CurveMark: Detecting AI-Generated Text via Probabilistic Curvature and Dynamic Semantic Watermarking

. 2025 Jul 24;27(8):784. doi: 10.3390/e27080784

Algorithm 3 Bayesian Multi-Hypothesis Detection Framework

Require: text, LLM_models = [GPT, LLaMA, PaLM, Claude], watermark_params, usage_priors
Ensure: most_likely_source, confidence_score, is_ai_generated

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// Stage 1: Curvature-Based Screening
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$f_{c u r v e} \leftarrow ExtractCurvatureFeatures (t e x t)$ ▹ Algorithm 2
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$p_{a i_c u r v e} \leftarrow ClassifyByCurvature (f_{c u r v e})$
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// Stage 2: Multi-Model Watermark Testing
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$hypotheses \leftarrow [H_{0} : human]$
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$likelihoods \leftarrow [P (X | H_{0})]$ ▹ From curvature classifier
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for each ${model}_{i}$ in LLM_models do
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for each ${watermark_param}_{j}$ in watermark_params do
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$H_{i j} \leftarrow hypothesis ({model}_{i}, {watermark params}_{j})$
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$f_{w a t e r m a r k} \leftarrow ExtractWatermarkFeatures (t e x t, {model}_{i}, {watermark_param}_{j})$
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$Λ_{i j} \leftarrow ComputeLikelihoodRatio (f_{w a t e r m a r k})$ ▹ Equation (8)
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$P (X | H_{i j}) \leftarrow CombineLikelihoods (p_{a i_c u r v e}, Λ_{i j})$
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hypotheses.append( $H_{i j}$ )
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likelihoods.append( $P (X | H_{i j})$ )
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end for
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end for
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// Stage 3: Bayesian Model Selection
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$posteriors \leftarrow []$
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for each hypothesis $H_{i}$ in hypotheses do
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$P (H_{i} | X) \leftarrow \frac{P (X | H_{i}) \cdot P (H_{i})}{\sum_{j} P (X | H_{j}) \cdot P (H_{j})}$ ▹ Bayes’ theorem
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posteriors.append( $P (H_{i} | X)$ )
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end for
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$best_idx \leftarrow arg {max}_{i} posteriors [i]$
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$confidence_score \leftarrow max (posteriors)$
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$most_likely_source \leftarrow hypotheses [best_idx]$
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$is_ai_generated \leftarrow most_likely_source \neq H_{0}$
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return most_likely_source, confidence_score, is_ai_generated