(128\)\\approx$3,217\.765,2$\\,\\mathrm\{G\},\\quad I\_\{\\text\{infer\}\}^\{\\text\{DiffLM\}\}=$201\.879,9$\.Tdec=2000,γclamp=0:FinferDiffLM\(128\)≈22,352\.166,9G,IinferDiffLM=1,402\.356\.T\_\{\\text\{dec\}\}=2000,\\;\\gamma\_\{\\text\{clamp\}\}=0:\\quad F\_\{\\text\{infer\}\}^\{\\text\{DiffLM\}\}\(128\)\\approx$22,352\.166,9$\\,\\mathrm\{G\},\\quad I\_\{\\text\{infer\}\}^\{\\text\{DiffLM\}\}=$1,402\.356$\.

#### C\.2\.5Summary table \(100M tier\)

Table 11:100M\-tier diffusion\-family FLOPs multipliers under a matmul\-dominant proxy\. \(All rows use the shared 100M reference configuration\.\)

### C\.3Group 3: Large\-Scale Diffusion NAR LMs

The large backbones used in this subsection \(e\.g\., LLaMA/Qwen families\) commonly use \(i\) a gated MLP with three linear maps \(gate\_proj,up\_proj,down\_proj\), and \(ii\) grouped\-query attention \(GQA\) where K/V have fewer heads than Q\. Lethhbe the number of query heads andhkvh\_\{\\text\{kv\}\}the number of K/V heads\. With head dimensiondhead=d/hd\_\{\\text\{head\}\}=d/h, define the effective K/V projection widthdkv≜hkv​dheadd\_\{\\text\{kv\}\}\\triangleq h\_\{\\text\{kv\}\}\\,d\_\{\\text\{head\}\}\. \(For standard MHA,hkv=hh\_\{\\text\{kv\}\}=hsodkv=dd\_\{\\text\{kv\}\}=d\.\)

Fornnpositions, Q and O are\(n,d\)×\(d,d\)\(n,d\)\\times\(d,d\), while K and V are\(n,d\)×\(d,dkv\)\(n,d\)\\times\(d,d\_\{\\text\{kv\}\}\):

FprojGQA​\(n;d,dkv\)≜2​Fmult​\(n,d,d\)\+2​Fmult​\(n,d,dkv\)\.F\_\{\\text\{proj\}\}^\{\\text\{GQA\}\}\(n;d,d\_\{\\text\{kv\}\}\)\\triangleq 2F\_\{\\text\{mult\}\}\(n,d,d\)\+2F\_\{\\text\{mult\}\}\(n,d,d\_\{\\text\{kv\}\}\)\.
A gated MLP uses three matmuls \(gate, up, down\):

Fmlpgated​\(n;d,dff\)≜3​Fmult​\(n,d,dff\)\.F\_\{\\text\{mlp\}\}^\{\\text\{gated\}\}\(n;d,d\_\{\\text\{ff\}\}\)\\triangleq 3F\_\{\\text\{mult\}\}\(n,d,d\_\{\\text\{ff\}\}\)\.
Ftransformerfull,gated​\(n;d,L,dff,dkv\)≜L​\(FprojGQA​\(n;d,dkv\)\+2​Fmult​\(n,n,d\)\+Fmlpgated​\(n;d,dff\)\)\.F\_\{\\text\{transformer\}\}^\{\\text\{full,gated\}\}\(n;d,L,d\_\{\\text\{ff\}\},d\_\{\\text\{kv\}\}\)\\triangleq L\\Big\(F\_\{\\text\{proj\}\}^\{\\text\{GQA\}\}\(n;d,d\_\{\\text\{kv\}\}\)\+2F\_\{\\text\{mult\}\}\(n,n,d\)\+F\_\{\\text\{mlp\}\}^\{\\text\{gated\}\}\(n;d,d\_\{\\text\{ff\}\}\)\\Big\)\.
Ftransformercausal,gated​\(n;d,L,dff,dkv\)≜L​\(FprojGQA​\(n;d,dkv\)\+n​\(n\+1\)​d\+Fmlpgated​\(n;d,dff\)\)\.F\_\{\\text\{transformer\}\}^\{\\text\{causal,gated\}\}\(n;d,L,d\_\{\\text\{ff\}\},d\_\{\\text\{kv\}\}\)\\triangleq L\\Big\(F\_\{\\text\{proj\}\}^\{\\text\{GQA\}\}\(n;d,d\_\{\\text\{kv\}\}\)\+n\(n\+1\)d\+F\_\{\\text\{mlp\}\}^\{\\text\{gated\}\}\(n;d,d\_\{\\text\{ff\}\}\)\\Big\)\.
#### C\.3\.1Large\-scale reference configurations \(native sizes\)

We keep each large model at its native architecture and compare to a size\-matched AR baseline of the same scale\. All comparisons use the same output lengthn=128n=128and the same FLOPs conventions as in[Section˜B\.2](https://arxiv.org/html/2609.20830#A2.SS2)\.

For a decoder\-only Transformer, we denote the number of layers byLL, hidden size bydd, MLP width bydffd\_\{\\text\{ff\}\}, and vocabulary size by\|V\|\|V\|\. For attention, lethhbe the number of query heads andhkvh\_\{\\text\{kv\}\}the number of K/V heads \(Grouped\-Query Attention, GQA\)\. With head dimensiondhead≜d/hd\_\{\\text\{head\}\}\\triangleq d/h, the effective K/V projection width isdkv≜hkv​dheadd\_\{\\text\{kv\}\}\\triangleq h\_\{\\text\{kv\}\}\\,d\_\{\\text\{head\}\}\. \(For standard multi\-head attention,hkv=hh\_\{\\text\{kv\}\}=hsodkv=dd\_\{\\text\{kv\}\}=d\.\)

L=64,d=5120,dff=27648,\|V\|=152064,h=40,hkv=8\.L=64,\\quad d=5120,\\quad d\_\{\\text\{ff\}\}=27648,\\quad\|V\|=152064,\\quad h=40,\\quad h\_\{\\text\{kv\}\}=8\.Heredhead=5120/40=128d\_\{\\text\{head\}\}=5120/40=128anddkv=8⋅128=1024d\_\{\\text\{kv\}\}=8\\cdot 128=1024\.

L=28,d=3584,dff=18944,\|V\|=152064,h=28,hkv=4\.L=28,\\quad d=3584,\\quad d\_\{\\text\{ff\}\}=18944,\\quad\|V\|=152064,\\quad h=28,\\quad h\_\{\\text\{kv\}\}=4\.Heredhead=3584/28=128d\_\{\\text\{head\}\}=3584/28=128anddkv=4⋅128=512d\_\{\\text\{kv\}\}=4\\cdot 128=512\.

For LLaDA\-8B we use the published LLaDA config \(full\-attention masked\-token predictor\):

LLaDA\-8B:​L=32,d=4096,dff=12288,\|V\|=126464,h=32,hkv=32,\\text\{LLaDA\-8B: \}L=32,\\quad d=4096,\\quad d\_\{\\text\{ff\}\}=12288,\\quad\|V\|=126464,\\quad h=32,\\quad h\_\{\\text\{kv\}\}=32,sodhead=4096/32=128d\_\{\\text\{head\}\}=4096/32=128anddkv=32⋅128=4096d\_\{\\text\{kv\}\}=32\\cdot 128=4096\(no GQA reduction\)\.

For the size\-matched AR baseline we use LLaMA3\-8B \(causal decoder with GQA\):

LLaMA3\-8B \(AR\):​L=32,d=4096,dff=14336,\|V\|=128256,h=32,hkv=8,\\text\{LLaMA3\-8B \(AR\): \}L=32,\\quad d=4096,\\quad d\_\{\\text\{ff\}\}=14336,\\quad\|V\|=128256,\\quad h=32,\\quad h\_\{\\text\{kv\}\}=8,sodhead=128d\_\{\\text\{head\}\}=128anddkv=8⋅128=1024d\_\{\\text\{kv\}\}=8\\cdot 128=1024\.

#### C\.3\.2AR baselines \(size\-matched\)

For each backbone, we use a LLaMA/Qwen\-style decoder proxy \(GQA \+ gated MLP\):

FinferAR​\(n\)≜Ftransformercausal,gated​\(n;d,L,dff,dkv\)\+Fmult​\(n,d,\|V\|\)\.F\_\{\\text\{infer\}\}^\{\\text\{AR\}\}\(n\)\\triangleq F\_\{\\text\{transformer\}\}^\{\\text\{causal,gated\}\}\(n;d,L,d\_\{\\text\{ff\}\},d\_\{\\text\{kv\}\}\)\+F\_\{\\text\{mult\}\}\(n,d,\|V\|\)\.
FinferAR \(Qwen2\.5\-32B\)​\(128\)≈4,099\.386,9​G\.F\_\{\\text\{infer\}\}^\{\\text\{AR \(Qwen2\.5\-32B\)\}\}\(128\)\\approx$4,099\.386,9$\\,\\mathrm\{G\}\.FinferAR \(Qwen2\.5\-7B\)​\(128\)≈906\.653,6​G\.F\_\{\\text\{infer\}\}^\{\\text\{AR \(Qwen2\.5\-7B\)\}\}\(128\)\\approx$906\.653,6$\\,\\mathrm\{G\}\.FinferAR \(LLaMA3\-8B\)​\(128\)≈962\.760,5​G\.F\_\{\\text\{infer\}\}^\{\\text\{AR \(LLaMA3\-8B\)\}\}\(128\)\\approx$962\.760,5$\\,\\mathrm\{G\}\.

