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Long-Context Drafting Does Not Require Long-Context Drafters

Aref Jafari, Vansh Bhatia, Matt Qin, Subhajit Dutta Chowdhury, Ben Lee, Vikram Appia, Ali Ghodsi, Mehdi Rezagholizadeh

arXiv:2610.20865v1cs.LG

TL;DR

At ultra-long context, full-prefix drafting inherits context-dependent cost, undermining speculative decoding’s efficiency. The paper freezes short-context target-conditioned drafters and combines attention windowing with rotary-index re-basing; the drafters retain their speedups at 2M tokens, subject to the speculative cost condition.

  • Problem

    At ultra-long context, a full-attention drafter’s cost grows with the prefix, eroding speculative decoding’s advantage over target-only decoding.

    Source: §1 · p. 1

  • Method

    The paper freezes target-conditioned short-context drafters and uses windowing plus rotary-index re-basing to bound their attention and positions without changing weights.

    Source: §1 · p. 2

  • Results

    At 2M, frozen Inferact and RadixArk retain 90% and 119% of their respective 8k speedups with the full method.

    Source: §1 · p. 3

  • Takeaways & Limitations

    The recipe spans 4k to 2M tokens without weight updates or a new checkpoint, with a short-context speedup cost of at most 0.16×.

    Source: §1 · p. 3

    Profitability is conditional on speculative cost per emitted token staying below matched target-only cost, which expensive verification can prevent.

    Source: §7 · p. 9

Abstract

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Speculative decoding pairs a cheap drafter with parallel verification against the target. At ultra-long context it stops paying, because a drafter that attends over the full prefix inherits the target's context-dependent cost, so the speedup it was meant to provide first erodes and then reverses. The standard response is to build a long-context drafter, by training or fine-tuning one, or by using a multi-token-prediction head shipped inside the target checkpoint. We argue this is unnecessary, because the drafters in use are target-conditioned, reading hidden states the target computed over the entire prefix, so distant context already reaches them without their own attention, and verification corrects what they miss. We therefore freeze released short-context drafters and run them far past their training length under two inference-time mechanisms, one bounding the attention cache they see, which fixes their cost, and one re-basing their rotary position indices into the trained range. No weight is touched and the only tunable saturates early, so one vLLM-side configuration spans 4k to two million tokens, costing at most 0.16x of speedup at short length. We prove when a common index shift leaves the drafter's computation exactly unchanged, and decompose acceptance into two measurable gaps with sharp bounds. Whatever speedup a frozen drafter delivers at short context, it retains out to two million tokens, across three target-drafter pairs and five corpora. The claim concerns the flatness rather than the multiple, and removing either mechanism eliminates it. The gain is conditional on the speculative cost per emitted token staying below the matched target-only cost.

1 Introduction

Full-prefix drafting loses its cost advantage at ultra-long context, but target-conditioned drafters receive distant-context information through target hidden states. Windowing and rotary-index re-basing let frozen short-context drafters retain their short-context speedup at much longer lengths.

1 Introduction

  • A full-attention drafter inherits context-dependent attention cost, and drafting rereads the N-sized KV cache K times per round while verification reads it once.The conventional response is to train long-context drafters or use a target checkpoint’s native multi-token-prediction head.Source: §1 · p. 1
  • Target-conditioned drafters receive target hidden states computed over the whole prefix, so limiting their attention window does not cut them off from distant-context information.Re-basing indices separately bounds rotary positions; the two mechanisms address distinct failure modes.Source: §1 · p. 2, Figure 2 · p. 2
  • The theory identifies when a common RoPE shift preserves computation and bounds acceptance using a target-truncation gap and a deployed-drafter fidelity gap.The measured recipe uses no weight updates and spans 4k to 2M tokens, with a short-context cost of at most 0.16×.Source: §1 · pp. 2–3
  • At 2M, the full method retains 90% and 119% of the two drafters’ 8k speedups; removing re-basing or windowing reduces retention substantially.The results are measured on frozen drafters; the claim is about flatness, not the absolute speedup multiple.Source: §1 · p. 3

2 Background

Speculative decoding drafts several tokens and verifies them against the target in one parallel pass. Its efficiency depends on proposal acceptance and on drafting cost relative to target decoding.

