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REVIEW 3 major objections 4 minor 53 references

SurpMark detects machine-generated text by scoring the dynamics of token surprisal—how predictable each token is to a proxy language model—against fixed human and machine reference transitions, and proves the resulting score is an asymptoti

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2026-08-04 10:56 UTC pith:4YDNK5Z5

load-bearing objection Strong empirical detector with a real error in the CLT proof; the method deserves a serious look once the theory is corrected. the 3 major comments →

arxiv 2510.07500 v3 pith:4YDNK5Z5 submitted 2025-10-08 cs.LG cs.ITmath.IT

Black-Box Detection of LLM-Generated Text Using Generalized Jensen-Shannon Divergence

Shuangyi Chen , Ashish Khisti This is my paper
classification cs.LG cs.ITmath.IT
keywords machine-generated text detectionsurprisal dynamicsgeneralized Jensen-Shannon divergenceMarkov transition matrixblack-box detectionlikelihood-free hypothesis testingdiscretization bias-variance tradeoffasymptotic normality
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper's aim is a black-box detector for LLM-generated text that is cheap, robust to proxy-model mismatch, and principled. SurpMark reduces a passage to a matrix of transitions between a handful of surprisal states—how predictable each token is under a proxy LM—then classifies by comparing that matrix against two fixed transition matrices, one built from human text and one from machine text. The score is the gap between two generalized Jensen-Shannon divergences, which the paper proves is exactly a normalized log-likelihood ratio for the human-vs-machine hypothesis and is asymptotically normal. If true, this gives a detector that needs only one pass over the test text, no per-input sampling, and no retraining, while matching or surpassing stronger-armed baselines across domains, generators, and languages. The theoretical claims also supply a rule for choosing the number of surprisal states from reference size.

Core claim

SurpMark's central discovery is that the temporal pattern of surprisal—whether a highly surprising token tends to be followed by a predictable one, and how often a predictable run spikes—is a stable fingerprint that separates human and machine writing even when the scoring model differs from the generating model. The paper formalizes the fingerprint as the first-order transition matrix of quantized surprisals and shows algebraically that the difference between the test's generalized Jensen-Shannon distance to the machine reference and to the human reference equals the normalized generalized likelihood ratio between two composite hypotheses over Markov chains. It then proves that this score i

What carries the argument

The key object is the surprisal-state transition matrix. Token surprisals from a proxy LM are quantized into k states via k-means (e.g., 'predictable', 'highly surprising'), and consecutive states are counted into a k-by-k matrix. The decision statistic is the gap ΔGJS = GJS(reference_machine, test) − GJS(reference_human, test) with reference/test length weight α = N/n; the generalized Jensen-Shannon divergence with this weight is the f-divergence whose structure makes ΔGJS equal to the normalized log-likelihood ratio of two Markov models. The same decomposition gives the bias-variance tradeoff k* = Θ(N^{1/5}).

Load-bearing premise

The load-bearing premise is that first-order transitions among a handful of learned surprisal states carry the entire human-vs-machine signal, and the formal guarantees additionally assume the state quantizer is fixed in advance even though the deployed algorithm estimates it by k-means.

What would settle it

Generate test passages by sampling directly from the two estimated transition kernels (human-shaped and machine-shaped surprisal chains). The theorem predicts the score distribution is Gaussian with mean separated by twice the generalized Jensen-Shannon divergence between the kernels; if real detector scores on such synthetic chains do not match that prediction, the likelihood-ratio justification is not what explains the empirical results.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • References are built once offline, so per-test cost is a single forward pass; after the reference cost is amortized, the method is much cheaper than sampling-based detectors.
  • The decision statistic is a normalized likelihood ratio, so threshold selection has a principled anchor rather than being purely empirical.
  • The optimal number of surprisal states grows as the fifth root of reference length, so a small fixed k (around 6–8) is near-optimal at practical reference sizes.
  • The reference/test length trade-off shows that shorter test passages can be compensated by longer or larger reference corpora at similar accuracy.

