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REVIEW 3 major objections 5 minor 2 cited by

Watermark in the Classroom: A Conformal Framework for Adaptive AI Usage Detection

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Conformal prediction recalibrates watermark p-values so classrooms can flag AI overuse while keeping false accusations at or below a chosen rate.

desk verdict A genuinely useful application of conformal prediction to watermark-based AI detection, but the classroom FPR guarantee hinges on an exchangeability assumption that real student AI use is likely to violate. read the letter →

arxiv 2507.23113 v1 pith:BEIO564B submitted 2025-07-30 stat.AP

Yangxinyu Xie , Xuyang Chen , Zhimei Ren , Weijie J. Su This is my paper · ORCID
classification stat.AP
keywords AIinEducationAcademicIntegrityLargeLanguageModelWatermarkingConformalPredictionFalsePositiveRateControlNon-NativeEnglishSpeakersHierarchicalWeighted
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

AI detectors used in schools today flag essays with heuristic scores that carry no statistical guarantee, and they disproportionately accuse non-native speakers. This paper's central claim is that watermarking, which produces genuine p-values for the null hypothesis that text is entirely human-written, can be repurposed as a classroom instrument by recalibrating those p-values with conformal prediction. Instead of asking whether a submission is AI-generated, the method asks whether its watermark signal is stronger than what permitted AI use would typically produce, and only then flags it. The paper argues that this gives instructors a provable cap on false positives: if calibration essays are representative, a student who follows the rules is flagged with probability at most the chosen rate, regardless of the distribution of watermark scores. Simulations across seven levels of AI editing, two language models, and two watermarking schemes support this in large classes, small classes with grouped past assignments, and classes with non-native-speaker subgroups.

What carries the argument

The load-bearing object is the conformal p-value $$\hat u(s)=\frac{1+\sum_{i=1}^n \mathbf{1}\{s_i\le s\}}{n+1},$$ where $s_i$ are watermark p-values from $n$ calibration essays produced under the permitted AI guidelines and $s$ is the new submission's watermark p-value. It is the proportion of guideline-following essays whose AI signal is at least as strong as the submission's; flagging when $\hat u(s)\le\alpha$ controls the false positive rate at $\alpha$ under exchangeability. Two extensions carry the same idea: a hierarchical conformal p-value, $$\hat $u^{{\mathrm{hier}}$}(s)=\frac{1}{K+1}\left(1+\sum_{k=1}^K \frac{\sum_i \mathbf{1}\{s_{k,i}\le s\}}{n_k}\right),$$ which weights each historical assignment equally even when group sizes differ, and a weighted conformal p-value that reweights calibration scores by an estimated density ratio $\hat q/\hat p$ to handle distribution shift toward a small subgroup. The argument rests on standard conformal theory, not on any parametric model of watermark scores.

What would settle it

Run the method on a new cohort where students use an allowed grammar prompt in several iterative passes rather than one editing pass, and count the fraction of compliant submissions flagged at $\alpha=0.05$; if the empirical false positive rate clearly exceeds 5%, the exchangeability premise is broken.

Watch

Extended reading notes

Core claim

The paper's core discovery is that the binary watermarking p-value, which measures evidence against the null hypothesis that a text is entirely human-written, is the wrong object for classroom enforcement because permitted AI edits also trigger it. The right object is a conformal p-value computed against a calibration set of essays that followed the instructor's allowed-AI guideline: a submission is flagged only when its watermark signal is at least as strong as the signals of a small proportion of guideline-following essays. This conformal step converts the question "is this AI-written?" into "does this submission look like more AI involvement than the rules permit?", and the finite-sample guarantee that the false positive rate is at most $\alpha$ holds without knowing the score distribution. In the small-class and subgroup settings, the same guarantee is carried by a hierarchical conformal p-value that treats assignments as exchangeable groups, and by a weighted conformal p-value that reweights majority calibration essays toward the target student group. In simulations, the empirical false positive rate stays near or below the nominal 5%, and detection power approaches 100% for severe violations such as generating the essay from a permitted-grammar baseline, while remaining modest for subtle ones.