2 Background

  • A speculative round proposes K tokens from drafter q and verifies them against target p in one parallel pass, correcting rejected proposals.The target and drafter predictive distributions at position t are denoted p_t and q_t.Source: §2 · p. 3
  • Under a geometric model with common independent acceptance probability α, expected emitted length including the bonus token is MAL(α, K) = Σ from j=0 to K of α^j.The passage describes this as an approximation because rejection changes later conditioning.Source: §2 · p. 3
  • RoPE rotates coordinate pair i of each head by mθ_i, with θ_i = 10000^(-2i/d); greedy decoding accepts on exact token agreement.The cited passage also notes a stage-specific bound without assuming independent acceptances.Source: §2 · p. 3

3 Related Work

Prior approaches to long-context speculative decoding train or specialize drafters, alter verification, or use other drafting strategies. This paper instead compares inference-time changes to a released drafter against its unwindowed and windowed-only configurations.

3 Related Work

  • Long-context drafters have been trained, while verification-side approaches use sparse caches or positional fine-tuning; this work leaves verification exact and changes only the drafter’s view.The authors describe these directions as composable rather than competing.Source: §3 · p. 3
  • The internal comparisons use a released drafter as the unwindowed arm and a bounded cache with true indices as the windowed-only arm.The authors report no external system baseline because the cited alternatives do not match the fixed-weight, full-context operating point.Source: §3 · p. 4

4 Method

The method freezes a target-conditioned short-context drafter, limits its visible attention cache, and re-bases rotary indices. Windowing controls attention cost; re-basing addresses position indices that otherwise exceed the implementation’s rotary reach.

4.1 Setup and windowing

  • The drafter’s cache holds only the latest W tokens, bounding its attention cost in context length N while the target verifies proposals against the complete context.Target hidden states are computed over the full prefix, so a window of features can carry information beyond its window of tokens.Source: §4.1 · p. 4

4.2 The position problem

  • Windowing bounds visible offsets but not rotary indices, which can exceed Pmax and quietly degrade acceptance while the verifier preserves the target’s intended output law.Renumbering each sliding window from zero would require re-rotating cached keys as their local indices change.Source: §4.2 · p. 4

4.3 Rotary index re-basing

  • Within an index band, re-basing assigns m mod Pmax, shifting all indices by a common constant and preserving attention scores while keeping evaluated indices in [0, Pmax).The scheme requires W ≤ Pmax and leaves positions below Pmax unchanged.Source: §4.3 · p. 4
  • Exact equivalence is not certified when a prediction’s visible keys or cached ancestors cross an index-band boundary.The proposition’s guarantee assumes identical per-position inputs, deterministic exact-arithmetic inference, fixed-frequency RoPE, and a translation-invariant mask.Source: §4.3 · p. 5

5 Why This Works

Windowing limits the drafter’s cost while target-computed hidden states preserve access to distant context; re-basing handles rotary indices beyond the drafter’s trained range. Acceptance is bounded by two measurable gaps, but those bounds do not guarantee constant acceptance across context lengths.

5 Why This Works

  • Target-conditioned drafters receive full-prefix information through target hidden states, while local attention bounds only the positions whose rotary indices enter their computation.Information dependency spans the prefix; index dependency stays local under local drafter attention.Source: §5 · p. 5

5.1 The truncation–fidelity decomposition

  • The truncation gap compares the full target with a fresh-window target, while the fidelity gap compares that windowed target with the deployed drafter.The triangle inequality bounds the target–drafter discrepancy, but choosing a window no larger than training length bounds neither gap.Source: §5.1 · p. 5

5.2 The bound: sampling and greedy verification

  • For every state law, mean acceptance lies between [1 − Ā − δ]+ and 1 − |Ā − δ|, where Ā and δ are the mean truncation and fidelity gaps.The endpoints are attainable for vocabularies of size at least three; the two errors can cancel as well as add.Source: §5.2 · pp. 5–6

5.3 Context length and window selection

  • Bounds at different context lengths use different state laws, so constant mean gaps do not imply constant acceptance; selecting W requires both gaps and decoding cost on a calibration grid.The bounds also extend to whole rounds without assuming independent acceptances.Source: §5.3 · p. 6

6 Experiments

Experiments compare frozen drafters under controlled context and position settings, measuring decode-phase speedup and emitted tokens per round. Windowing plus re-basing preserves short-context speedup at extreme lengths across three target–drafter pairs, while the ablations and gap measurements distinguish cost from acceptance effects.

