Beyond Sub-Gaussian Detector Scores: Robust Weighted Profile-Loss Change Point Detection for Human-LLM Text Segmentation

Wan Tian; Zhongyi Li; Yawen Li; Rui Zhang; Yijie Peng; Fuzhen Zhuang

cs.AISep 29, 2026

Beyond Sub-Gaussian Detector Scores: Robust Weighted Profile-Loss Change Point Detection for Human-LLM Text Segmentation

Authors: Wan Tian, Zhongyi Li, Yawen Li, Rui Zhang, Yijie Peng, Fuzhen Zhuang

Organizations: Peking University · Beihang University · Capital Normal University · Renmin University of China · Nanjing University

Abstract

Mixed human-LLM documents require locating authorship transitions from detector scores whose reliability varies across text units. Existing weighted mean contrasts are vulnerable to extreme scores, while directly replacing means with robust centers obscures how a misplaced boundary changes the population objective. We propose Robust Weighted Profile-Loss Change Point Detection (RWCP), which combines capped reliability weights, Huber profile gains, and narrowest-over-threshold search in reliability coordinates. Our key analysis expresses the population gap between a true and a displaced split as a merge cost, avoiding a closed-form solution for the nonlinear center of a mixed segment. Under explicit curvature, spacing, and dependence conditions, core RWCP recovers the number of changes and localizes their boundaries; its quadratic-loss limit recovers squared weighted CUSUM. We also study RWCP-R, a separately evaluated decoder that shares source centers across nonadjacent passages. Across five retrospective cached-score benchmark families, core RWCP reduces family-macro WindowDiff by 17.6% relative to weighted change-point detection, and RWCP-R lowers it further. Boundary recovery improves most clearly for isolated changes, while both fixed configurations miss changes in collaborative and densely alternating text.

Figures & tables

Figure 1: Core RWCP: capped reliability weights, Huber profile gains, and weighted-coordinate narrowest-over-threshold search. The recovery theorem covers this procedure. RWCP-R separately decodes recurrent source states using ( 6 ).

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

Experiment	Settings	Instances	Score	Count protocol
Single change	3	300	FT	Unknown $K$
CoAuthor	1	290	NFT	Unknown $K$
Multiple changes	10	1,000	NFT	Unknown $K$
Text attacks	6	600	NFT	Unknown $K$
LLM proportion	5	500	NFT	Unknown $K$

Appendix

Table 5: Completed benchmark inventory. Counts are evaluated document instances; transformed copies can share a source. FT is the repository’s fine-tuned score and NFT its normalized score. The retained benchmarks use the unknown-count protocol for segmentation.

Family	Setting	WCP WD	Core WD	Core MAE	Core F1	Zero CP
Single	WikiQA	0.284	0.279	0.580	0.380	60%
Single	News	0.370	0.119	0.130	0.760	8%
Single	Story	0.534	0.296	0.470	0.320	26%
CoAuthor	Sessions	0.488	0.490	10.159	0.057	82%
Multiple	Claude $K=1$	0.400	0.319	0.920	0.070	92%
Multiple	Claude $K=2$	0.404	0.393	1.900	0.047	91%

Appendix

Table 7: Per-setting standard WD for WCP and fixed analytic-threshold core RWCP, with core count MAE, boundary F1 at one-sentence tolerance, and no-boundary fraction. Each setting contains 100 documents except CoAuthor (290). The six one-sentence WikiQA records follow the common empty-boundary convention.

Family	Setting	WCP	RWCP-R		RWCP-R–WCP
Family	Setting	WD	WD	F1 ( $h=1$ )	$\Delta$ WD [95% CI]
Single	WikiQA	0.284	0.223	0.490	-0.060 [-0.107, -0.013]
Single	News	0.370	0.102	0.790	-0.268 [-0.327, -0.210]
Single	Story	0.534	0.243	0.353	-0.291 [-0.342, -0.238]
CoAuthor	290 sessions	0.488	0.487	0.058	-0.001 [-0.019, 0.015]
Multiple	Claude $K=1$	0.400	0.288	0.180	-0.112 [-0.156, -0.072]

Appendix

Table 20: Primary 25-setting study: standard raw-boundary WD and RWCP-R F1 (tolerance one). Every controlled setting includes 100 records; CoAuthor has 290. Intervals are pointwise paired 95% source-component bootstrap intervals for RWCP-R minus WCP (2,000 draws); negative values favor RWCP-R. Singleton boundary conventions are applied to all methods.

Family	Setting	Best baseline		WCP	RWCP-R
Family	Setting	Method	$\operatorname{WD}_{\mathrm{sup}}$	$\operatorname{WD}_{\mathrm{sup}}$	$\operatorname{WD}_{\mathrm{sup}}$	CE
Single	WikiQA	VCP	0.200	0.200	0.184	0.47
Single	News	WCP	0.123	0.123	0.097	0.03
Single	Story	VCP	0.306	0.372	0.235	0.34
CoAuthor	290 sessions	VCP	0.480	0.483	0.478	10.17
Multiple	Claude $K=1$	VCP	0.293	0.313	0.273	0.58

Appendix

Table 21: Primary 25-setting legacy final-label window error

\operatorname{WD}_{\mathrm{sup}}

and RWCP-R raw count error. Best base is the smallest available non-RWCP mean in each setting. Bold marks the smaller legacy error between it and RWCP-R before rounding. These are distinct from raw-boundary WD and matched-boundary F1.

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LA-CPD: Local-Evidence-Aware Change-Point Detection for Human-LLM Authorship Segmentation

Qing Yang, Zhenyu Mao, Zixiang Luo, Zezheng Wu+4

Guilin University of Electronic Technology, China · Jinan Unaiversity, China · Jilin University, China+1

Authorship Machine-Generated Text Detection Document Segmentation Change-Point Detection

Open paper AskPDF arXiv

As LLM-generated text becomes increasingly human-like, accurately localizing LLM-authored spans in human-LLM co-authored documents is important for attribution and accountability in cases involving copyright infringement, fraud, and other harmful uses of AI-generated content. Sentence-level detectors provide local authorship evidence, but content variation can cause score fluctuations even among sentences from the same source, creating spurious boundaries. Recovering a coherent document partition therefore remains challenging when both the number and locations of authorship transitions are unknown. We propose Local-Evidence-Aware Change-Point Detection (LA-CPD), a structured method that transforms noisy sentence-level score sequences into coherent authorship segments. Given scores from a frozen local detector, LA-CPD combines a length-weighted within-segment residual with a windowed two-mean contrast to capture segment consistency and sustained changes around candidate cut points. Dynamic programming optimizes cut locations for each candidate count, while an AIC-style criterion selects the final partition, yielding sentence labels, authorship boundaries, and maximal LLM-authored spans. On a held-out human-LLM co-authored test set, LA-CPD outperforms WCP+AIC, increasing sentence-level accuracy from 0.747 to 0.796 while improving boundary localization and LLM-span delineation.

Abstract

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