Load-bearing premise

The whole false-positive guarantee rests on calibration essays being statistically interchangeable with new submissions, which fails if students revise iteratively with AI, if prompts or models change, or if past essays were written without AI.

Editorial extensions

If this is right

  • A classroom can set a nominal false positive level such as $\alpha=0.05$ and know that, under exchangeability, guideline-following students are accused with probability no more than 5% regardless of how watermark scores are distributed.
  • Extreme guideline violations, such as expanding a grammar-corrected essay into a full generated text, are detected with near-perfect power even with only 30 calibration essays, while subtle violations such as an unallowed readability rewrite are detected weakly.
  • Calibration sets built from past cohorts or from other assignments allow the same guarantee in small classes, at the cost of lower detection power when available data are grouped and scarce.
  • Weighted conformal recalibration lowers the false positive rate for non-native-speaker subgroups relative to unweighted pooling, although imperfect density estimates can keep the achieved rate above the nominal level.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: because the conformal guarantee depends only on exchangeability of calibration and test scores, the same workflow could in principle recalibrate any single AI-likelihood score, not only watermark p-values; the paper's simulations do not establish this for classifier scores.
  • Beyond the paper: the strongest practical bottleneck implied by the paper's own scenarios is data stewardship, since institutions need curated, guideline-compliant calibration essays, which shifts the deployment problem from detection algorithms to record-keeping and policy design.
  • Beyond the paper: a natural next experiment would simulate iterative, multi-pass AI use, such as several rounds of grammar tools across drafts, and measure how far the empirical false positive rate rises above the nominal level; the paper explicitly flags this as an open gap.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper proposes conformal prediction frameworks for detecting AI-usage guideline violations in classroom settings, rather than the standard human-vs-AI text classification. Three methods are presented: standard split-conformal p-values for large classes with similar past assignments, hierarchical conformal prediction for small classes with grouped historical data, and weighted conformal prediction for distribution shift across native and non-native speaker groups. The methods are evaluated in simulations based on the ETS and LOCNESS corpora, with seven AI-editing prompts, two language models, and two watermarking schemes. The central theoretical claim is that conformal p-values, applied to watermark scores, control the false positive rate at a pre-specified level α when calibration scores and the new submission are exchangeable under the permitted-AI-use null hypothesis.

Significance. If the FPR guarantee holds in deployment, the framework would be a meaningful improvement over classifier-based AI detectors, which lack calibrated false-positive control and have documented bias against non-native speakers. The paper's core mathematical observation—that Eq. (1) is a split-conformal p-value and inherits the distribution-free FPR bound under exchangeability—is correct and clearly presented. The empirical work is extensive, covering multiple models, watermarking schemes, calibration sizes, and subgroup shifts; the code repository is provided. The hierarchical extension and the fairness-oriented weighted method address realistic classroom constraints. The significance is moderate-to-high for an applied statistics audience, provided the gap between the simulation protocol and real student-AI interaction is resolved or explicitly bounded.