6 Experiments

  • The experiments use three target–drafter pairs and five corpora; timing and acceptance use deployment states, while the gap measurements use a fresh-drafter law.Measurements are single-stream and greedy, with decode-phase timing excluding prefill and speedup paired against target-only runs on identical prompts.Source: §6 · p. 6, §6.1 · p. 6

6.1 Setup and measurement controls

  • A single flag changes rebasing between the two windowed arms, while the controlled comparison holds target, prompts, block size, and samples fixed.The main ladder compares unwindowed, windowed-only, and windowed plus re-based drafting.Source: §6.2 · pp. 6–7

6.2 Windowed drafting to two million tokens

  • 90% and 119% of 8k speedup are retained at 2M by windowed, re-based Inferact and RadixArk, respectively; the claim is flatness, not a particular speedup multiple.The table reports three arms on Kimi-K3 and PG19; its retention row compares each arm’s 2M speedup with its own 8k speedup.Source: §6.2 · p. 7, Table 1 · p. 7
  • Unwindowed drafting loses speedup as context grows, while windowing alone fixes its cost but collapses beyond Pmax; both mechanisms are needed for flatness.At 2M, windowing-only retains S/MAL of 0.78 but emits only the bonus token, indicating an acceptance failure; unwindowed drafting can become too costly even when MAL remains above one.Source: §6.2 · pp. 7–8

6.3 Beyond Kimi-K3 and DSpark

  • The pattern also holds on Qwen EAGLE-3 and MiniMax-M3 EAGLE-3.1, including a target whose decode rate falls only 26% over 250× context.On MiniMax-M3, windowed drafting retains 1.11 of its 4k speedup at 1M, versus 0.74 unwindowed; it answers 120/120 single-needle RULER tasks.Source: §6.3 · p. 8

6.4 Window and sink ablations

  • On the measured drafter, mean MAL at W = 1024 and W = 2048 differs by at most 0.02, showing saturation by 1024 without establishing equivalence.The sink sweep supports s = 0 for Inferact, but RadixArk responds in the opposite direction.Source: §6.4 · p. 8

6.5 Measuring the two gaps

  • Fresh-drafter fidelity stays near 0.68 across a 64× window range, while the truncation gap falls by 0.159 and measured acceptance moves by only 0.019.The target-state feature channel differs by 0.22–0.33 in TV between full-pass and truncated-pass inputs; these measurements characterize the checkpoint, not the deployed cache.Source: §6.5 · pp. 8–9

7 Limitations

The evidence and guarantees have defined experimental and architectural boundaries: profitability is conditional, re-basing exactness depends on RoPE and masking assumptions, and measured gaps do not establish deployment-wide behavior. The paper also describes its AI assistance and planned reproducibility materials.

7 Limitations

  • Profitability requires speculative cost per emitted token to stay below matched target-only cost, and no formal lossless-decoding claim is made.The theory assumes fixed-frequency RoPE with translation-invariant masking; recurrence, learned absolute positions, and finite precision require separate treatment.Source: §7 · p. 9
  • The reported ladder is single-stream, greedy, on one platform, with five samples per cell; batched serving was spotchecked on one pair and differed at short context.The paper also states that re-basing was exercised only on the pair whose rotary reach is crossed by the served context.Source: §7 · p. 9

AI use statement

  • The authors report using generative AI to proofread and assist with writing, and say they reviewed the assisted text, citations, and mathematical transcription.They take responsibility for the final content, including AI-assisted text, claims, and artifacts.Source: AI use statement · p. 9

Reproducibility statement

  • The paper says checkpoints, prompt manifests, per-sample logs, gap sweeps, and the vLLM patch implementing both mechanisms will accompany it.It identifies the pinned engine build used to revalidate the length ladder.Source: Reproducibility statement · p. 9

A.1 RoPE, cached dependency spans, and band boundaries

  • Within one index band, a common RoPE shift preserves outputs under the stated hypotheses; boundary-crossing dependency graphs are not certified, and the theory excludes several position and precision settings.The boundary-position bound counts predictions not certified by exactness, not discrepancy magnitude or observed errors.Source: §A.1 · pp. 12–13

A.2 Sharpness of the sampling mean bounds

  • The mean acceptance bounds are sharp over arbitrary distributions and state laws, but their constructions do not assert that one trained model realizes every case.Joint gap information can give strictly stronger bounds when the two gaps are not almost surely ordered the same way.Source: §A.2 · p. 13, §A.3 · p. 13