#### C\.3\.3SDLM\-32B\-D4 \(Sequential Diffusion Language Model\)

SDLM predicts a fixed block ofDDtokens per forward pass, then selects the longest high\-confidence prefix \(lengthk∈\{1,…,D\}k\\in\\\{1,\\dots,D\\\}\) and commits it\. KV\-cache states for committed tokens are reused\. Here,DDis the block size \(we useD=4D=4\), andk¯≜𝔼​\[k\]\\bar\{k\}\\triangleq\\mathbb\{E\}\[k\]is the average committed tokens per pass\.

To propose a block ofDDnew tokens given a cached prefix of lengthnpren\_\{\\text\{pre\}\}, we count: \(i\) Q/K/V/O projections \+ gated MLP on theDDnew positions, and \(ii\) attention matmuls forDDqueries attending to the cached prefix plus the causal within\-block keys\. Letdkvd\_\{\\text\{kv\}\}be the K/V projection width \(for GQA; for MHA,dkv=dd\_\{\\text\{kv\}\}=d\)\. We use:

Fkvblk​\(D,npre;dff,dkv\)≜\\displaystyle F\_\{\\text\{kvblk\}\}\(D,n\_\{\\text\{pre\}\};d\_\{\\text\{ff\}\},d\_\{\\text\{kv\}\}\)\\triangleq\{\}L\(2​Fmult​\(D,d,d\)\+2​Fmult​\(D,d,dkv\)⏟Q,O and K,V projections\+3​Fmult​\(D,d,dff\)⏟gated MLP\\displaystyle L\\Big\(\\underbrace\{2F\_\{\\text\{mult\}\}\(D,d,d\)\+2F\_\{\\text\{mult\}\}\(D,d,d\_\{\\text\{kv\}\}\)\}\_\{\\text\{Q,O and K,V projections\}\}\+\\underbrace\{3F\_\{\\text\{mult\}\}\(D,d,d\_\{\\text\{ff\}\}\)\}\_\{\\text\{gated MLP\}\}\+2​Fmult​\(D,npre,d\)\+Fmult​\(D,D\+1,d\)⏟attn \(prefix \+ causal within\-block\)\)\.\\displaystyle\\qquad\+\\underbrace\{2F\_\{\\text\{mult\}\}\(D,n\_\{\\text\{pre\}\},d\)\+F\_\{\\text\{mult\}\}\(D,D\{\+\}1,d\)\}\_\{\\text\{attn \(prefix \+ causal within\-block\)\}\}\\Big\)\.
WithS≈⌈n/k¯⌉S\\approx\\lceil n/\\bar\{k\}\\rceilpasses and prefix lengthnpre≈\(s−1\)​k¯n\_\{\\text\{pre\}\}\\approx\(s\-1\)\\bar\{k\}:

FinferSDLM​\(n\)≜∑s=1S\(Fkvblk​\(D,\(s−1\)​k¯;dff,dkv\)\+Fmult​\(D,d,\|V\|\)\)\.F\_\{\\text\{infer\}\}^\{\\text\{SDLM\}\}\(n\)\\triangleq\\sum\_\{s=1\}^\{S\}\\Big\(F\_\{\\text\{kvblk\}\}\(D,\(s\-1\)\\bar\{k\};d\_\{\\text\{ff\}\},d\_\{\\text\{kv\}\}\)\+F\_\{\\text\{mult\}\}\(D,d,\|V\|\)\\Big\)\.
FinferSDLM\-32B\-D4​\(128\)≈8,198\.941,6​G,IinferSDLM\-32B\-D4=2\.F\_\{\\text\{infer\}\}^\{\\text\{SDLM\-32B\-D4\}\}\(128\)\\approx$8,198\.941,6$\\,\\mathrm\{G\},\\quad I\_\{\\text\{infer\}\}^\{\\text\{SDLM\-32B\-D4\}\}=$2$\.

#### C\.3\.4Dream\-7B \(diffusion LLM; Qwen2\.5\-7B backbone\)

Dream performs masked discrete diffusion: starting from a fully masked response, it iteratively denoises forTdecT\_\{\\text\{dec\}\}steps using a full\-attention Transformer denoiser\.

Letmtm\_\{t\}be the number of masked positions scored at steptt\. For a simple closed form we approximate a linear schedule:∑t=1Tdecmt≈n​Tdec\+12\\sum\_\{t=1\}^\{T\_\{\\text\{dec\}\}\}m\_\{t\}\\approx n\\frac\{T\_\{\\text\{dec\}\}\+1\}\{2\}\.

FinferDream​\(n\)≈Tdec​Ftransformerfull​\(n\)\+Tdec\+12​Fvocab​\(n;\|V\|\)\.F\_\{\\text\{infer\}\}^\{\\text\{Dream\}\}\(n\)\\approx T\_\{\\text\{dec\}\}\\,F\_\{\\text\{transformer\}\}^\{\\text\{full\}\}\(n\)\+\\frac\{T\_\{\\text\{dec\}\}\+1\}\{2\}\\,F\_\{\\text\{vocab\}\}\(n;\|V\|\)\.
Tdec=10:FinferDream\-7B\(128\)≈8,768\.930,7G,IinferDream\-7B=9\.671,8\.T\_\{\\text\{dec\}\}=10:\\quad F\_\{\\text\{infer\}\}^\{\\text\{Dream\-7B\}\}\(128\)\\approx$8,768\.930,7$\\,\\mathrm\{G\},\\quad I\_\{\\text\{infer\}\}^\{\\text\{Dream\-7B\}\}=$9\.671,8$\.Tdec=20:FinferDream\-7B\(128\)≈17,502\.981,6G,IinferDream\-7B=19\.305\.T\_\{\\text\{dec\}\}=20:\\quad F\_\{\\text\{infer\}\}^\{\\text\{Dream\-7B\}\}\(128\)\\approx$17,502\.981,6$\\,\\mathrm\{G\},\\quad I\_\{\\text\{infer\}\}^\{\\text\{Dream\-7B\}\}=$19\.305$\.

#### C\.3\.5LLaDA\-8B \(diffusion mask predictor; compared to LLaMA3\-8B AR\)

LLaDA predicts masked tokens with a full\-attention Transformer \(no causal mask\) and runs a reverse masking/denoising process forTdecT\_\{\\text\{dec\}\}steps\. For instruct\-style decoding, it can also generate left\-to\-right in blocks, applying the reverse process inside each block\. Because this configuration useshkv=hh\_\{\\text\{kv\}\}\{=\}h\(no GQA reduction\), its K/V\-side projection terms are larger than in GQA AR baselines, which contributes to the larger compute multiplier\.

FinferLLaDA​\(n\)≈Tdec​Ftransformerfull​\(n\)\+Tdec\+12​Fvocab​\(n;\|V\|\)\.F\_\{\\text\{infer\}\}^\{\\text\{LLaDA\}\}\(n\)\\approx T\_\{\\text\{dec\}\}\\,F\_\{\\text\{transformer\}\}^\{\\text\{full\}\}\(n\)\+\\frac\{T\_\{\\text\{dec\}\}\+1\}\{2\}\\,F\_\{\\text\{vocab\}\}\(n;\|V\|\)\.
Partition the response intoB=⌈n/b⌉B=\\lceil n/b\\rceilblocks of sizebb, and runTbT\_\{b\}reverse steps per block\. We approximate full\-attention trunk length asnj=min⁡\(j​b,n\)n\_\{j\}=\\min\(jb,n\)for blockjj, and vocab logits only for thebbblock positions:

Finfer,blkLLaDA​\(n\)≜∑j=1B\(Tb​Ftransformerfull​\(nj\)\+Tb\+12​Fvocab​\(b;\|V\|\)\)\.F\_\{\\text\{infer,blk\}\}^\{\\text\{LLaDA\}\}\(n\)\\triangleq\\sum\_\{j=1\}^\{B\}\\Big\(T\_\{b\}\\,F\_\{\\text\{transformer\}\}^\{\\text\{full\}\}\(n\_\{j\}\)\+\\frac\{T\_\{b\}\+1\}\{2\}\\,F\_\{\\text\{vocab\}\}\(b;\|V\|\)\\Big\)\.
Tdec=256:FinferLLaDA\-8B\(128\)≈238,317\.937,4G,IinferLLaDA\-8B=247\.536\.T\_\{\\text\{dec\}\}=256:\\quad F\_\{\\text\{infer\}\}^\{\\text\{LLaDA\-8B\}\}\(128\)\\approx$238,317\.937,4$\\,\\mathrm\{G\},\\quad I\_\{\\text\{infer\}\}^\{\\text\{LLaDA\-8B\}\}=$247\.536$\.semi\-AR:b=32,Tb=16:Finfer,blkLLaDA\-8B\(128\)≈36,426\.557,2G,Iinfer,blkLLaDA\-8B=37\.835,5\.\\text\{semi\-AR: \}b=32,\\ T\_\{b\}=16:\\quad F\_\{\\text\{infer,blk\}\}^\{\\text\{LLaDA\-8B\}\}\(128\)\\approx$36,426\.557,2$\\,\\mathrm\{G\},\\quad I\_\{\\text\{infer,blk\}\}^\{\\text\{LLaDA\-8B\}\}=$37\.835,5$\.