major comments (3)
  1. [§2.1, §3.3, §5.2] The abstract claims the framework 'effectively control[s] FPR across diverse classroom settings,' but the FPR guarantee in Eq. (1) requires exchangeability of calibration and test watermark scores. The calibration protocol in §3.3 applies a single AI-editing pass to completed essays, and the test set is generated the same way. Section 5.2 explicitly acknowledges that students engage iteratively with AI tools such as Grammarly throughout the writing process. Under iterative, multi-pass editing, the distribution of watermark scores need not match the one-shot calibration distribution, so the exchangeability assumption is not met for the deployment scenario the paper targets. The same concern applies to the hierarchical method in §2.2, where groups of one-shot edits are not shown to be exchangeable with a real class's multi-pass behavior. This does not invalidate the theoretical guarantee, but it means the paper's central deployment claim is not established. I recommend either substantially qualifying the abstract and Section 1 claims, or adding experiments or analysis that model iterative editing and show when the FPR bound approximately holds.
  2. [Table 3, §2.3] Section 2.3 states that under weighted exchangeability the method 'retains the guarantee as before,' but the empirical results in Table 3 show that estimated-weight conformal methods frequently exceed the nominal 5% FPR. For example, with null=1, alt=7, m=5, the quantile-weighted method has FPR 6.4% and the mean-shift method 9.7%; with null=2, alt=7, m=5, the mean-shift FPR is 10.1%. This is consistent with the acknowledged imperfection of the KDE-based density ratio, but the text overstates the finite-sample guarantee. I recommend that the paper explicitly state that the FPR control in Scenario 3 is asymptotic or approximate, quantify the inflation across all model/watermark combinations, and either propose a calibration step for the density-ratio estimate or weaken the guarantee language in Section 2.3 and the abstract.
  3. [Appendix B.3, §3.4, Figure 8] The definition of an 'outlier'—and therefore the reported detection power—depends on the test dataset itself. Appendix B.3 classifies an essay as an outlier only if its BLEU score is below the α=0.05 quantile of the test dataset's BLEU scores, and Section 3.4 excludes cells where the outlier proportion is below 5% or raw counts are below 30. This makes the power numbers in Figure 8 and Table 3 relative to a post-hoc, data-dependent labeling, not a pre-specified ground-truth threshold. The circularity does not affect the FPR guarantee, but it does affect the interpretation of detection power as a measure of practical usefulness. I recommend reporting power under at least one alternative BLEU threshold and clarifying that the reported power is conditional on the chosen test-based outlier definition.
minor comments (5)
  1. [§2.2] The inequality 'Pr (uhier(s) ≤ α) ≤ α' should use the estimated p-value notation: Pr(û_hier(s) ≤ α) ≤ α.
  2. [§3.3, Scenario 2] The phrase 'apple hierarchical conformal methods' contains a typo; it should read 'apply hierarchical conformal methods.'
  3. [§4, opening paragraph] The text says the section analyzes 'false discovery rates and detection powers,' but the evaluation metric defined in §3.4 is the false positive rate, not the false discovery rate. Please correct the terminology.
  4. [Figure captions and Appendix B.3] The captions in Figures 1, 2, 5, and 10 refer to a 'log100 scale,' which is likely intended to mean a logarithmic scale with base 100 or a log10 scale with percentages; please clarify the notation.
  5. [References] Some references are incomplete or inconsistently formatted, e.g., 'Kirchenbauer et al.' appears without a year in Section 5.2, and the reference list entry for Kirchenbauer et al. lacks a year. Please standardize all citations.

Circularity Check

1 steps flagged · score 3.0 of 10

The central conformal guarantee is standard and non-circular; the test-fitted BLEU quantile in Appendix B.3 makes the reported power and 'corrected FPR' partially self-referential.

  1. fitted input called prediction [Appendix B.3, 'Refining the Definition of Guideline Violation'; used by Section 3.4 evaluation metrics.]
    "Specifically, we classify an edited essay as a clear outlier if it satisfy both conditions: (1) the resulting BLEU score by following the AI-usage guidelines is higher than that by violating the guidelines, and (2) the resulting BLEU score by violating the guidelines is below the α = 0.05 quantile of the test dataset (explained below)."

    The ground-truth 'outlier' label is defined by a BLEU threshold fitted to the same test dataset that is then used to compute detection power and 'corrected' FPR. Power is the proportion of these test-defined outliers that are flagged, so the reported numbers are partly a function of the chosen α-quantile rather than an independent prediction about a fixed population of clear violations. Section 3.4 further states BLEU is used 'to quantify and correct our reported FPR,' meaning the reported FPR excludes minor infractions using this same test-fitted threshold. This is a post-hoc, data-dependent relabeling of the evaluation set; however, the conformal p-values themselves are standard and not fitted to test data, so the circularity is confined to the evaluation protocol.