A.3 Joint forms and acceptance drift

  • Uniform bounds on both mean gaps imply a lower bound on acceptance across tested lengths; measured gaps cannot be transferred between different evaluation laws or comparators.With constant truncation and fidelity at most b, the guaranteed pairwise drift is at most 2b.Source: §A.3 · p. 13

A.4 Extended discussion of the decomposition

  • Choosing W at or below training length and keeping rotary indices in range bounds neither fidelity nor resemblance of mid-document windows to training inputs.Explaining an implementation requires measuring both gaps under the corresponding evaluation law; fresh-drafter comparisons are distinct from deployed-cache behavior.Source: §A.4 · p. 14

A.5 Greedy case analysis, sharpness, and a margin condition

The appendix sharpens greedy-acceptance bounds, identifies a margin condition for agreement, and qualifies how finite-prefix behavior and emitted-length guarantees depend on their assumptions. Related work addresses distinct operating points, mechanisms, and benchmark coverage.

A.5 Greedy case analysis, sharpness, and a margin condition

  • For vocabularies with at least three symbols, the mean greedy-acceptance bounds are sharp, with constructions attaining their endpoints.Binary vocabularies are an exception because the all-distinct construction is unavailable.Source: §A.5 · p. 15
  • A target-margin condition guarantees that the drafter selects the full target’s greedy token, while arbitrarily small softmax TV alone need not prevent disagreement.The condition compares the target margin with the two TV gaps.Source: §A.5 · p. 15

A.6 Finite-prefix corrections and stationarity

  • Finite-prefix deviations and exceptional positions bound the correction to each acceptance endpoint by ηA + ηB + 2ϵN.The stationarity argument applies to a shared finite-suffix state, not automatically to the full target or a target-conditioned drafter.Source: §A.6 · pp. 15–16

A.7 Emitted-length proof and the geometric model

  • A lower bound on acceptance hazards at every reachable stage gives a lower bound on expected emitted block length without assuming independent acceptances.Emitted length alone does not determine speedup, and the result assumes fixed K.Source: §A.7 · p. 16

B Extended related work

  • Prior work addresses long-context drafting through training, target-resident multi-token heads, altered verification, or surface-based retrieval rather than this paper’s frozen external drafter setting.The cited approaches have different prerequisites or output rules, so they address distinct operating points.Source: B Extended related work · p. 17
  • Existing speculative-decoding benchmarks are mostly short-context; SPEED-Bench reaches 32k, while LongBench and RULER extend farther but do not instrument acceptance or emitted length.The paper uses SPEED-Bench for gap measurements and a window ablation, and collects per-round quantities itself.Source: B Extended related work · pp. 16–17

C Why the comparison is internal

The paper compares internal arms because published alternatives either change the drafter, require an unavailable target property, alter verification, or operate at shorter contexts. Its arms run under shared conditions, while a relevant positioning alternative remains untested.

C Why the comparison is internal

  • Training-based alternatives change the drafter, Windowed-MTP requires a target-resident head, and SpecPV or RAPID change the verification rule or target distribution.These differences make the alternatives answer a different comparison question or require a property absent from the evaluated setting.Source: C Why the comparison is internal · p. 17
  • The internal arms share an engine build, node, and prompt set, and the windowed-only and re-based arms differ by one environment flag.This setup isolates a single factor in each contrast rather than comparing systems built under different conditions.Source: C Why the comparison is internal · p. 18
  • StreamingLLM’s cache-relative indexing is not evaluated; comparing its wall-clock cost with re-basing requires fused-kernel and bandwidth accounting that remains future work.The stated trade-off is recurring cache re-rotation versus possible band-boundary effects.Source: C Why the comparison is internal · p. 18

D Additional experimental tables

The additional experiments test whether the flatness result extends across target–drafter pairs, corpora, retrieval tasks, and batching, while identifying measurement and configuration qualifications. They find that bounded drafting retains speedups at long contexts, with scope and reliability varying by setting.