#### C\.3\.6Summary table \(large\-scale\)

Table 12:Large\-scale diffusion\-family FLOPs multipliers under a matmul\-dominant proxy\. Each block uses a size\-matched AR baseline \(Qwen2\.5\-32B, Qwen2\.5\-7B, or LLaMA3\-8B\)\.

### C\.4Group 4\. Refinement NAR LMs \(MT\)

#### C\.4\.1Levenshtein Transformer \(LevT\)

Guet al\.\([2019](https://arxiv.org/html/2609.20830#bib.bib7)\)describe the Levenshtein Transformer \(LevT\), which runsRRrefinement iterations\. Each iteration applies three predictors in sequence: deleteπdel\\pi^\{\\text\{del\}\}, placeholder\-countπplh\\pi^\{\\text\{plh\}\}, and token\-fillπtok\\pi^\{\\text\{tok\}\}\. This corresponds to three trunk evaluations per iteration, with optional early exit for the first two:fdel=bdelLf\_\{\\text\{del\}\}=\\frac\{b\_\{\\text\{del\}\}\}\{L\}andfplh=bplhLf\_\{\\text\{plh\}\}=\\frac\{b\_\{\\text\{plh\}\}\}\{L\}, withfdel,fplh∈\(0,1\]f\_\{\\text\{del\}\},f\_\{\\text\{plh\}\}\\in\(0,1\]\.

We evaluate delete \+ placeholder predictors at an average lengthn0≜0\.8​nn\_\{0\}\\triangleq 0\.8n, and we evaluate the token\-fill predictor at lengthnn\(after insertion returns to the target length\)\. For the token\-fill vocabulary head, we assume only placeholder positions require vocab logits, withm≜0\.4​nm\\triangleq 0\.4ndenoting the estimated number of placeholder tokens to fill at each refinement iteration\. This LevT accounting is a decoder\-side iterative\-edit proxy \(matching the LevT edit cycle\) rather than a full source\-conditioned MT accounting with separate encoder/cross\-attention terms\.

LevT runs bidirectional/refinement\-style passes, so we use full attention in the trunk terms:

FiterLevT​\(n\)≈\\displaystyle F\_\{\\text\{iter\}\}^\{\\text\{LevT\}\}\(n\)\\;\\approxfdel​Ftransformerfull​\(n0\)⏟delete trunk\+fplh​Ftransformerfull​\(n0\)⏟placeholder trunk\+Ftransformerfull​\(n\)⏟token trunk\\displaystyle\\underbrace\{f\_\{\\text\{del\}\}\\,F\_\{\\text\{transformer\}\}^\{\\text\{full\}\}\(n\_\{0\}\)\}\_\{\\text\{delete trunk\}\}\+\\underbrace\{f\_\{\\text\{plh\}\}\\,F\_\{\\text\{transformer\}\}^\{\\text\{full\}\}\(n\_\{0\}\)\}\_\{\\text\{placeholder trunk\}\}\+\\underbrace\{F\_\{\\text\{transformer\}\}^\{\\text\{full\}\}\(n\)\}\_\{\\text\{token trunk\}\}\+Fmult​\(n0,d,2\)⏟delete head\+Fmult​\(n0\+1,2​d,Kmax\+1\)⏟placeholder\-count head\+Fvocab​\(m\)⏟vocab projection on placeholders,\\displaystyle\+\\underbrace\{F\_\{\\text\{mult\}\}\(n\_\{0\},d,2\)\}\_\{\\text\{delete head\}\}\+\\underbrace\{F\_\{\\text\{mult\}\}\(n\_\{0\}\+1,2d,K\_\{\\max\}\+1\)\}\_\{\\text\{placeholder\-count head\}\}\+\\underbrace\{F\_\{\\text\{vocab\}\}\(m\)\}\_\{\\text\{vocab projection on placeholders\}\},wheren0=0\.8​nn\_\{0\}=0\.8nandm=0\.4​nm=0\.4n\. These are average\-case analytical surrogates and need not be integers\. Total decoding cost is

FinferLevT​\(n\)≈R⋅FiterLevT​\(n\)\.F\_\{\\text\{infer\}\}^\{\\text\{LevT\}\}\(n\)\\approx R\\cdot F\_\{\\text\{iter\}\}^\{\\text\{LevT\}\}\(n\)\.
Using the shared reference configuration withn=128n=128,n0=102\.4n\_\{0\}=102\.4, andm=51\.2m=51\.2:

Ftransformerfull​\(102\.4\)≈8\.890,6​G,Ftransformerfull​\(128\)≈11\.173,6​G,F\_\{\\text\{transformer\}\}^\{\\text\{full\}\}\(102\.4\)\\approx$8\.890,6$\\,\\mathrm\{G\},\\quad F\_\{\\text\{transformer\}\}^\{\\text\{full\}\}\(128\)\\approx$11\.173,6$\\,\\mathrm\{G\},and head costs

Fmult​\(102\.4,768,2\)≈0\.157,3​M,Fmult​\(103\.4,1536,17\)≈2\.7​M,Fvocab​\(51\.2\)≈1\.966,1​G\.F\_\{\\text\{mult\}\}\(102\.4,768,2\)\\approx$0\.157,3$\\,\\mathrm\{M\},\\quad F\_\{\\text\{mult\}\}\(103\.4,1536,17\)\\approx$2\.7$\\,\\mathrm\{M\},\\quad F\_\{\\text\{vocab\}\}\(51\.2\)\\approx$1\.966,1$\\,\\mathrm\{G\}\.
Setfdel=fplh=1f\_\{\\text\{del\}\}=f\_\{\\text\{plh\}\}=1\. Then:

Fiter,noEELevT​\(128\)≈30\.923,7​G\.F\_\{\\text\{iter,noEE\}\}^\{\\text\{LevT\}\}\(128\)\\approx$30\.923,7$\\,\\mathrm\{G\}\.WithR=5R=5andR=10R=10:

Finfer,noEELevT​\(128,R=5\)≈154\.618,6​G,Finfer,noEELevT​\(128,R=10\)≈309\.237,3​G\.F\_\{\\text\{infer,noEE\}\}^\{\\text\{LevT\}\}\(128,R=5\)\\approx$154\.618,6$\\,\\mathrm\{G\},\\qquad F\_\{\\text\{infer,noEE\}\}^\{\\text\{LevT\}\}\(128,R=10\)\\approx$309\.237,3$\\,\\mathrm\{G\}\.
Setfdel=fplh=0\.5f\_\{\\text\{del\}\}=f\_\{\\text\{plh\}\}=0\.5\. Then:

Fiter,EELevT​\(128\)≈22\.033,1​G\.F\_\{\\text\{iter,EE\}\}^\{\\text\{LevT\}\}\(128\)\\approx$22\.033,1$\\,\\mathrm\{G\}\.WithR=5R=5andR=10R=10:

Finfer,EELevT​\(128,R=5\)≈110\.165,7​G,Finfer,EELevT​\(128,R=10\)≈220\.331,5​G\.F\_\{\\text\{infer,EE\}\}^\{\\text\{LevT\}\}\(128,R=5\)\\approx$110\.165,7$\\,\\mathrm\{G\},\\qquad F\_\{\\text\{infer,EE\}\}^\{\\text\{LevT\}\}\(128,R=10\)\\approx$220\.331,5$\\,\\mathrm\{G\}\.
UsingFinferAR​\(128\)≈15\.939​GF\_\{\\text\{infer\}\}^\{\\text\{AR\}\}\(128\)\\approx$15\.939$\\,\\mathrm\{G\}:

Iinfer,noEELevT​\(R=5\)=9\.700,6,Iinfer,noEELevT​\(R=10\)=19\.401,3,I\_\{\\text\{infer,noEE\}\}^\{\\text\{LevT\}\}\(R=5\)=$9\.700,6$,\\quad I\_\{\\text\{infer,noEE\}\}^\{\\text\{LevT\}\}\(R=10\)=$19\.401,3$,Iinfer,EELevT​\(R=5\)=6\.911,7,Iinfer,EELevT​\(R=10\)=13\.823,4\.I\_\{\\text\{infer,EE\}\}^\{\\text\{LevT\}\}\(R=5\)=$6\.911,7$,\\quad I\_\{\\text\{infer,EE\}\}^\{\\text\{LevT\}\}\(R=10\)=$13\.823,4$\.

