Auditing Cross-Lingual Fairness in Language Model Watermarking
Organizations: Case Western Reserve University
Abstract
Watermarking schemes for large language model output are evaluated almost exclusively on English text using each scheme's detection threshold and a narrow set of quality measurements. Multilingual deployment exposes evaluation-design choices that are inconsequential on English but determine conclusions cross-lingually. We propose an evaluation framework with four components: detection thresholds calibrated empirically per deployment context, a threshold-independent companion measurement that distinguishes calibration failures from detection failures, three disjoint quality measurement paradigms (distributional, paired-semantic, and reference-perplexity), and a generalized-entropy decomposition of cross-language disparity over a typological family partition. Applied to six watermarking schemes, three open-weight generators, eleven languages spanning four scripts and eight typological families, and both base and instruction-tuned regimes, the framework reveals failure modes that single-language single-paradigm evaluation cannot surface. Across detection and quality, observed disparity is predominantly between-family on the typological partition, indicating that cross-lingual fairness gaps in watermarking are structural to language properties rather than idiosyncratic to particular languages.
Figures & tables
| ISO 639-3 | Language | Script | Typological family | Joshi et al. tier |
|---|---|---|---|---|
| eng | English | Latin | Germanic | 5 |
| nld | Dutch | Latin | Germanic | 4 |
| fra | French | Latin | Romance | 5 |
| spa | Spanish | Latin | Romance | 5 |
| por | Portuguese | Latin | Romance | 4 |
| tur | Turkish | Latin | Turkic | 4 |
| AUC | TPR at (global) | TPR at (per-lang) | ||||||||
| Scheme | Gen. | Mean | Min | Mean TPR | Min TPR | DI <.8 | GE 2 | Btw. % | Mean TPR | |
| Base regime (FLORES+ continuation prompts) | ||||||||||
| KGW | Mistral | 0.999 | 0.997 | 0.992 [0.987, 0.996] | 0.978 | 0 | 83.6 | 0.991 | ||
| Gemma | 0.997 | 0.991 | 0.969 [0.959, 0.979] | 0.934 | 0 | 72.4 | 0.974 | |||
| Qwen | 0.996 | 0.987 | 0.965 [0.939, 0.986] | 0.880 | 0 | 85.1 | 0.966 | |||
| Unigram | Mistral | 0.996 | 0.981 | 0.868 [0.802, 0.927] | 0.638 | 3 | 0.008 | 61.3 | 0.971 | |
| Scheme | MAUVE BS | MAUVE PPL | BS PPL |
|---|---|---|---|
| KGW | +0.61 (+0.45) | +0.03 ( 0.80) | +0.03 ( 0.76) |
| Unigram | +0.56 (+0.23) | +0.14 ( 0.39) | +0.20 ( 0.67) |
| SynthID | +0.76 (+0.47) | +0.81 (+0.27) | +0.77 (+0.45) |
| EXPEdit | +0.68 (+0.26) | +0.75 (+0.39) | +0.70 (+0.46) |
| DIP | +0.46 ( 0.03) | +0.43 (+0.05) | +0.50 ( 0.05) |
| XSIR | +0.42 ( 0.09) | +0.10 ( 0.71) | +0.00 ( 0.76) |
Appendix figures & tables18 assets
Supplementary material from the paper’s appendix.
