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arxiv: 2606.24163 · v1 · pith:RN6PLMLBnew · submitted 2026-06-23 · 💻 cs.CR · cs.CL

CORE-BREW: LLR-Based Soft Decoding for Robust Multi-Bit LLM Watermarking

Joeun Kim , HoEun Kim , Young-Sik Kim This is my paper

Pith reviewed 2026-06-25 23:41 UTC · model grok-4.3

classification 💻 cs.CR cs.CL
keywords LLM watermarkingsoft decodinglog-likelihood ratiomulti-bit watermarkrobustnessfalse positive rateLLR
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The pith

CORE-BREW derives closed-form per-token LLRs for soft-decision decoding in multi-bit LLM watermarks by targeting a fixed hit rate.

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

The paper introduces CORE-BREW as an extension to block-wise BREW that embeds watermarks while holding the hit rate at a chosen constant p-star. This calibration step produces exact log-likelihood ratios for each token, which soft-decision decoding can then use instead of discarding reliability information. The method offers two operating modes that keep false-positive rates under control even when text is edited or paraphrased. A reader would care because multi-bit watermarks need to survive real-world modifications if they are to serve as reliable provenance signals for LLM outputs.

Core claim

CORE-BREW calibrates the watermark channel by targeting a fixed hit rate p-star, yielding closed-form per-token log-likelihood ratios for principled soft-decision decoding. It supports Strict-Safe mode, which preserves the bounded-distance designated-codeword acceptance region, and FPR-Calibrated mode, which uses likelihood-based scoring together with lightweight list decoding. Experiments on open-source LLMs under token-level edits and paraphrasing show improved low-FPR discrimination and robustness over prior multi-bit watermarking baselines while maintaining comparable semantic quality.

What carries the argument

Constant-hit-rate embedding that produces per-token LLRs for soft decoding of the watermark.

If this is right

  • Token reliability information can be retained and used rather than thrown away by hard decisions.
  • Strict-Safe mode keeps the original acceptance region while FPR-Calibrated mode trades off detection thresholds explicitly.
  • Low false-positive performance improves under both local edits and global paraphrasing.
  • Semantic quality of the watermarked text stays comparable to unwatermarked baselines.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same fixed-hit-rate calibration step could be applied to other embedding families to obtain analogous LLR expressions.
  • Standard soft-decision algorithms from communication theory become directly usable once the LLRs are available.
  • List decoding in the FPR-Calibrated mode opens a path to message-length scaling without exponential growth in search cost.

Load-bearing premise

A fixed target hit rate p-star produces accurate closed-form LLRs that remain reliable under token-level edits and paraphrasing without further adjustments.

What would settle it

A test in which the measured hit rate after paraphrasing deviates enough from p-star that the LLR decoder no longer outperforms hard-decision baselines at the target false-positive rate.

Figures

Figures reproduced from arXiv: 2606.24163 by HoEun Kim, Joeun Kim, Young-Sik Kim.

Figure 1
Figure 1. Figure 1: Overview of CORE-BREW. Constant Hit-Rate embedding provides calibrated reliability [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: ROC curves under the clean setting. (a) Full ROC comparison. (b) Zoomed view of the low-FPR region. CORE-BREW variants and BREW [9] achieve strong discrimination, while MPAC [27] and Qu et al. [19] remain close to random guessing. 0.0 0.2 0.4 0.6 0.8 1.0 False Positive Rate (FPR) 0.0 0.2 0.4 0.6 0.8 1.0 True Positive Rate (TPR) Ideal (FPR=0, TPR=1) C4 MPAC (AUC=0.580) Qu et al. (AUC=0.512) BREW (AUC=0.828)… view at source ↗
Figure 5
Figure 5. Figure 5: ROC curves under 10% token-level in￾sertion on C4 (left) and OpenGen (right). All methods degrade under insertion, but CORE￾BREW and BREW [9] maintain stronger perfor￾mance than MPAC [27] and Qu et al. [19]. 6.4 Paraphrasing and Semantic Editing (Q3) 0.0 0.2 0.4 0.6 0.8 1.0 False Positive Rate (FPR) 0.0 0.2 0.4 0.6 0.8 1.0 True Positive Rate (TPR) Ideal (FPR=0, TPR=1) C4 MPAC (AUC=0.710) Qu et al. (AUC=0.4… view at source ↗
Figure 6
Figure 6. Figure 6: ROC curves under T5-based paraphras￾ing on C4 and OpenGen. CORE-BREW maintains strong low-FPR discrimination, while MPAC and Qu et al. [19] suffer from high FPR. We evaluate robustness against realistic para￾phrasing attacks that aim to remove watermark signals while preserving semantic content. Para￾phrases are generated using models distinct from the watermark generator, following prior work [23, 15, 11,… view at source ↗
Figure 7
Figure 7. Figure 7: Ablation on entropy-aware erasures under the clean setting at [PITH_FULL_IMAGE:figures/full_fig_p027_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Sensitivity of detection performance to the window-shift budget [PITH_FULL_IMAGE:figures/full_fig_p028_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: ROC curves under 10% token-level substitution attacks on C4 (left) and OpenGen (right). [PITH_FULL_IMAGE:figures/full_fig_p029_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: ROC curves under 10% deletion attacks on C4 (left) and OpenGen (right). CORE-BREW [PITH_FULL_IMAGE:figures/full_fig_p029_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: ROC curves under 10% insertion attacks on C4 (left) and OpenGen (right). All methods [PITH_FULL_IMAGE:figures/full_fig_p030_11.png] view at source ↗
read the original abstract