#### C\.4\.2Insertion\-based Generation: Insertion Transformer \(Stern et al\., 2019\)

Sternet al\.\([2019](https://arxiv.org/html/2609.20830#bib.bib6)\)propose the Insertion Transformer \(InsT\), which generates a sequence by iteratively inserting tokens into slots \(gaps\)\. At iterationtt, the current partial sequence has lengthntn\_\{t\}\. The model runs a Transformer pass on the current sequence and predicts, for each slot, either a vocabulary token to insert or a specialno\-insertaction\.

Insertion Transformer uses bidirectional passes over the current partial sequence, so we use full attention:

FiterInsT​\(nt\)≜Ftransformerfull​\(nt\)\+Fvocab​\(nt\+1\),F\_\{\\text\{iter\}\}^\{\\text\{InsT\}\}\(n\_\{t\}\)\\triangleq F\_\{\\text\{transformer\}\}^\{\\text\{full\}\}\(n\_\{t\}\)\+F\_\{\\text\{vocab\}\}\(n\_\{t\}\+1\),wherent\+1n\_\{t\}\+1slots are scored\. \(The extrano\-insertclass changes\|Vc\|\|V\_\{c\}\|by\+1\+1, which is negligible at\|Vc\|=50​k\|V\_\{c\}\|=50\\text\{k\}\.\) AR baseline:FinferAR​\(128\)≈15\.939​GF\_\{\\text\{infer\}\}^\{\\text\{AR\}\}\(128\)\\approx$15\.939$\\,\\mathrm\{G\}\. Takent∈\{1,2,4,8,16,32,64,128\}n\_\{t\}\\in\\\{1,2,4,8,16,32,64,128\\\}\. Then:

∑tFtransformerfull​\(nt\)≈22\.061​G,∑tFvocab​\(nt\+1\)≈10\.099,2​G,\\sum\_\{t\}F\_\{\\text\{transformer\}\}^\{\\text\{full\}\}\(n\_\{t\}\)\\approx$22\.061$\\,\\mathrm\{G\},\\qquad\\sum\_\{t\}F\_\{\\text\{vocab\}\}\(n\_\{t\}\+1\)\\approx$10\.099,2$\\,\\mathrm\{G\},so

Finfer,balInsT​\(128\)≈32\.160,2​G,Iinfer,balInsT=2\.017,7\.F\_\{\\text\{infer,bal\}\}^\{\\text\{InsT\}\}\(128\)\\approx$32\.160,2$\\,\\mathrm\{G\},\\qquad I\_\{\\text\{infer,bal\}\}^\{\\text\{InsT\}\}=$2\.017,7$\.
Takent∈\{1,2,…,128\}n\_\{t\}\\in\\\{1,2,\\dots,128\\\}\. Then:

∑tFtransformerfull​\(nt\)≈714\.256,8​G,∑tFvocab​\(nt\+1\)≈321\.945,6​G,\\sum\_\{t\}F\_\{\\text\{transformer\}\}^\{\\text\{full\}\}\(n\_\{t\}\)\\approx$714\.256,8$\\,\\mathrm\{G\},\\qquad\\sum\_\{t\}F\_\{\\text\{vocab\}\}\(n\_\{t\}\+1\)\\approx$321\.945,6$\\,\\mathrm\{G\},so

Finfer,serInsT​\(128\)≈1,036\.202,4​G,Iinfer,serInsT=65\.010,5\.F\_\{\\text\{infer,ser\}\}^\{\\text\{InsT\}\}\(128\)\\approx$1,036\.202,4$\\,\\mathrm\{G\},\\qquad I\_\{\\text\{infer,ser\}\}^\{\\text\{InsT\}\}=$65\.010,5$\.

#### C\.4\.3One\-shot NAT \(fertility / length latents\): Non\-Autoregressive NMT \(Gu et al\., 2018\)

Guet al\.\([2018](https://arxiv.org/html/2609.20830#bib.bib3)\)propose one\-shot non\-autoregressive translation \(NAT\), which predicts all target tokens in parallel by using discrete fertility/length latents and a single encoder–decoder pass\.

For this numerical instantiation we usensrc=n=128n\_\{\\text\{src\}\}=n=128\. LetKfertK\_\{\\text\{fert\}\}denote the number of discrete fertility classes \(the maximum fertility bucketed by the model\), so each source token predicts a fertilityfi∈\{0,1,…,Kfert−1\}f\_\{i\}\\in\\\{0,1,\\dots,K\_\{\\text\{fert\}\}\-1\\\}; here we setKfert=50K\_\{\\text\{fert\}\}=50\.

One\-shot NAT runs a single encoder–decoder evaluation:

FinferNAT​\(n,nsrc\)≜Fenc​\(nsrc\)\+Fmult​\(nsrc,d,Kfert\)\+\(Ftransformerfull​\(n\)\+Fxattn​\(n,nsrc\)\)\+Fvocab​\(n\)\.F\_\{\\text\{infer\}\}^\{\\text\{NAT\}\}\(n,n\_\{\\text\{src\}\}\)\\triangleq F\_\{\\text\{enc\}\}\(n\_\{\\text\{src\}\}\)\+F\_\{\\text\{mult\}\}\(n\_\{\\text\{src\}\},d,K\_\{\\text\{fert\}\}\)\+\\Big\(F\_\{\\text\{transformer\}\}^\{\\text\{full\}\}\(n\)\+F\_\{\\text\{xattn\}\}\(n,n\_\{\\text\{src\}\}\)\\Big\)\+F\_\{\\text\{vocab\}\}\(n\)\.
Withn=nsrc=128n=n\_\{\\text\{src\}\}=128:

Fxattn​\(128,128\)≈3\.925,9​G,Ffert​\(128\)=Fmult​\(128,768,50\)≈4\.915,2​M\.F\_\{\\text\{xattn\}\}\(128,128\)\\approx$3\.925,9$\\,\\mathrm\{G\},\\qquad F\_\{\\text\{fert\}\}\(128\)=F\_\{\\text\{mult\}\}\(128,768,50\)\\approx$4\.915,2$\\,\\mathrm\{M\}\.Therefore:

FinferNAT​\(128,128\)≈31\.193,2​G,IinferNAT=1\.957\.F\_\{\\text\{infer\}\}^\{\\text\{NAT\}\}\(128,128\)\\approx$31\.193,2$\\,\\mathrm\{G\},\\qquad I\_\{\\text\{infer\}\}^\{\\text\{NAT\}\}=$1\.957$\.

#### C\.4\.4Iterative Mask Refinement: Mask\-Predict / CMLM \(Ghazvininejad et al\., 2019\)

Ghazvininejadet al\.\([2019](https://arxiv.org/html/2609.20830#bib.bib5)\)start Mask\-Predict from a fully\-masked target and performTmpT\_\{\\text\{mp\}\}refinement cycles, each time masking low\-confidence tokens and re\-predicting them in parallel\.

We instantiateTmp=10T\_\{\\text\{mp\}\}=10and the common linear decay schedule:

m0=n,mt=⌊n⋅Tmp−tTmp⌋\(t=1,…,Tmp−1\)\.m\_\{0\}=n,\\qquad m\_\{t\}=\\left\\lfloor n\\cdot\\frac\{T\_\{\\text\{mp\}\}\-t\}\{T\_\{\\text\{mp\}\}\}\\right\\rfloor\\ \\ \(t=1,\\dots,T\_\{\\text\{mp\}\}\-1\)\.Forn=128n=128,Tmp=10T\_\{\\text\{mp\}\}=10:

\(m0,…,m9\)=\(128,115,102,89,76,64,51,38,25,12\),∑t=09mt=700\.\(m\_\{0\},\\dots,m\_\{9\}\)=\(128,115,102,89,76,64,51,38,25,12\),\\qquad\\sum\_\{t=0\}^\{9\}m\_\{t\}=700\.
At each iteration we pay decoder trunk \+ cross\-attention \+ vocab projection on only the masked tokens:

FiterCMLM​\(t,n,nsrc\)=Ftransformerfull​\(n\)\+Fxattn​\(n,nsrc\)\+Fvocab​\(mt\)\.F\_\{\\text\{iter\}\}^\{\\text\{CMLM\}\}\(t,n,n\_\{\\text\{src\}\}\)=F\_\{\\text\{transformer\}\}^\{\\text\{full\}\}\(n\)\+F\_\{\\text\{xattn\}\}\(n,n\_\{\\text\{src\}\}\)\+F\_\{\\text\{vocab\}\}\(m\_\{t\}\)\.Encoder cost is paid once:Fenc​\(nsrc\)=Ftransformerfull​\(nsrc\)F\_\{\\text\{enc\}\}\(n\_\{\\text\{src\}\}\)=F\_\{\\text\{transformer\}\}^\{\\text\{full\}\}\(n\_\{\\text\{src\}\}\)\.