Where Pith is reading between the lines

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

  • Because the score is asymptotically normal, one could calibrate a confidence or p-value from the fitted Gaussian and report uncertainty rather than a binary label; the paper does not develop this.
  • The same two-reference scheme could be repurposed for other attribution questions—e.g., which of two generators wrote a passage—by swapping the reference corpora, since the likelihood-ratio identity only needs two reference chains.
  • The paper's theory assumes a fixed quantizer while the algorithm learns it by k-means; a natural testable extension is to compare against a fixed quantile quantizer to see whether the N^{1/5} bin rule and normality hold for the actual estimator.
  • The first-order Markov summary ignores long-range structure; a detector that adds second-order transitions or length-aware states could keep the one-pass advantage while catching generators that mimic local surprisal dynamics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper proposes SurpMark, a black-box detector for LLM-generated text that summarizes a passage by the surprisal dynamics of its tokens: it discretizes surprisals into k states, estimates a first-order Markov transition matrix for the test text, and scores it by a generalized Jensen-Shannon (GJS) gap against two fixed reference transition matrices built once from human and machine corpora. The authors claim two theoretical contributions: a bias-variance analysis yielding k = Θ(N^{1/5}) as the principled discretization scale, and an asymptotic-normality result for the GJS gap, motivated by an exact log-likelihood-ratio interpretation. Empirically, the paper reports that SurpMark matches or surpasses ten baselines across XSum, WritingPrompts, SQuAD, WMT19, and HC3, for nine open-source and three closed-source generators, while requiring a single pass over the test text and no per-instance regeneration.

Significance. The empirical core of the paper is strong and practically valuable. SurpMark is a rare reference-based detector that is simultaneously single-pass at test time, robust across domains and proxy models, and competitive with much more expensive distribution-based detectors. The experiments are extensive: multiple datasets, 12 source models, ablations on k, reference length, test length, proxy model, throughput, non-English text, and paraphrase attacks. The reported gains on closed-source models such as GPT-5-Chat are notable. However, the theoretical justification is the weakest part of the manuscript. The claimed exact LLR identity and the stated asymptotic normality both have serious technical gaps. These gaps do not necessarily invalidate the empirical detector—the method could still be justified by a delta-method argument—but they do mean the current paper overstates what Section 4 establishes. The paper is likely publishable after a substantive revision of the theoretical section.