Reliable provenance for LLM outputs requires multi-bit watermarks that remain robust under editing while maintaining strict false-positive control. Existing ECC-based LLM watermarks rely largely on hard-decision decoding, discarding token-level reliability information. We propose CORE-BREW, a Constant-hit-Rate Embedding extension of block-wise BREW for robust multi-bit watermarking. CORE-BREW calibrates the watermark channel by targeting a fixed hit rate p-star, yielding closed-form per-token log-likelihood ratios (LLRs) for principled soft-decision decoding. It supports two detection modes: Strict-Safe, which preserves the bounded-distance designated-codeword acceptance region, and FPR-Calibrated, which uses likelihood-based scoring and lightweight list decoding to characterize the FPR-TPR trade-off. Experiments on open-source LLMs under token-level edits and paraphrasing demonstrate improved low-FPR discrimination and robustness over prior multi-bit watermarking baselines while maintaining comparable semantic quality.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes CORE-BREW, a constant-hit-rate extension of block-wise BREW watermarking for multi-bit LLM provenance. By targeting a fixed hit rate p-star during embedding, it derives closed-form per-token LLRs that enable soft-decision decoding. Two detection modes are supported: Strict-Safe (preserving bounded-distance acceptance) and FPR-Calibrated (likelihood scoring with list decoding). Experiments on open-source LLMs claim improved low-FPR discrimination and robustness to token edits and paraphrasing relative to prior multi-bit baselines, while preserving semantic quality.

Significance. If the LLR derivation remains valid under editing, the work supplies a principled soft-information channel model for multi-bit watermark detection that could tighten FPR-TPR trade-offs without sacrificing the designated-codeword guarantees of earlier hard-decision schemes.

major comments (2)
  1. [§3] §3 (CORE-BREW construction): the closed-form LLR expressions are obtained under the assumption that the per-token hit probability equals the design parameter p-star exactly and is stationary across tokens and contexts. Token-level edits and paraphrasing change both the token distribution and the effective embedding behavior, so the observed hit/miss statistics deviate from p-star; no explicit bound is supplied showing that the resulting LLR mismatch remains small enough to preserve the claimed FPR calibration.
  2. [§5] §5 (robustness experiments): the reported gains in low-FPR discrimination are shown only via aggregate ROC curves; the manuscript does not report the empirical per-token hit rates after each edit type, nor does it compare the LLRs computed from the nominal p-star against LLRs recomputed from the observed post-edit statistics, leaving open whether the soft-decision advantage survives the distribution shift.
minor comments (2)
  1. [Abstract] The abstract states that the scheme 'yields closed-form per-token log-likelihood ratios' but does not cite the equation number or subsection containing the derivation.
  2. [§4] Notation for the two detection modes (Strict-Safe vs. FPR-Calibrated) is introduced without a compact table summarizing the acceptance region, scoring function, and list-decoding parameters for each mode.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and for highlighting the importance of validating the LLR model under distribution shift. We respond to each major comment below.

read point-by-point responses

  1. Referee: [§3] §3 (CORE-BREW construction): the closed-form LLR expressions are obtained under the assumption that the per-token hit probability equals the design parameter p-star exactly and is stationary across tokens and contexts. Token-level edits and paraphrasing change both the token distribution and the effective embedding behavior, so the observed hit/miss statistics deviate from p-star; no explicit bound is supplied showing that the resulting LLR mismatch remains small enough to preserve the claimed FPR calibration.

    Authors: The closed-form LLRs are indeed derived under the modeling assumption that the constant-hit-rate embedding achieves exactly p-star on average. CORE-BREW enforces this target by construction via per-context adjustment of the embedding probability; the Strict-Safe detector does not use the LLR values at all and therefore inherits the same bounded-distance guarantees as the original BREW scheme. For the FPR-Calibrated detector we treat the nominal LLRs as an approximation. The current manuscript does not supply a formal bound on the mismatch induced by edits. In revision we will add an explicit statement of the stationarity assumption in §3 together with a short discussion of its implications. revision: partial

  2. Referee: [§5] §5 (robustness experiments): the reported gains in low-FPR discrimination are shown only via aggregate ROC curves; the manuscript does not report the empirical per-token hit rates after each edit type, nor does it compare the LLRs computed from the nominal p-star against LLRs recomputed from the observed post-edit statistics, leaving open whether the soft-decision advantage survives the distribution shift.

    Authors: We agree that reporting the post-edit hit-rate statistics and a direct comparison of nominal versus observed LLRs would strengthen the robustness claims. In the revised manuscript we will add a table (or supplementary figure) that lists the empirical per-token hit rates measured after each edit type and paraphrasing attack, together with the corresponding ROC curves obtained when LLRs are recomputed from the observed statistics. This will allow readers to assess how much of the reported soft-decision gain persists under the observed distribution shift. revision: yes

Circularity Check

0 steps flagged

No circularity: LLRs derived from explicit modeling assumption, not from fitted evaluation data

full rationale

The abstract presents targeting a fixed hit rate p-star as a deliberate design choice that directly yields closed-form LLRs under the assumed stationary channel model. This is a standard modeling step (LLR = log(p*/(1-p*)) for hit/miss) rather than a statistical fit to the same data later used for robustness evaluation. No equations or claims in the provided text reduce a 'prediction' or central result to its own inputs by construction. Experimental claims rest on external tests under edits/paraphrasing, not on self-referential definitions or self-citation chains. The derivation chain is self-contained against the stated assumptions.

Axiom & Free-Parameter Ledger

1 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so the ledger is populated from the high-level description; p-star appears as a design parameter whose value is chosen rather than derived from external benchmarks.

free parameters (1)
  • p-star
    Target hit rate used to calibrate the watermark channel and obtain closed-form LLRs; its specific value is not stated in the abstract.

pith-pipeline@v0.9.1-grok · 5695 in / 1253 out tokens · 20309 ms · 2026-06-25T23:41:06.420239+00:00 · methodology

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