Withnsrc=n=128n\_\{\\text\{src\}\}=n=128:

Ftransformerfull​\(128\)\+Fxattn​\(128,128\)≈15\.099,5​G\.F\_\{\\text\{transformer\}\}^\{\\text\{full\}\}\(128\)\+F\_\{\\text\{xattn\}\}\(128,128\)\\approx$15\.099,5$\\,\\mathrm\{G\}\.Masked\-only vocab projection across all iterations:

∑t=0Tmp−1Fvocab​\(mt\)≈26\.88​G\.\\sum\_\{t=0\}^\{T\_\{\\text\{mp\}\}\-1\}F\_\{\\text\{vocab\}\}\(m\_\{t\}\)\\approx$26\.88$\\,\\mathrm\{G\}\.Therefore:

FinferCMLM​\(128,128\)=Fenc​\(128\)\+∑t=0Tmp−1FiterCMLM​\(t,128,128\)≈189\.048,6​G,F\_\{\\text\{infer\}\}^\{\\text\{CMLM\}\}\(128,128\)=F\_\{\\text\{enc\}\}\(128\)\+\\sum\_\{t=0\}^\{T\_\{\\text\{mp\}\}\-1\}F\_\{\\text\{iter\}\}^\{\\text\{CMLM\}\}\(t,128,128\)\\approx$189\.048,6$\\,\\mathrm\{G\},IinferCMLM=11\.860,7\.I\_\{\\text\{infer\}\}^\{\\text\{CMLM\}\}=$11\.860,7$\.

#### C\.4\.5Summary table

Table 13:Summary of inference compute under a matmul\-dominant FLOPs proxy\.

## Appendix DMore Qualitative Examples

[Table˜14](https://arxiv.org/html/2609.20830#A4.T14)gives a concrete obfuscation–restoration trajectory example used for qualitative inspection\.

### D\.1Obfuscation–Restoration Trajectory Example

The example referred to in this subsection is[Table˜14](https://arxiv.org/html/2609.20830#A4.T14)\.

We illustrate how an obfuscation trajectory \(left\) can be inverted to form a restoration trajectory \(right\)\. The cursor is shown as a vertical bar “∣\\mid” inside the bracketed canvas\.

Obfuscation \(corrupt target→\\rightarrowblank\)Restoration \(invert & apply→\\rightarrowtarget\)1\.Initial
\[Mary had a∣\\midlittle lamb\.\]2\.Delete
\[Mary had∣\\midlittle lamb\.\]3\.Move​\(−1\)\\text\{\{Move\}\}\(\-1\)
\[Mary∣\\midhad little lamb\.\]4\.Delete
\[∣\\midhad little lamb\.\]5\.Insert​\(hello\)\\text\{\{Insert\}\}\(\\texttt\{hello\}\)
\[hello∣\\midhad little lamb\.\]6\.Move​\(\+2\)\\text\{\{Move\}\}\(\+2\)
\[hello had little∣\\midlamb\.\]7\.Delete
\[hello had∣\\midlamb\.\]8\.Delete
\[hello∣\\midlamb\.\]9\.Delete
\[∣\\midlamb\.\]10\.Move​\(\+1\)\\text\{\{Move\}\}\(\+1\)
\[lamb\.∣\\mid\]11\.Delete
\[∣\\mid\]1\.Initial
\[∣\\mid\]2\.Insert​\(lamb\.\)\\text\{\{Insert\}\}\(\\texttt\{lamb\.\}\)
\[lamb\.∣\\mid\]3\.Move​\(−1\)\\text\{\{Move\}\}\(\-1\)
\[∣\\midlamb\.\]4\.Insert​\(hello\)\\text\{\{Insert\}\}\(\\texttt\{hello\}\)
\[hello∣\\midlamb\.\]5\.Insert​\(had\)\\text\{\{Insert\}\}\(\\texttt\{had\}\)
\[hello had∣\\midlamb\.\]6\.Insert​\(little\)\\text\{\{Insert\}\}\(\\texttt\{little\}\)
\[hello had little∣\\midlamb\.\]7\.Move​\(−2\)\\text\{\{Move\}\}\(\-2\)
\[hello∣\\midhad little lamb\.\]8\.Delete
\[∣\\midhad little lamb\.\]9\.Insert​\(Mary\)\\text\{\{Insert\}\}\(\\texttt\{Mary\}\)
\[Mary∣\\midhad little lamb\.\]10\.Move​\(\+1\)\\text\{\{Move\}\}\(\+1\)
\[Mary had∣\\midlittle lamb\.\]11\.Insert​\(a\)\\text\{\{Insert\}\}\(\\texttt\{a\}\)
\[Mary had a∣\\midlittle lamb\.\]12\.Stop
\[Mary had a∣\\midlittle lamb\.\]Table 14:Side\-by\-side obfuscation and restoration \(richer\-action\-space variant for illustration\)\. Restoration is obtained by reversing the obfuscation actions and inverting each step \(Delete↔\\leftrightarrowInsert of the deleted token, Move\(Δ\\Delta\)↔\\leftrightarrowMove\(−Δ\-\\Delta\), Insert\(token\)↔\\leftrightarrowDelete\)\.Concatenating the executed edit actions, the obfuscation trajectory is:

B=\[Delete,Move​\(−1\),Delete,Insert​\(hello\),Move​\(\+2\),Delete,Delete,Delete,Move\(\+1\),Delete\]\.B=\\begin\{aligned\} \[&\\text\{\{Delete\}\},\\,\\text\{\{Move\}\}\(\-1\),\\,\\text\{\{Delete\}\},\\,\\text\{\{Insert\}\}\(\\texttt\{hello\}\),\\,\\text\{\{Move\}\}\(\+2\),\\,\\text\{\{Delete\}\},\\,\\text\{\{Delete\}\},\\,\\text\{\{Delete\}\},\\\\ &\\text\{\{Move\}\}\(\+1\),\\,\\text\{\{Delete\}\}\]\.\\end\{aligned\}Reversing the order and inverting each action yields the restoration trajectory:

A=\[Insert​\(lamb\.\),Move​\(−1\),Insert​\(hello\),Insert​\(had\),Insert​\(little\),Move​\(−2\),Delete,Insert\(Mary\),Move\(\+1\),Insert\(a\),Stop\]\.A=\\begin\{aligned\} \[&\\text\{\{Insert\}\}\(\\texttt\{lamb\.\}\),\\ \\text\{\{Move\}\}\(\-1\),\\ \\text\{\{Insert\}\}\(\\texttt\{hello\}\),\\ \\text\{\{Insert\}\}\(\\texttt\{had\}\),\\ \\text\{\{Insert\}\}\(\\texttt\{little\}\),\\ \\text\{\{Move\}\}\(\-2\),\\ \\text\{\{Delete\}\},\\\\ &\\text\{\{Insert\}\}\(\\texttt\{Mary\}\),\\ \\text\{\{Move\}\}\(\+1\),\\ \\text\{\{Insert\}\}\(\\texttt\{a\}\),\\ \\text\{\{Stop\}\}\]\.\\end\{aligned\}ApplyingAAto the blank state deterministically reconstructs the original canvas shown on the left\.

## Appendix ESelected Ranked Responses and Restoration Trajectories

Interactive HTML visualizations for the examples in this section are available in the[GitHub](https://github.com/Sean-Diab/Reviser)repository undervisualizations/\.

### E\.1100M Examples

#### 100M Reviser Example 1

Text\(prompt segment in blue\)\.

Claudine started ballet at the age of three in Chapel Hill, North Carolina and continued at Pofahl Studios under the instruction of Kim Tuttle and Judy Skinner in Gainesville, Texas\. She taught at various studios including New York City Dance Center, the Brooklyn School of Dance, and the Center for Arts & Dance at Syracuse Dance Studio in Little Rock, New York\. Claudine began ballet at the age of three\. She started teaching at the same time, and continued teaching at the age of two teaching\. She also taught with several dance classes during her time in the private and private classes\. She has taught classes both in the private and semi private areas, She has taught for years as an educator and has had to have more than as many dancers have taught\.

Restoration trajectory \(189 actions\)\.