major comments (3)
  1. [Theorem 4.4 (Section 4.3, Appendix A2.3.3)] The stated normalization is internally inconsistent. With α = N/n, the expression σ_H0² = α²/N² σ_{1,0}² + 1/n² σ_{2,0}² equals (σ_{1,0}² + σ_{2,0}²)/n², since α²/N² = 1/n². This is O(n⁻²). But the proof's own Eq. (129)–(132) gives Var(Δ_GJS) = α²/N² Var(Σ_{i=2}^N ι₁) + 1/n² Var(Σ_{i=2}^n ι₂). If σ_{1,0}² and σ_{2,0}² are the long-run variances per step (as Lemma A2.12 uses them), then Var(Σ_{i=2}^N ι₁) ≈ N σ_{1,0}² and Var(Σ_{i=2}^n ι₂) ≈ n σ_{2,0}², so Var(Δ_GJS) ≈ (α σ_{1,0}² + σ_{2,0}²)/n. If, instead, σ_{1,0}² and σ_{2,0}² denote the variance of the whole sum, then the theorem's expression is dimensionally wrong for a different reason. Under either reading, √n(Δ−μ)/σ_H0 does not converge to N(0,1) under the stated σ_H0; the normalized quantity grows as n^{3/2} in the first reading. Since Theorem 4.4 is the paper's central 'principled justification' for the decision statistic, this m
  2. [Proposition 4.3 (Appendix A2.3.2)] The claimed exact equality Δ_GJS = Λ_{n,N} is not established. In Eqs. (93)–(98), the authors replace the supremum over Markov models on the concatenated sequence (a^P_{1:N}, a^T_{1:n}) by 2^{-(N+n)H(·)} and then identify the resulting entropy expression with the GJS divergence. However, the maximum-likelihood transition matrix of the concatenated sequence is not generally the length-weighted mixture \widehat M_{α1} = (α \widehat M_P + \widehat M_T)/(1+α): the row-wise mixture weights are state-specific visit counts (N_P(s) + n_T(s)), which are not proportional to N and n when the stationary distributions differ. Relatedly, the entropy of the concatenated empirical process is not the weighted entropy of the mixture unless the state frequencies coincide. Thus the LLR interpretation of Δ_GJS is not proved under the stated assumptions. This matters because the asymptotic-normality proof and
  3. [Section 4.1 vs. Algorithm 1] The theoretical analysis assumes a fixed, shared quantizer q_k, but the algorithm estimates q_k from the reference corpus by k-means (Algorithm 1, Steps 2–3). Consequently, the transition matrices M_P and M_Q in Theorem 4.2 and Theorem 4.4 are random targets that depend on the same data used to build the references, and the stated non-asymptotic bounds and CLT do not cover the actual estimator evaluated in Section 5. The paper should either (a) extend the analysis to the estimated quantizer, e.g., via a stability bound for k-means under sampling, or (b) explicitly state that all theoretical results are conditional on the realized quantizer and provide supporting experiments quantifying the additional variability. As written, the theory is not directly about the method whose performance is claimed.
minor comments (4)
  1. [Table 1] The reported Avg column is inconsistent for two rows. For LogRank, (53.87 + 66.8 + 49.83)/3 = 56.83, not 46.53. For DetectLRR, (44.51 + 63.29 + 49.83)/3 = 52.54, not 62.11. Please check whether the table entries or the averages are correct.
  2. [Section 3] There is an indexing inconsistency in the definition of the surprisal sequence: the paper writes {s_t}_{t=1}^n then defines s_1 = −log p_θ(x_2|x_1), so s_n is never defined on the token sequence x_1,...,x_n. The definition should start at t=2 or use x_{1:t} consistently.
  3. [Figure 7 / Appendix A3.2.2] The claim that observed score distributions 'align closely with Gaussian curves' is only visual. Since the asymptotic normality theorem is under dispute, a quantitative check (e.g., QQ plots, Kolmogorov–Smirnov statistics, or estimated skewness/kurtosis over repeated trials) would be more informative.
  4. [Eq. (7) and Section 3] The notation f^w_JS in Eq. (7) uses α in the displayed formula, but the text says 'abbreviate f^α_JS as f'. Please make the weight variable consistent (w vs. α) to avoid confusion between the α in GJS and the f-divergence generator.

Circularity Check

0 steps flagged

No significant circularity: SurpMark's references are built from separate labeled corpora, its statistic is an LLR-type comparison to fixed references, and its theoretical claims do not reduce to fitted inputs.

full rationale

SurpMark's derivation chain is self-contained in the sense relevant to circularity. The reference transition matrices M̂P and M̂Q are estimated once from separate human/machine corpora (Algorithm 1), the test passage is scored against those fixed references (Algorithm 2), and the decision statistic ΔGJS_n is a proper difference of GJS divergences rather than a parameter fitted to the labels it is asked to predict. Proposition 4.3's equality ΔGJS_n = Λ_{n,N} is an algebraic identification of the statistic with a generalized log-likelihood ratio; it is not a reduction of a predicted quantity to a fitted one. Theorem 4.4's CLT is obtained from a second-order Taylor expansion plus standard Markov additive-functional CLTs (Holzmann), not from self-citation. The discretization scaling k* = Θ(N^{1/5}) is derived by balancing an O(1/k) bias with O(k^{3/2}/√N) statistical error; because the constant C is unspecified, the later statement that 'the constant factor and finite-sample effects yield a broad optimum where k=6−7 remains near-optimal' (Section 5.2) is a post hoc rationalization but not a statistically forced prediction. There are no self-citations carrying a load-bearing uniqueness or ansatz. The skeptical note's variance-formula concern (σ²_H0 has O(n^{-2}) units if σ²_{1,0}, σ²_{2,0} are per-step long-run variances) is a mathematical correctness issue in the theorem statement/proof, not a circularity, so it does not change the circularity score.