D Additional experimental tables

  • The Qwen ladder’s revalidation matches the original MAL values within one standard error through 128k; the 1M table column is excluded from paper claims.An exploratory K sweep finds K = 3 at or near the throughput optimum, while the K=3 to K=5 change flips sign with context.Source: D Additional experimental tables · p. 18, Table 2 · p. 19

E.1 A third pair: MiniMax-M3 with EAGLE-3.1

  • At 1M, MiniMax-M3’s windowed arm retains 1.11 of its 4k speedup, versus 0.74 for the unwindowed arm; the gap reflects acceptance, not target collapse.The target loses only 26% of its decode rate from 4k to 1M, and MAL/S stays 1.27–1.37 for the windowed arm.Source: §E.1 · p. 19, Table 5 · p. 20

E.2 Re-basing ablation

  • At 1M, a matched toggle confirms re-basing is inert below Pmax, while exceeding the rotary table limit causes MAL to collapse near one.The collapse leaves text correct but can push speedup below 1×; re-basing rescues only the windowed drafter.Source: §E.2 · p. 20, Table 6 · p. 21

E.3 Beyond PG19: LongBench, BEAM, and SPEED-Bench

  • Across LongBench, windowed Inferact holds 2.29–2.62× from 8k to 2M, while windowed RadixArk holds 1.68–2.18× except for one 32k dip.The unwindowed arms show distinct failures: Inferact’s acceptance collapses, while RadixArk’s full-KV read drives speedup down to 0.14× at 2M.Source: §E.3 · p. 21, Table 7 · p. 21
  • On BEAM v2, both windowed drafters retain 0.96 and 0.88 of their 8k speedup at 2M after chat-template prompts and EOS stopping remove forced-continuation loops.The 2M BEAM result is less secure because that tier changes both prompt construction and source data; SPEED-Bench separately finds at most a 0.16× short-context speedup cost for windowed Inferact.Source: §E.3 · p. 22

E.4 Retrieval under a bounded drafter view

  • On RULER single-needle tasks, the target and windowed Inferact both answer 120 of 120 correctly on each of three variants from 8k to 1M.Speedup varies with the haystack: 2.41× on synthetic noise and 1.54× and 1.38× on natural-prose haystacks.Source: §E.4 · p. 22, Table 8 · p. 23

E.5 Batched serving

  • With batching, windowed Inferact stays above break-even in all 19 measured cells at 1.14–2.45×, while unwindowed falls below break-even in 10 cells.The long-context ordering survives from 131k onward, but the windowed advantage decays toward break-even as batch size rises.Source: §E.5 · pp. 22–23

E.6 Sink-size ablation

The long-context window sweep found acceptance nearly unchanged across window sizes, while the sink ablation favored no pinned prefix tokens on Inferact. These results support short-length window calibration, but do not establish a generally optimal window or sink setting for RadixArk.

E.6 Sink-size ablation

  • At 1M context, any sink budget reduced MAL by more than one point on Inferact, and the penalty did not shrink from 4 to 32 sink tokens.The sweep held other settings fixed at W = 4096, with n = 5 per point.Source: §E.6 · p. 23, Table 10 · p. 24
  • The paired s ∈ {0, 128} sweep, together with the sink ablation, supports s = 0 for Inferact.RadixArk responded in the opposite direction on a single sweep, so the paper reports no evidence that s = 0 is its best setting; it was used there for comparability.Source: §E.6 · p. 24

E.7 Window-size ablation at long context

  • At 1M context, acceptance spread only 0.09 MAL across a 4× range of window sizes, less than the sample spread within any one setting.The result supports selecting a saturating window at a short calibration length, but does not establish the generally optimal W: the gaps need not be monotone, and cost depends on the serving stack.Source: §E.7 · pp. 24–25
  • The long-context window sweep supports carrying a saturating window forward as context grows, rather than reselecting it at each length.The authors report the 1M sweep on Inferact only; the matching RadixArk sweep predates the re-basing fix and its 1M points are not considered trustworthy.Source: §E.7 · pp. 24–25

F Gap measurement details

The gap measurements show consistent entropy-tier separation and distinct greedy rejection patterns, but the authors qualify their interpretation because the measurements and several controls differ from deployment conditions. Their measurement controls address large shifts in reported quantities caused by asymmetric execution or precision.