Appendix
| Base regime (FLORES+ continuation prompts) | Instruct regime (AYA native-speaker prompts) | ||||||||||||
| Mistral | Gemma | Qwen | Mistral | Gemma | Qwen | ||||||||
| Lang | NWM% | NWM% | NWM% | NWM% | NWM% | NWM% | |||||||
| eng | 99.6 | 98.8 | 98.4 | 92.6 | 80.6 | 93.2 | |||||||
| fra | 99.2 | 97.6 | 89.2 | 91.4 | 86.2 | 94.8 | |||||||
| spa | 100.0 | 96.8 | 91.2 | 95.2 | 62.6 | 92.0 | |||||||
| por | 99.2 | 96.8 | 98.2 | 96.2 | 70.6 | 96.4 | |||||||
| Regime | Subset | kept | skipped | Mean | Median | Min | Max |
|---|---|---|---|---|---|---|---|
| Base | on_target_only | 231 | 0 | 1.003 | 1.000 | 0.996 | 1.081 |
| Base | off_target_only | 8 | 223 | 0.929 | 0.908 | 0.859 | 1.023 |
| Instruct | on_target_only | 231 | 0 | 1.000 | 1.000 | 0.964 | 1.057 |
| Instruct | off_target_only | 26 | 205 | 1.025 | 1.017 | 0.947 | 1.119 |
| conf_floor | on_target_ratio | vs default | Mean on-target % | Mean (pp) | Max (pp) |
|---|---|---|---|---|---|
| 0.3 | 0.7 | 0.9347 | 92.0 | 2.19 | 13.60 |
| 0.3 | 0.8 | 0.9468 | 90.7 | 0.91 | 13.00 |
| 0.3 | 0.9 | 0.8627 | 86.3 | 4.87 | 31.00 |
| 0.5 | 0.7 | 0.9910 | 91.1 | 1.26 | 11.80 |
| 0.5 † | 0.8 | 1.0000 | 89.8 | 0.00 | 0.00 |
| 0.5 | 0.9 | 0.9317 | 85.4 | 4.43 | 31.20 |
| Germanic | Romance | Indic | Semitic | Sinitic | Japonic | Turkic | Aus. | |||||
| Scheme | Gen. | eng | nld | fra | spa | por | hin | arb | zho | jpn | tur | vie |
| Base regime (FLORES+ continuation prompts) | ||||||||||||
| KGW | Mistral | |||||||||||
| Gemma | ||||||||||||
| Qwen | ||||||||||||
| Unigram | Mistral | |||||||||||
| TPR at (global) | TPR at (per-lang) | |||||||
| Scheme | Gen. | Mean TPR | Min TPR | DI <.8 | GE 2 | Btw. % | Mean TPR | |
| Base regime (FLORES+ continuation prompts) | ||||||||
| KGW | Mistral | 0.997 | 0.992 | 0 | 61.1 | 0.997 | ||
| Gemma | 0.991 | 0.980 | 0 | 93.2 | 0.993 | |||
| Qwen | 0.987 | 0.952 | 0 | 57.8 | 0.986 | |||
| Unigram | Mistral | 0.977 | 0.920 | 0 | 54.9 | 0.988 | ||
| Base regime (FLORES+ continuation) | Instruct regime (AYA native-speaker) | ||||||||
| Scheme | Gen. | Mean TPR | Min TPR | DI <.8 | vs. all | Mean TPR | Min TPR | DI <.8 | vs. all |
| KGW | Mistral | 0.995 | 0.983 | 0 | 0.681 | 0.425 | 6 | ||
| Gemma | 0.973 | 0.939 | 0 | 0.426 | 0.264 | 10 | |||
| Qwen | 0.987 | 0.963 | 0 | 0.697 | 0.520 | 8 | |||
| Unigram | Mistral | 0.885 | 0.654 | 2 | 0.388 | 0.011 | 7 | ||
| Gemma | 0.987 | 0.974 | 0 | 0.020 | 0.000 | 9 | |||
| Base regime (FLORES+) | Instruct regime (AYA) | ||||||
|---|---|---|---|---|---|---|---|
| Scheme | Gen. | Min TPR | Bot.-q mean | Bot.-q langs | Min TPR | Bot.-q mean | Bot.-q langs |
| KGW | Mistral | 0.978 | 0.979 | zho, hin | 0.386 | 0.447 | fra, por |
| Gemma | 0.934 | 0.943 | arb, por | 0.222 | 0.251 | por, vie | |
| Qwen | 0.880 | 0.894 | tur, nld | 0.510 | 0.564 | por, nld | |
| Unigram | Mistral | 0.638 | 0.672 | nld, spa | 0.022 | 0.029 | spa, fra |
| Gemma | 0.000 | 0.000 | eng, fra | 0.010 | 0.010 | por, tur | |
| Base regime (FLORES+) | Instruct regime (AYA) | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Scheme | Gen. | Total | Btw. % | Total | Btw. % | Total | Btw. % | Total | Btw. % |
| KGW | Mistral | 83.6 | 83.7 | 0.026 | 95.3 | 0.027 | 91.4 | ||
| Gemma | 72.4 | 72.7 | 0.053 | 82.4 | 0.046 | 73.3 | |||