Axiom & Free-Parameter Ledger

4 free parameters · 6 axioms · 0 invented entities

The central claim rests on several domain assumptions about the stochastic structure of surprisal sequences (ergodicity, Markov property, mixing time) and on a fixed-quantizer idealization that the actual k-means-based algorithm does not satisfy. The free parameters are mainly the number of bins and the quantizer boundaries, both chosen empirically with only a rate-level theoretical guide.

free parameters (4)
  • k (number of surprisal states) = 6-7 (best across experiments; also 8)
    Number of bins in the quantizer. Theory gives only k* = Θ(N^{1/5}) with an unknown constant; the actual value is selected by tuning on reference/test performance (Section 5.2).
  • k-means quantizer boundaries = Estimated from pooled reference surprisals (values not reported)
    The quantizer qk is fit to reference corpora via k-means; theory treats it as fixed. This is a data-dependent parameter set affecting the transition matrices (Algorithm 1).
  • Markov order = 1
    First-order Markov assumption chosen based on Figure 2(b); higher orders give no notable gains. This is a modeling choice, not a fitted number but a hyperparameter.
  • decision threshold τ = tunable
    The test threshold for the decision rule in Eq. 2; AUROC is threshold-independent, but the operating point is a free parameter.
axioms (6)
  • domain assumption Each discretized surprisal-state chain is an irreducible, aperiodic Markov chain with stationary distribution π_min ≳ 1/k and maximum hitting time O(1).
    Assumption A2.1 is imposed to apply Markov concentration inequalities (Wolfer, Chung et al.); not verified for real language-model surprisal sequences.
  • domain assumption The underlying continuous surprisal sequences from the proxy LM form ergodic first-order Markov processes on R.
    Section 4.1 models reference and test surprisals as Markov; real text is not strictly Markov, so this is an idealization.
  • domain assumption The transition kernels of the continuous surprisal process are TV-Lipschitz (Assumption A2.4).
    Used in the discretization error bound (Proposition 4.1); no evidence that surprisal kernels satisfy this.
  • standard math The f-divergence generator for GJS satisfies the growth conditions in Assumption A2.2.
    Regularity conditions borrowed from Pillutla et al.; these are mild and standard.
  • ad hoc to paper In the theoretical analysis, the quantizer qk is fixed and shared across all three sequences; the estimation of qk from reference data is not modeled.
    The theory (Section 4.1) assumes a fixed quantizer, while Algorithm 1 fits qk via k-means; this mismatch means the bounds and the asymptotic result do not cover the actual algorithm.
  • domain assumption The first-order Markov assumption for discretized surprisal sequences of real text.
    Section 3 adopts first-order Markov; supported empirically by Figure 2(b) but not proven for arbitrary LLM text.

pith-pipeline@v1.3.0-alltime-deepseek · 35552 in / 19377 out tokens · 148719 ms · 2026-08-04T10:56:01.573942+00:00 · methodology

0 comments
read the original 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 discretizes 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 existing corpora. Theoretically, we derive design guidance for how the discretization bins should scale with data and provide a principled justification for our test statistic. Empirically, across multiple datasets, source models, and scenarios, SurpMark consistently matches or surpasses baselines, demonstrating strong robustness across domains and generators; our experiments on hyperparameter sensitivity exhibit trends that our theoretical results help to explain.

Figures

Figures reproduced from arXiv: 2510.07500 by Ashish Khisti, Shuangyi Chen.

Figure 1
Figure 1. Figure 1: SurpMark framework. Offline, we build human/machine reference transition matrices by [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) Visualizes the key feature driving our detector by comparing the conditional probabilities [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Effect of the number of bins k on de￾tection performance for source models including GPT-J-6B (left) and Llama-3.2-3B (right). Effect of bins k [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a) AUROC vs. number of reference samples. The blue curve (“ [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a-b) AUROC contour maps (WritingPrompts/Gemma-7B). Left: [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Left: Throughput (items per second) versus the number of test texts for SurpMark compared [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: SurpMark’s score distribution. A3.2.3 EFFECT OF TEST LENGTH [PITH_FULL_IMAGE:figures/full_fig_p033_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: AUROC vs test length. A3.2.4 PARAPHRASING ATTACK Here we examine the robustness of detection methods to the paraphrasing attack. For SurpMark, we consider three paraphrase scenarios. Ref-P applies paraphrasing only to the offline references. Test-P paraphrases only the incoming text, which is the most realistic case in practice. Both-P paraphrases both sides. We follow the setup of Lastde++ and Fast-Detect… view at source ↗

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