full rationale

The core methodological derivation is not circular. The conformal p-value in Eq. (1), the hierarchical conformal p-value in Eq. (2), and the weighted conformal procedure are textbook split-conformal constructions (Vovk et al., Lee et al., Tibshirani et al.); no parameter is fitted to the test data when computing the p-values, and the FPR bound follows from exchangeability. The paper does not rely on any load-bearing self-citation or imported uniqueness theorem; self-citations to prior watermarking work are background, not the basis of the conformal guarantee. The one genuine circular element is in the evaluation protocol: Appendix B.3 defines 'clear outlier' essays using the α=0.05 BLEU quantile of the test dataset, and Section 3.4 reports power and 'corrected' FPR against that definition. Because the threshold is computed on the same test set that is then scored, the reported power is in part a property of the chosen threshold rather than an independent predictive result, and the 'corrected FPR' is conditional on a test-dependent relabeling. This does not undermine the conformal FPR guarantee itself, which is external and assumption-based, so the overall circularity is partial, not central.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The framework rests on standard conformal prediction assumptions (exchangeability) rather than invented constructs. The key additional burden is the calibration-data assumption: historical essays edited with the permitted AI prompt must have the same watermark-score distribution as new submissions. The evaluation also introduces a test-fitted BLEU threshold to define violations, which is a data-dependent construct rather than a pre-specified rule.

free parameters (3)
  • KDE bandwidth = 0.5
    Gaussian KDE bandwidth chosen in Section 3.3 for density estimates p-hat and q-hat in the weighted conformal method; no sensitivity analysis is provided, and the quality of density ratio estimates directly affects FPR control (Section 4.3).
  • BLEU outlier threshold = α=0.05 quantile of test-set BLEU scores
    Appendix B.3 defines an edited essay as a clear outlier if its BLEU score falls below the α=0.05 quantile of the test dataset; this threshold is fitted to the test data and determines which violations count as 'outliers' when computing power.
  • Quantile-shift fallback levels = quantile 2α when 1/(2α) < m ≤ 1/α; min when m ≤ 1/(2α)
    Algorithm 1 in Appendix B.2 replaces the α-quantile with more conservative levels for small minority samples; these ad hoc choices affect the estimated density ratio and the reported FPR/power of the quantile-shift weighted method.
assumptions (5)
  • domain assumption Calibration and test watermark scores are i.i.d. for standard conformal prediction.
    Section 2.1 states the FPR guarantee holds 'for independent, identically distributed (i.i.d.) essays genuinely following permitted AI usage'. Real student submissions are unlikely to be i.i.d. over time, across prompts, or across AI tool versions.
  • domain assumption Groups and observations within groups are hierarchically exchangeable.
    Section 2.2 requires that past assignment groups can be randomly reordered and essays within a group reordered without changing the analysis; this fails if different cohorts or assignment topics have systematically different watermark score distributions.
  • domain assumption The density ratio q(s)/p(s) for the target subgroup is correctly specified or well estimated.
    Section 2.3's weighted conformal guarantee assumes weighted exchangeability with the true likelihood ratio; the paper estimates the ratio via KDE with shifts, and Section 4.3 shows FPR above 5% when the estimate is imperfect.
  • domain assumption Student-facing AI tools produce watermarked outputs with valid p-values.
    The entire framework assumes submissions carry watermark scores from the AI models used; Section 5.4 notes watermarking is not yet widely deployed, so the method cannot be applied to unwatermarked tools like many current ChatGPT configurations.
  • domain assumption A single-pass AI edit of a completed essay approximates real student-AI interaction.
    Section 5.2 acknowledges students engage iteratively with AI tools throughout writing, whereas the simulations apply one edit to a finished essay; the resulting watermark distributions may differ from real classroom submissions.

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Cite this review

Pith. "Pith review of Watermark in the Classroom: A Conformal Framework for Adaptive AI Usage Detection." pith.science (2026). https://pith.science/paper/BEIO564B

@misc{pith2026250723113,
  author       = {Pith},
  title        = {Pith review of: Watermark in the Classroom: A Conformal Framework for Adaptive AI Usage Detection},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BEIO564B}},
  note         = {Machine review of arXiv:2507.23113}
}
abstract

As artificial intelligence tools become ubiquitous in education, maintaining academic integrity while accommodating pedagogically beneficial AI assistance presents unprecedented challenges. Current AI detection systems fail to control false positive rates (FPR) and suffer from bias against minority student groups, prompting institutional suspensions of these technologies. Watermarking techniques offer statistical rigor through precise $p$-values but remain untested in educational contexts where students may use varying levels of permitted AI edits. We present the first adaptation of watermarking-based detection methods for classroom settings, introducing conformal methods that effectively control FPR across diverse classroom settings. Using essays from native and non-native English speakers, we simulate seven levels of AI editing interventions--from grammar correction to content expansion--across multiple language models and watermarking schemes, and evaluate our proposal under these different setups. Our findings provide educators with quantitative frameworks to enforce academic integrity standards while embracing AI integration in the classroom.