| Qwen | 0.001 | 85.1 | 0.001 | 85.1 | 0.011 | 78.6 | 0.011 | 72.5 | |
| Unigram | Mistral | 0.008 | 61.3 | 0.009 | 55.7 | 0.297 | 99.8 | 0.556 | 94.8 |
| Base regime (FLORES+) | Instruct regime (AYA) | ||||||
|---|---|---|---|---|---|---|---|
| Btw. % | Btw. % | ||||||
| Scheme | Gen. | Family | Script | Family | Script | ||
| KGW | Mistral | 83.6 | 46.2 | 0.026 | 95.3 | 32.8 | |
| Gemma | 72.4 | 62.2 | 0.053 | 82.4 | 29.8 | ||
| Qwen | 0.001 | 85.1 | 26.2 | 0.011 | 78.6 | 26.7 | |
| Unigram | Mistral | 0.008 | 61.3 | 28.8 | 0.297 | 99.8 | 46.3 |
| MAUVE | BERTScore F1 (rescaled) | PPL preservation (XGLM-7.5B) | ||||||||
| Scheme | Gen | mean (min) | DI .8 | GE 2 | Btw. % | mean (min) | mean (min) | DI .8 | GE 2 | Btw. % |
| Base regime (FLORES+ continuation) | ||||||||||
| KGW | Mistral | 0.947 (0.879) jpn | 0 | 0.001 | 86.0 | -0.041 (-0.079) vie | 0.866 (0.793) spa | 0 | 0.002 | 66.4 |
| KGW | Gemma | 0.855 (0.435) arb | 1 | 0.013 | 98.9 | -0.081 (-0.194) vie | 0.899 (0.812) fra | 0 | 0.002 | 91.0 |
| KGW | Qwen | 0.889 (0.471) hin | 1 | 0.012 | 95.6 | -0.034 (-0.091) tur | 0.834 (0.686) hin | 3 | 0.005 | 94.0 |
| Unigram | Mistral | 0.747 (0.420) arb | 5 | 0.026 | 49.5 | -0.070 (-0.134) arb | 0.872 (0.811) spa | 0 | 0.002 | 96.4 |
| Covariate | KGW | Unigram | SynthID | EXPEdit | DIP | XSIR |
|---|---|---|---|---|---|---|
| Base regime (FLORES+ continuation, ) | ||||||
| Fertility (tokens/sent.) | 0.016 | 0.052 | 0.008 | 0.834 ∗∗ | 0.238 ∗∗ | 0.001 |
| NWM surprisal (XGLM) | 0.066 | 0.074 | 0.058 | 0.261 ∗∗ | 0.156 ∗ | 0.003 |
| Latin script | 0.029 | 0.001 | 0.005 | 0.051 | 0.009 | 0.019 |
| NWM adherence | 0.600 ∗∗ | 0.006 | 0.415 ∗∗ | 0.001 | 0.461 ∗∗ | 0.091 |
| Instruct regime (AYA native-speaker, ) | ||||||
| Covariate | KGW | Unigram | SynthID | EXPEdit | DIP | XSIR |
|---|---|---|---|---|---|---|
| Base regime (FLORES+ continuation, ) | ||||||
| Fertility (tokens/sent.) | 0.392 ∗∗ | 0.249 ∗∗ | 0.027 | 0.005 | 0.234 ∗∗ | 0.093 |
| NWM surprisal (XGLM) | 0.026 | 0.023 | 0.018 | 0.001 | 0.007 | 0.009 |
| Latin script | 0.136 ∗ | 0.036 | 0.062 | 0.052 | 0.083 | 0.000 |
| NWM adherence | 0.031 | 0.007 | 0.101 | 0.074 | 0.219 ∗∗ | 0.072 |
| Instruct regime (AYA native-speaker, ) | ||||||
| Covariate | KGW | Unigram | SynthID | EXPEdit | DIP | XSIR |
|---|---|---|---|---|---|---|
| Base regime ( ) | ||||||
| Fertility (tokens/sent.) | 0.000 | 0.013 | 0.024 | 0.054 | 0.039 | 0.095 |
| NWM surprisal (XGLM) | 0.036 | 0.016 | 0.000 | 0.032 | 0.039 | 0.094 |
| Latin script | 0.068 | 0.207 ∗∗ | 0.004 | 0.022 | 0.003 | 0.008 |
| NWM adherence | 0.239 ∗∗ | 0.004 | 0.378 ∗∗ | 0.259 ∗∗ | 0.298 ∗∗ | 0.188 ∗ |
| Instruct regime ( ) | ||||||
| Covariate | KGW | Unigram | SynthID | EXPEdit | DIP | XSIR |
|---|---|---|---|---|---|---|
| Base regime ( ) | ||||||
| Fertility (tokens/sent.) | 0.191 ∗ | 0.327 ∗∗ | 0.013 | 0.000 | 0.121 ∗ | 0.148 ∗ |
| NWM surprisal (XGLM) | 0.003 | 0.179 ∗ | 0.017 | 0.018 | 0.094 | 0.183 ∗ |
| Latin script | 0.022 | 0.001 | 0.126 ∗ | 0.105 | 0.052 | 0.056 |
| NWM adherence | 0.186 ∗ | 0.014 | 0.164 ∗ | 0.123 ∗ | 0.109 | 0.015 |
| Instruct regime ( ) | ||||||
LLM Watermarking
Large language model watermarking embeds or detects signals in text and models to trace provenance, ownership, and unauthorized use.
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