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Black-box Detection of LLM-generated Text Using Generalized Jensen-Shannon Divergence

Shuangyi Chen, Ashish Khisti

TL;DR

This work addresses black-box detection of LLM-generated text by leveraging token surprisal dynamics without per-instance regeneration. SurpMark discretizes surprisal into a finite state space and models state transitions as a Markov chain, scoring test texts against fixed human and machine references via a generalized Jensen-Shannon divergence. The authors provide a principled discretization criterion, prove the decision statistic is a normalized log-likelihood ratio with asymptotic normality, and demonstrate strong empirical performance across multiple datasets, models, and languages. The approach offers scalable, low-latency detection suitable for real-world deployment, with robust performance under domain and proxy-model shifts. The framework also highlights a favorable trade-off between reference cost and detection accuracy, achieving competitive results while reducing per-input computational burden.

Abstract

We study black-box detection of machine-generated text under practical constraints: the scoring model (proxy LM) may mismatch the unknown source model, and per-input contrastive generation is costly. We propose SurpMark, a reference-based detector that summarizes a passage by the dynamics of its token surprisals. SurpMark quantizes surprisals into interpretable states, estimates a state-transition matrix for the test text, and scores it via a generalized Jensen-Shannon (GJS) gap between the test transitions and two fixed references (human vs. machine) built once from historical corpora. We prove a principled discretization criterion and establish the asymptotic normality of the decision statistic. Empirically, across multiple datasets, source models, and scenarios, SurpMark consistently matches or surpasses baselines; our experiments corroborate the statistic's asymptotic normality, and ablations validate the effectiveness of the proposed discretization.

Black-box Detection of LLM-generated Text Using Generalized Jensen-Shannon Divergence

TL;DR

This work addresses black-box detection of LLM-generated text by leveraging token surprisal dynamics without per-instance regeneration. SurpMark discretizes surprisal into a finite state space and models state transitions as a Markov chain, scoring test texts against fixed human and machine references via a generalized Jensen-Shannon divergence. The authors provide a principled discretization criterion, prove the decision statistic is a normalized log-likelihood ratio with asymptotic normality, and demonstrate strong empirical performance across multiple datasets, models, and languages. The approach offers scalable, low-latency detection suitable for real-world deployment, with robust performance under domain and proxy-model shifts. The framework also highlights a favorable trade-off between reference cost and detection accuracy, achieving competitive results while reducing per-input computational burden.

Abstract

We study black-box detection of machine-generated text under practical constraints: the scoring model (proxy LM) may mismatch the unknown source model, and per-input contrastive generation is costly. We propose SurpMark, a reference-based detector that summarizes a passage by the dynamics of its token surprisals. SurpMark quantizes surprisals into interpretable states, estimates a state-transition matrix for the test text, and scores it via a generalized Jensen-Shannon (GJS) gap between the test transitions and two fixed references (human vs. machine) built once from historical corpora. We prove a principled discretization criterion and establish the asymptotic normality of the decision statistic. Empirically, across multiple datasets, source models, and scenarios, SurpMark consistently matches or surpasses baselines; our experiments corroborate the statistic's asymptotic normality, and ablations validate the effectiveness of the proposed discretization.

Paper Structure

This paper contains 55 sections, 14 theorems, 100 equations, 8 figures, 10 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Main Contributions
  3. Related Work
  4. SurpMark: Detailed Methodology
  5. Surprisal Sequence Estimation via Proxy Model.
  6. Surprisal Discretization by K-means.
  7. Modeling State Transitions as Markov Chain.
  8. Reference-based Detection with Generalized JS Divergence.
  9. Analysis
  10. Setup
  11. Discretization Effect
  12. Discretization Error.
  13. Statistical Error.
  14. Balancing Two Errors.
  15. Decision Statistic Analysis
  16. ...and 40 more sections

Key Result

Proposition 4.1

Let $\mathcal{S}_P,\mathcal{S}_Q$ be the population first-order Markov transition kernels on the continuous surprisal space $\mathbb{R}$. Consider a shared $k$-bin quantizer $q_k:\mathbb{R} \rightarrow \mathcal{A}$ and, from it, form the discretized $k$-state Markov chains $M_P, M_Q$. For any row-ag where $C$ depends on $(P,Q,f)$ but not on the reference length $N$.

Figures (8)

  • Figure 1: SurpMark framework. Offline, we build human/machine reference transition matrices by scoring corpora with a proxy LM, discretizing surprisal via a shared $q_k$, and counting state transitions. Online, a test passage is summarized the same way and assigned a GJS score to measure proximity to human vs. machine references. Details are in Algorithm \ref{['alg:surpmark-offline']} and \ref{['alg:surpmark-online']} in Appendix \ref{['sec:alg']}.
  • Figure 2: (a) Visualizes the key feature driving our detector by comparing the conditional probabilities of transitioning into and out of the "Highly Surprising" state under a 4-bin discretization. This reveals distinct dynamic patterns, including a stronger recovery tendency and a more pronounced spiking tendency from low-surprisal contexts in LLM-generated text. (b) A heatmap illustrating the detector's performance (AUROC) on SQuAD across different hyperparameter settings, justifying our choice of model order. (c) The final score distributions of our detector.
  • Figure 3: Effect of the number of bins $k$ on detection performance for source models including GPT-J-6B (left) and Llama-3.2-3B (right).
  • Figure 4: (a) AUROC vs. number of reference samples. The blue curve (“$k$-optimized”) picks the best $k$ at each number of reference. orange/green curves fix $k \in \{7,8\}$. (b) AUROC vs. test length $n$ under different reference lengths. Solid lines are k-optimized for each reference sample truncated to 50/100/200 tokens; shaded bands show the attainable range across $k$ at each $n$. (c) Detection results of 7 detection methods on 6 test lengths.
  • Figure 5: (a-b) AUROC contour maps (WritingPrompts/Gemma-7B). Left: $k=7$; right: $k=8$. The x-axis is reference length (tokens) and the y-axis is test length (tokens). Colors encode AUROC. In both panels, contours tilt up-right, indicating a trade-off: larger reference length allows smaller test length at similar performance. (c) AUROC vs. proxy model.
  • ...and 3 more figures

Theorems & Definitions (20)

  • Proposition 4.1
  • Theorem 4.2
  • Proposition 4.3
  • Theorem 4.4: Asymptotic normality of $\Delta\mathrm{GJS}_n$ (informal)
  • Lemma A2.3: Approximate Lipschitz Property of the $f$-divergence, Lemma 20 in pillutla2023mauvescoresgenerativemodels
  • Proposition A2.5: Quantization Error of f-Divergence, Proposition 13 in pillutla2023mauvescoresgenerativemodels
  • Lemma A2.6: Row-wise TV bound, wolfer2023empiricalinstancedependentestimationmarkov
  • Lemma A2.7: Missing Mass Bound, Theorem 1 in skorski2020missingmassconcentrationmarkov
  • Lemma A2.8: Theorem 3.1 of chung2012chernoffhoeffdingboundsmarkovchains
  • Lemma A2.9
  • ...and 10 more