F Gap measurement details

  • Low-entropy prompts had higher MAL than high-entropy prompts in every arm and tier: 1.713 versus 1.634 at 32k windowed.The authors do not count this as independent confirmation because a stratum labeled by a measured gap cannot certify that same gap.Source: F Gap measurement details · p. 25
  • At 32k mid-document, the 1024-token-trained EAGLE-3 head had 33–35% argmax agreement with the truncated target, versus 61.8% on its training distribution.The mismatch may affect measured δ ≈ 0.68, but the comparisons establish neither direction nor magnitude; whether the observations persist under domain-matched deployment remains untested.Source: F Gap measurement details · p. 25
  • Across six windows, high-entropy documents had δ of 0.715–0.735 and Eµ[αt] of 0.263–0.276, versus 0.558–0.592 and 0.406–0.439 for low-entropy documents.The tier labels are third-party benchmark labels, so the authors treat this as a consistency check, not independent confirmation of the gaps; only four clean low-entropy documents remained after filtering.Source: F Gap measurement details · p. 25
  • At W = 2048, fidelity-only flips rose from 0.442 to 0.598 as truncation-driven rejections fell from 0.214 to 0.070, while greedy agreement stayed near 0.332–0.355.The greedy fidelity flip rate is bounded by δg ∈ [0.573, 0.675].Source: F Gap measurement details · p. 25

G Measurement controls

  • The measurement controls were consequential: asymmetric graph capture shifted one speedup ratio from 0.38× to 2.21×, and bf16 control TV reached 3.0 × 10^-2 versus 3.0 × 10^-11 median in fp32.The controls also synchronize shared-node runs after loading and collect timings without a per-forward profiler, which taxes speculative and target-only arms unequally.Source: G Measurement controls · p. 26

H What the measurements do not establish

The paper identifies limits in how its gap measurements map to deployment and in what its theory covers. It also reports unresolved greedy-output divergence on Kimi-K3, which complicates interpretation of the proposed gap decomposition.

H What the measurements do not establish

  • The gap measurements use clean forward passes at corpus positions, not reached proposal states from the cached drafter under eviction, re-basing, and rollback.The logged aggregates cannot reconstruct per-step greedy data; the authors propose an instrumented run recording target, fresh truncated-target, and cached-drafter tokens at sampled reached states.Source: H What the measurements do not establish · p. 26
  • Proposition 3 covers rotary index locality, not information in full-context features, and the boundary bound counts positions not certified exact rather than observed discrepancies.MAL remains a geometric model, while Proposition 8 needs stage-specific laws the paper does not yet have.Source: H What the measurements do not establish · p. 26
  • The 1024-token-trained drafter is evaluated far outside its training distribution, so δ includes graph mismatch and model difference, with unknown direction and magnitude.At million-token contexts, target hidden states also come from sequence lengths the draft head did not see in training; the theory does not bound that feature-channel shift.Source: H What the measurements do not establish · p. 26
  • On Kimi-K3, greedy speculative decoding diverged from target-only output in every run, sometimes at the first generated token, and the benign-numerical-nondeterminism explanation is unproven.A target-only rerun at matched and differing batch shapes is described as necessary before interpreting the reached-state gap decomposition.Source: H What the measurements do not establish · p. 26

I The full truncation grid and the threshold screen

The target-only truncation screen is nearly monotone in aggregate, but many individual positions reverse direction as the window grows. The threshold screen is the weaker bound and does not measure δ.

I The full truncation grid and the threshold screen

  • The sweep covered 34 windows on 14 usable 32k documents and 1,750 positions after excluding six documents with padding-dominated tails.Those excluded tails yielded ρ̂ = 0 at every window, which would have manufactured an apparent low-entropy-tier floor.Source: I The full truncation grid and the… · p. 27, Table 13 · p. 27
  • Across 1,347 positions crossing below τ = 0.05, 590 later returned above it (43.8%), although aggregate ρ̂(W, 0.05) fell from 0.719 to 0.321 with one 0.006 increase.A window sufficient at one position need not suffice at a larger one, so the paper claims no monotonicity guarantee.Source: I The full truncation grid and the… · p. 27
  • At W = 512, 2048, and 8192, cache-eviction and fresh hard-truncation passes had median TV of 0.261, 0.211, and 0.206, respectively.The comparator must specify its input construction, not just its nominal window length.Source: I The full truncation grid and the… · p. 27
  • At W = 2048, ρ̂(W, 0.05) was 0.709 on ten high-entropy documents versus 0.276 on the four clean low-entropy documents.The tier ordering held at every window, but the authors call this preliminary because only four clean low-entropy documents survived filtering.Source: I The full truncation grid and the… · p. 27
  • At every window, 1 − Ā exceeded B(W) by 0.14–0.27, making the threshold-screen bound weaker; Figure 3 plots B(W) and does not measure δ.The optimizing tolerance τ* ranged from 0.310 at W = 128 to 0.130 at W = 11776.Source: I The full truncation grid and the… · p. 27, Figure 3 · p. 28

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