Figures

Figures reproduced from arXiv: 2507.23113 by the authors.

Figure 1
Figure 1. Distribution of watermarking p-values (on log100 scale) for human-written essays (gray) and essays with permitted AI grammar assistance (blue). Prompt 1 (blue) refers to prompting an AI model for minimal grammar correction; see definition in Section 3.2. Meanwhile, generative watermarking techniques have emerged as a potentially promising alternative [Zhao et al., 2024, Lancaster, 2023, Xie et al., 2023, Majovsky et… view at source ↗
Figure 2
Figure 2. Histogram of watermarking p-values (on log100 scale) across 100 simulated student submissions. We encourage the reader to examine panel (a) and determine a threshold that would optimally differentiate between permitted and prohibited AI usage. The right panel (b) reveals ground truth labels, demonstrating the inherent difficulty of threshold selection without proper calibration data. Despite this theoretical promise… view at source ↗
Figure 3
Figure 3. Distribution of conformal p-values. Left: Essays following guidelines (Inliers) exhibit approx￾imately uniform distribution of p-values between 0 and 1, with only 4.69% falling below α = 0.05 (red line)—confirming the theoretical guarantee on false positive rate. Middle: Essays with clear violations (Outliers) show a sharp concentration of p-values near zero, indicating high detectability. A clear violation describe… view at source ↗
Figures from the paper (13 more)
Figure 4
Figure 4. Figure 4: Distribution of hierarchical conformal p-values. Left: Essays following guidelines show p￾values with only 4.32% falling below. Middle: Essays with clear violations show extreme concentration of p-values below 0.05, with a different x-axis scale highlighting the separa…
Figure 5
Figure 5. Figure 5: Comparative analysis of AI assistance impact across language backgrounds. (a) BLEU score dis [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: Average proportion of adjusted outliers when comparing each allowed “null” edit (rows, prompts [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]
Figure 7
Figure 7. Figure 7: Average FPR in Scenario 1 and Scenario 2. [PITH_FULL_IMAGE:figures/full_fig_p016_7.png]
Figure 8
Figure 8. Figure 8: Detection Power. Top: Scenario 1 (ETS), Standard Conformal Method. Bottom: Scenario 2 [PITH_FULL_IMAGE:figures/full_fig_p016_8.png]
Figure 9
Figure 9. Figure 9: Detection Power. Top: Scenario 1, Standard Conformal Method using [PITH_FULL_IMAGE:figures/full_fig_p020_9.png]
Figure 10
Figure 10. Figure 10: Complementary views of AI assistance categorization. 100 sample essays from the ETS corpus [PITH_FULL_IMAGE:figures/full_fig_p034_10.png]
Figure 11
Figure 11. Figure 11: Average FPR in Scenario 1 and Scenario 2. Model: [PITH_FULL_IMAGE:figures/full_fig_p036_11.png]
Figure 12
Figure 12. Figure 12: Average FPR in Scenario 1 and Scenario 2. Model: [PITH_FULL_IMAGE:figures/full_fig_p036_12.png]
Figure 13
Figure 13. Figure 13: Average FPR in Scenario 1 and Scenario 2. Model: [PITH_FULL_IMAGE:figures/full_fig_p037_13.png]
Figure 14
Figure 14. Figure 14: Detection Power. Top: Scenario 1, Standard Conformal Method. (ETS); Bottom: Scenario 2 [PITH_FULL_IMAGE:figures/full_fig_p037_14.png]
Figure 15
Figure 15. Figure 15: Detection Power. Top: Scenario 1 (ETS), Standard Conformal Method. Bottom: Scenario 2 [PITH_FULL_IMAGE:figures/full_fig_p038_15.png]
Figure 16
Figure 16. Figure 16: Detection Power. Top: Scenario 1 (ETS), Standard Conformal Method. Bottom: Scenario 2 [PITH_FULL_IMAGE:figures/full_fig_p039_16.png]

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