INSERT ‘Cl’,INSERT ‘aud’,INSERT ‘ine’,INSERT ‘ started’,INSERT ‘ ballet’,INSERT ‘ at’,INSERT ‘ the’,INSERT ‘ age’,INSERT ‘ of’,INSERT ‘ three’,INSERT ‘ in’,INSERT ‘ Chapel’,INSERT ‘ Hill’,INSERT ‘,’,INSERT ‘ North’,INSERT ‘ Carolina’,INSERT ‘ and’,INSERT ‘ continued’,INSERT ‘ at’,INSERT ‘ P’,INSERT ‘of’,INSERT ‘ahl’,INSERT ‘ Studios’,INSERT ‘ under’,INSERT ‘ the’,INSERT ‘ instruction’,INSERT ‘ of’,INSERT ‘ Kim’,INSERT ‘ Tut’,INSERT ‘tle’,INSERT ‘ and’,INSERT ‘ Judy’,INSERT ‘ Skinner’,INSERT ‘ in’,INSERT ‘ Gain’, INSERT ‘\.’, \[MOVE \-1\], INSERT ‘ have’, INSERT ‘ taught’, \[MOVE \-2\], INSERT ‘ as’, INSERT ‘ many’, INSERT ‘ dancers’, \[MOVE \-2\], \[MOVE \-1\], INSERT ‘ and’, INSERT ‘ has’, INSERT ‘ had’, INSERT ‘ to’, \[MOVE \-4\], INSERT ‘,’, \[MOVE \-1\], INSERT ‘,’, INSERT ‘\.’, \[MOVE \-2\], \[MOVE \+2\], \[MOVE \-1\], \[MOVE \-1\], INSERT ‘ New’, INSERT ‘ York’, INSERT ‘\.’, INSERT ‘\\n’, INSERT ‘Cl’, INSERT ‘aud’, INSERT ‘ine’, INSERT ‘ began’, \[MOVE \-8\], INSERT ‘ in’, INSERT ‘ Little’, INSERT ‘ Rock’, INSERT ‘,’, \[MOVE \+8\], INSERT ‘ ballet’, INSERT ‘ at’, INSERT ‘ She’, INSERT ‘ started’, INSERT ‘ teaching’, INSERT ‘ at’, \[MOVE \-4\], INSERT ‘ the’, INSERT ‘ age’, INSERT ‘ of’, INSERT ‘ three’, INSERT ‘\.’, \[MOVE \+4\], INSERT ‘ the’, INSERT ‘ same’, INSERT ‘ time’, \[MOVE \+1\], INSERT ‘ and’, INSERT ‘ teaching’, \[MOVE \+2\], INSERT ‘ as’, \[MOVE \+4\], \[MOVE \-8\], INSERT ‘ continued’, \[MOVE \+4\], INSERT ‘ an’, INSERT ‘ educator’, \[MOVE \-32\], \[MOVE \+32\], \[MOVE \-4\], INSERT ‘ She’, INSERT ‘ also’, INSERT ‘ taught’, INSERT ‘ with’, INSERT ‘ several’, INSERT ‘ dance’, INSERT ‘ classes’, INSERT ‘ during’, INSERT ‘ her’, INSERT ‘ time’, INSERT ‘ in’, INSERT ‘ the’, INSERT ‘ private’, INSERT ‘ private’, INSERT ‘ classes’, INSERT ‘\.’, INSERT ‘ She’, INSERT ‘ has’, INSERT ‘ taught’, INSERT ‘ classes’, INSERT ‘ both’, INSERT ‘ in’, INSERT ‘ the’, INSERT ‘ private’, INSERT ‘ and’, INSERT ‘ semi’, INSERT ‘ private’, INSERT ‘ areas’, \[MOVE \+8\], INSERT ‘ more’, INSERT ‘ than’, \[MOVE \-2\], INSERT ‘ have’, \[MOVE \-8\], \[MOVE \-16\], INSERT ‘ and’, \[MOVE \-16\], INSERT ‘ teaching’, INSERT ‘ at’, INSERT ‘ the’, INSERT ‘ age’, INSERT ‘ of’, INSERT ‘ two’, \[MOVE \+32\], INSERT ‘ She’, INSERT ‘ has’, INSERT ‘ taught’, INSERT ‘ for’, INSERT ‘ years’, \[MOVE \-64\], \[MOVE \-8\], INSERT ‘esville’, INSERT ‘,’, INSERT ‘ Texas’, INSERT ‘\.’, INSERT ‘ She’, INSERT ‘ taught’, INSERT ‘ at’, INSERT ‘ various’, INSERT ‘ Dance’, INSERT ‘ Studio’, \[MOVE \-2\], INSERT ‘ studios’, INSERT ‘ including’, INSERT ‘ New’, INSERT ‘ York’, INSERT ‘ City’, INSERT ‘ Dance’, INSERT ‘ Center’, INSERT ‘,’, INSERT ‘ the’, INSERT ‘ Brooklyn’, INSERT ‘ School’, INSERT ‘ of’, INSERT ‘ Dance’, INSERT ‘,’, INSERT ‘ and’, INSERT ‘ the’, INSERT ‘ Center’, INSERT ‘ for’, INSERT ‘ Arts’, INSERT ‘ &’, INSERT ‘ Dance’, INSERT ‘ at’, INSERT ‘ Syracuse’, \[MOVE \-32\],Stop

#### 100M Reviser Example 2

Text\(prompt segment in blue\)\.

Do you want to hire a trusted Professional Cleaners in Mitcham Wandsworth London SW17’ Hire our dependable Professional Cleaners company in Mitcham Wandsworth London Wandsworth for a free no\-obligation quote\. With 15 years of experience, we’re a professional cleaning company and have experience with everything from carpeting, cleaning, cleaning to cleaning and so forth\. For a complete list of the services available, please contact us today\. If you’d like to hire, we’ll be able to look at your work and bring you the best solution to your requirements\. We will also assist you\. We know that working with an experienced man and team will make the key difference\.

Restoration trajectory \(186 actions\)\.

INSERT ‘Do’,INSERT ‘ you’,INSERT ‘ want’,INSERT ‘ to’,INSERT ‘ hire’,INSERT ‘ a’,INSERT ‘ trusted’,INSERT ‘ Professional’,INSERT ‘ Clean’,INSERT ‘ers’,INSERT ‘ in’,INSERT ‘ Mitch’,INSERT ‘am’,INSERT ‘ W’,INSERT ‘ands’,INSERT ‘worth’,INSERT ‘ London’,INSERT ‘ SW’,INSERT ‘17’,INSERT ‘’’,INSERT ‘\\n’,INSERT ‘H’,INSERT ‘ire’,INSERT ‘ our’,INSERT ‘ depend’,INSERT ‘able’,INSERT ‘ Professional’,INSERT ‘ Clean’,INSERT ‘ers’,INSERT ‘ company’,INSERT ‘ in’,INSERT ‘ Mitch’,INSERT ‘am’,INSERT ‘ W’,INSERT ‘ands’, INSERT ‘\.’, \[MOVE \-1\], \[MOVE \+1\], \[MOVE \-1\], \[MOVE \+1\], \[MOVE \-1\], INSERT ‘ the’, \[MOVE \-1\], INSERT ‘\.’, INSERT ‘\\n’, INSERT ‘We’, INSERT ‘ know’, \[MOVE \-2\], \[MOVE \-2\], INSERT ‘ you’, \[MOVE \+4\], \[MOVE \+1\], INSERT ‘ key’, INSERT ‘ difference’, \[MOVE \-8\], INSERT ‘’’, INSERT ‘’’, INSERT ‘ll’, INSERT ‘ be’, INSERT ‘ able’, INSERT ‘ to’, INSERT ‘ and’, INSERT ‘ bring’, INSERT ‘ you’, INSERT ‘ your’, INSERT ‘ requirements’, INSERT ‘\.’, INSERT ‘ We’, INSERT ‘ will’, INSERT ‘ also’, INSERT ‘ assist’, \[MOVE \-16\], \[MOVE \+8\], \[MOVE \-2\], INSERT ‘ look’, INSERT ‘ at’, INSERT ‘ work’, \[MOVE \-1\], INSERT ‘ your’, \[MOVE \+16\], INSERT ‘ that’, INSERT ‘ working’, INSERT ‘ with’, INSERT ‘ an’, INSERT ‘ experienced’, INSERT ‘ man’, INSERT ‘ and’, INSERT ‘ team’, INSERT ‘ will’, INSERT ‘ make’, \[MOVE \-8\], \[MOVE \-16\], \[MOVE \+4\], \[MOVE \+2\], \[MOVE \-4\], INSERT ‘ the’, INSERT ‘ best’, INSERT ‘ solution’, INSERT ‘ to’, \[MOVE \-16\], INSERT ‘d’, INSERT ‘ like’, INSERT ‘ to’, INSERT ‘ hire’, INSERT ‘,’, INSERT ‘ we’, INSERT ‘’’, \[MOVE \-8\], INSERT ‘ a’, INSERT ‘\\n’, INSERT ‘If’, INSERT ‘ you’, INSERT ‘’’, \[MOVE \-4\], INSERT ‘ professional’, INSERT ‘ services’, \[MOVE \-1\], INSERT ‘ the’, \[MOVE \-2\], \[MOVE \-1\], INSERT ‘worth’, INSERT ‘ London’, INSERT ‘ W’, INSERT ‘ands’, INSERT ‘worth’, INSERT ‘ for’, INSERT ‘ a’, INSERT ‘ free’, INSERT ‘ no’, INSERT ‘\-’, INSERT ‘ob’, INSERT ‘lig’, INSERT ‘ation’, INSERT ‘ quote’, INSERT ‘\.’, INSERT ‘ With’, INSERT ‘ 15’, INSERT ‘ years’, INSERT ‘ of’, INSERT ‘ experience’, INSERT ‘,’, INSERT ‘ we’, INSERT ‘’’, INSERT ‘’’, INSERT ‘re’, \[MOVE \+2\], INSERT ‘ cleaning’, INSERT ‘ company’, INSERT ‘ with’, INSERT ‘ everything’, INSERT ‘ from’, INSERT ‘ carpet’, INSERT ‘ing’, INSERT ‘,’, INSERT ‘ cleaning’, INSERT ‘,’, INSERT ‘ cleaning’, INSERT ‘ to’, INSERT ‘ cleaning’, INSERT ‘ and’, INSERT ‘ so’, INSERT ‘ forth’, INSERT ‘\.’, INSERT ‘\\n’, INSERT ‘For’, INSERT ‘ a’, INSERT ‘ complete’, INSERT ‘ list’, INSERT ‘ of’, \[MOVE \+2\], INSERT ‘ available’, INSERT ‘,’, INSERT ‘ please’, INSERT ‘ contact’, INSERT ‘ us’, INSERT ‘ today’, INSERT ‘\.’, \[MOVE \+32\], \[MOVE \-64\], \[MOVE \+2\], INSERT ‘ and’, INSERT ‘ have’, INSERT ‘ experience’, \[MOVE \-1\], \[MOVE \-32\],Stop

#### 100M Reviser Example 3

Text\(prompt segment in blue\)\.

5 beds \| 3 baths \| 2,340 sqft \| $597 per sq\. ft\. Run, dont walk\. Come see this beautiful custom home near the beach\! This is a beautiful home, and this home has a beautiful fireplace in the main living room and a large open living room\. There is a nice large dining room, a dining room, full kitchen, a large gas stove the master bathroom with and a living\. The entire home features room a gorgeous outdoor dining room\. The 2 bedrooms are spacious and open\-plan, and open\-plan\! Great location,; open concept kitchen convenient in the community\. Open floor plan, walk\-in closet & den\. The location\! This is a small town, and is a short\- walk from the beach\. Come to enjoy\!

Restoration trajectory \(192 actions\)\.

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#### 100M Reviser Example 4

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Being able to present the findings of research into how effective Cognitive Behavioural Therapy is in a digital and online setting \- specifically for treating youth anxiety – and in comparison to atraditional mental therapy approach, it has led to new challenges for children with cognitive disorders: they are now at the forefront of psychological change; that the technology can make changes to behavior of their children, the social and behavioral problems\. The authors report that brain\-related research, or in the course of memory, can provide a comprehensive assessment of the effective therapy with their personal and psychological concerns, their own self, and this are a new challenge\. For more information on the full text of the authors’ case studies, please contact first to share article\(s\) of their authors, and submitting a review by\.

Restoration trajectory \(228 actions\)\.

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#### 100M Reviser Example 5

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This article describes the international safety standards that iPhone batteries meet\. Underwriters Laboratory \(UL\) 2054: Covers safety of lithium\-ion batteries in general use\. This is the standard of safety, but it is also strictly acceptable for batteries in general use\. The Standard refers to some battery manufacturers which other manufacturers must rely on the standard as a result of the standard\. On other hand, if an iPhone is used to use a battery to replace or replace an old battery, there is no better the more reliable way to use the standard\. As with other standard and in of batteries, safety of battery and battery batteries use in the case of battery performance issues\. The standards used in this standard are described as part of the strict quality of the standard\.

Restoration trajectory \(202 actions\)\.

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### E\.2300M Examples

#### 300M Reviser Example 1

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Home to 279 units, Scarborough Wood Condos offers one and two bedroom \+ den suites\. They range in size from 860 sq ft to 1120 sq ft\. Building amenitiesinclude a fitness center, a fitness center, and private parking available\. Information is deemed correct at the time of publishing and is subject to change\. Real estate listings obtained from third party sources are for consumers’ personal purchasing decisions and should not be relied upon for any purpose other than to identify prospective properties consumers may be interested in purchasing\. The MLS should correct floor plans as required by the listing agents; however, all information provided by the listing agent may be different\. Not all properties are the same and the brokers may change\. Information should be independently verified, accuracy and accuracy are provided\. All information is supplied by the MLS®, a program of the MLS\. We do not guarantee the accuracy of this information\. Please call us today\! Copyright 2016\. All Rights Reserved\.

Restoration trajectory \(230 actions\)\.

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#### 300M Reviser Example 2

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with the new year, new content comes along\. The Argent Dawn will start its operations in the Plaguelands on the 23rd of January – unlocking new missions to complete\. We will be adding more games and activities in the coming months, so make sure that you follow our page on Facebook and Twitter in order to get more information on the mission\. We will be happy to help you with the new content\. As well as these new missions, we look forward to continue working on this new mission for more people\! This is a great time for our customers\. Thanks to everyone who has supported us\. As always, we are happy to use this opportunity to thank all those who have provided feedback, input and suggestions\. Thank you\.

Restoration trajectory \(203 actions\)\.

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#### 300M Reviser Example 3

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Go from black screen from your security cameras to full coverage of your retail or commercial security system with our security camera repair service\. Our customers are at the center of our universeand our service is second to none\. Security cameras come to us when their needs aren’t met\. We can also repair or replace entire systems or use additional security equipment\. We are passionate about the safety and security of our customers, and we are proud of our reputation\. If you need an solution to your security camera immediate repair problem, please contact us\. Our goal is to give you a professional, cost\-effective and affordable solution that is suitable for you\. Our professional technicians have the time and expertise to provide you with excellent solutions, and the best prices and solutions available\. To learn more, visit our website to learn more about our company and your security solutions\.

Restoration trajectory \(200 actions\)\.

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#### 300M Reviser Example 4

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Mobile optimization is one of the top priorities for any website now\-a\-days because of increased traffic & conversions from devices like mobiles & tablets\. So, folks who wishto get their business on Google and Google\+ can also boost the ranking of your site in the search engines which will increase the visibility & engagement of your website and result more traffic and revenue to your website\. And, it will also get search engines to believe in their website\. Whether you are looking for a complete mobile optimization for your website or simply want to know more about our mobile optimisation services now, we will provide you with the best mobile internet and mobile optimization services in your area\. Our website optimization services are designed to ensure that your page is accessible in all browsers and if your website is not working efficiently, we will work with you to improve your page speed\.

Restoration trajectory \(202 actions\)\.

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#### 300M Reviser Example 5

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Workplace Injury Lawyer \| Robert P\. Schuster, P\.C\. A fundamental and appropriate expectation of any employer is that a safe workplace is provided for all employeesin the workplace\. This is essential, and we are available to assist you with your legal needs\. We represent all types of clients in numerous criminal cases, including local, state, and federal\. Robert P\. Schuster and his staff are business injury lawyers, personal injury legal, and other types of business injury and can help you in a number of different fields in every aspect of your legal career\. Contact Robert P\. Schuster, P\.C\. at \(888\) 876\-3088 right away\. © 2014 Robert C\. Law Firm, Inc\.

Restoration trajectory \(171 actions\)\.

INSERT ‘Work’,INSERT ‘place’,INSERT ‘ Injury’,INSERT ‘ Law’,INSERT ‘yer’,INSERT ‘ \|’,INSERT ‘ Robert’,INSERT ‘ P’,INSERT ‘\.’,INSERT ‘ Sch’,INSERT ‘uster’,INSERT ‘,’,INSERT ‘ P’,INSERT ‘\.’,INSERT ‘C’,INSERT ‘\.’,INSERT ‘\\n’,INSERT ‘A’,INSERT ‘ fundamental’,INSERT ‘ and’,INSERT ‘ appropriate’,INSERT ‘ expectation’,INSERT ‘ of’,INSERT ‘ any’,INSERT ‘ employer’,INSERT ‘ is’,INSERT ‘ that’,INSERT ‘ a’,INSERT ‘ safe’,INSERT ‘ workplace’,INSERT ‘ is’,INSERT ‘ provided’,INSERT ‘ for’,INSERT ‘ all’,INSERT ‘ employees’, INSERT ‘,’, \[MOVE \-1\], \[MOVE \+1\], INSERT ‘\.’, \[MOVE \-1\], \[MOVE \-1\], INSERT ‘,’, INSERT ‘ personal’, INSERT ‘ injury’, INSERT ‘ legal’, \[MOVE \+1\], INSERT ‘ Inc’, \[MOVE \-2\], INSERT ‘,’, INSERT ‘ and’, INSERT ‘ and’, INSERT ‘ can’, \[MOVE \-8\], INSERT ‘ injury’, INSERT ‘ lawyers’, \[MOVE \-2\], INSERT ‘ business’, \[MOVE \+8\], INSERT ‘ other’, INSERT ‘ types’, INSERT ‘ of’, INSERT ‘ business’, INSERT ‘ injury’, \[MOVE \+2\], INSERT ‘ help’, INSERT ‘ you’, INSERT ‘ in’, INSERT ‘ a’, INSERT ‘ number’, INSERT ‘ of’, INSERT ‘ different’, INSERT ‘ fields’, INSERT ‘ in’, INSERT ‘ every’, INSERT ‘ aspect’, INSERT ‘ of’, INSERT ‘ your’, INSERT ‘ legal’, INSERT ‘ career’, INSERT ‘\.’, INSERT ‘ Robert’, INSERT ‘uster’, INSERT ‘,’, INSERT ‘ P’, INSERT ‘\.’, INSERT ‘ C’, INSERT ‘\.’, INSERT ‘ Law’, INSERT ‘ Firm’, \[MOVE \-8\], INSERT ‘ P’, INSERT ‘\.’, INSERT ‘ Sch’, \[MOVE \-4\], INSERT ‘\\n’, INSERT ‘Contact’, \[MOVE \+8\], INSERT ‘C’, INSERT ‘\.’, INSERT ‘ at’, INSERT ‘ \(’, INSERT ‘888’, INSERT ‘\)’, INSERT ‘ 8’, INSERT ‘76’, INSERT ‘\-’, INSERT ‘30’, INSERT ‘88’, INSERT ‘ right’, INSERT ‘ away’, INSERT ‘\.’, INSERT ‘\\n’, INSERT ‘©’, INSERT ‘ 2014’, INSERT ‘ Robert’, \[MOVE \+4\], \[MOVE \-64\], INSERT ‘ are’, INSERT ‘ local’, INSERT ‘,’, INSERT ‘ state’, INSERT ‘,’, INSERT ‘ and’, INSERT ‘ federal’, INSERT ‘\.’, INSERT ‘\\n’, INSERT ‘Robert’, INSERT ‘ P’, INSERT ‘\.’, INSERT ‘ Sch’, INSERT ‘uster’, INSERT ‘ and’, INSERT ‘ his’, INSERT ‘ staff’, INSERT ‘ are’, \[MOVE \-16\], \[MOVE \-2\], INSERT ‘ in’, INSERT ‘ the’, INSERT ‘ workplace’, INSERT ‘\.’, INSERT ‘ This’, INSERT ‘ is’, INSERT ‘ essential’, INSERT ‘,’, INSERT ‘ and’, INSERT ‘ we’, \[MOVE \+1\], INSERT ‘ available’, INSERT ‘ to’, INSERT ‘ assist’, INSERT ‘ you’, INSERT ‘ with’, INSERT ‘ your’, INSERT ‘ legal’, INSERT ‘ needs’, INSERT ‘\.’, INSERT ‘ We’, INSERT ‘ represent’, INSERT ‘ all’, INSERT ‘ types’, INSERT ‘ of’, INSERT ‘ clients’, INSERT ‘ in’, INSERT ‘ numerous’, INSERT ‘ criminal’, INSERT ‘ cases’, INSERT ‘,’, INSERT ‘ including’, \[MOVE \-32\],Stop

## Appendix FReproducibility Checklist

This appendix records the key artifacts and settings needed to reproduce the reported quality, trajectory, and FLOPs results\. The paper source is self\-contained in this single main\.tex file \(no external appendix \\input files are required\)\.

### F\.1Artifacts, data, and runtime

- •
- •
- •Environment: scripts/requirements\.txt \(Python package list for training, inference, evaluation, and HTML visualization scripts\)\.
- •Core runtime: PyTorch 2\.11, CUDA 13, RTX 5090\.
- •Evaluation dataset: allenai/c4 \(English validation split\), GPT\-2 tokenizer \(use\_fast=False\), keep total token length in144to216144216, fixed 35\-token prompt, target total length 180\.
- •Evaluation set size: 1000 prompts per seed\.
- •Data release policy: code is released end\-to\-end, but raw training/evaluation data and internal checkpoints are not bundled; all scripts accept user\-provided local file paths\.

### F\.2End\-to\-end code path

- •Training scripts: scripts/train/train\_ar\.py and scripts/train/train\_reviser\.py\.
- •Inference scripts:scripts/inference/run\_ar\_inference\.pyandscripts/inference/run\_reviser\_inference\.py\.
- •Evaluation scripts:scripts/eval/evalppl\.py,scripts/eval/arena\_from\_judgments\.py, andscripts/eval/trajectory\_stats\.py\.
- •HTML restoration\-trajectory viewer: scripts/viz/build\_restoration\_trajectory\_html\.py\.
- •Single\-command orchestration: scripts/reproduce\_paper\.py\.
- •Usage examples and CLI commands are documented in scripts/README\.md\.

### F\.3Model and training

- •Reviser architecture: 100M uses\(L,d,h,dff\)=\(24,512,8,2048\)\(L,d,h,d\_\{\\text\{ff\}\}\)=\(24,512,8,2048\); 300M uses\(26,896,14,3584\)\(26,896,14,3584\); RoPE and tied embeddings\.
- •Context limits: 100M\(Tmax,Lmax\)=\(255,512\)\(T\_\{\\max\},L\_\{\\max\}\)=\(255,512\); 300M\(511,512\)\(511,512\)\.
- •Action space:ℳ=\{±1,±2,±4,±8,±16,±32,±64,±128,±256,±512\}\\mathcal\{M\}=\\\{\\pm 1,\\pm 2,\\pm 4,\\pm 8,\\pm 16,\\pm 32,\\pm 64,\\pm 128,\\pm 256,\\pm 512\\\}\.
- •Optimizer/training: AdamW \(β1=0\.9,β2=0\.95,ϵ=10−8\\beta\_\{1\}=0\.9,\\beta\_\{2\}=0\.95,\\epsilon=10^\{\-8\}, wd=0\.1\), cosine schedule with 2000\-step warmup, bf16, dropout 0\.1, grad clip 1\.0\.
- •Learning rates: 100M peak/min10−4/2×10−510^\{\-4\}/2\\times 10^\{\-5\}; 300M peak/min10−5/10−610^\{\-5\}/10^\{\-6\}\.
- •Effective batching: 100M \(bs 64, accum 1, seq 256\); 300M \(bs 16, accum 4, seq 512\)\.
- •Training budget: 30B processed tokens\.
- •Trajectory construction: obfuscation mixp​\(Delete\)=0\.8p\(\\text\{\{Delete\}\}\)=0\.8,p​\(Move\)=0\.2p\(\\text\{\{Move\}\}\)=0\.2\.

### F\.4Hardware and FLOPs accounting

- •Hardware: single RTX 5090 \(32GB VRAM\), single\-node PCIe setup \(no DDP/FSDP/pipeline parallelism\)\.
- •Software: PyTorch 2\.11 \+ CUDA 13; PyTorch SDPA attention kernels; no external flash\_attn\.
- •FLOPs protocol for Appendix metrics: dominant\-matmul proxy in[Appendix˜B](https://arxiv.org/html/2609.20830#A2)with shared constantsn=128n=128,\|Vc\|=50000\|V\_\{c\}\|=50000,d=768d=768,L=12L=12,dff=4​dd\_\{\\text\{ff\}\}=4d,Kmax=16K\_\{\\max\}=16\.

### F\.5Decoding and inference configuration

- •Action selection: multinomial sampling with temperatureτ=0\.9\\tau=0\.9, top\-k=50k=50, and no top\-pptruncation\.
- •Stop criteria: stop on END\_OF\_RESPONSE \(id 50260\); decoding caps generation at 256 actions\.
- •Validity masking: enforce cursor bounds, canvas length bounds, and operator validity \(e\.g\.,Deleteinvalid at cursor position 0; reserved tokens never trained/selected\)\.
- •Prompting/conditioning \(if any\): no special delimiter tokens; boundary is positional\. Prompt prefix occupies positions\[0,35\)\[0,35\)and continuation/editable region is\[35,180\)\[35,180\)\. For SEDD/MDLM, prefix projection clampsx\[:,0:35\]=prefix\_idsx\[:,0:35\]=\\text\{prefix\\\_ids\}at every diffusion step; for Reviser, the prompt is provided as the first 35 inserted prompt tokens and continuation actions are generated thereafter\.
- •Diffusion baselines: SEDD and MDLM are decoded with 128 diffusion steps\.

### F\.6Evaluation protocol and reporting

- •Primary quality metrics: evalPPL and with\-input arena win rates; implementation/library: GPT\-2 Large scoring \+ Skywork\-Critic\-8B arena judge\.
- •Aggregation: mean±\\pmstd over 3 seeds \(123, 124, 125\)\.