OLMo-Detect: A Multi-Stage, Confounder-Controlled Benchmark for Membership Inference on Large Language Models

Tao Shi; Chaoyi Xiang; Qiongkai Xu; Jey Han Lau

cs.CLOct 2, 2026

OLMo-Detect: A Multi-Stage, Confounder-Controlled Benchmark for Membership Inference on Large Language Models

Authors: Tao Shi, Chaoyi Xiang, Qiongkai Xu, Jey Han Lau

Organizations: The University of Melbourne · Macquarie University

Abstract

Membership inference on large language models (LLMs) aims to determine whether a given text sample was included in an LLM's training data, without access to its training corpus. Despite recent progress, existing benchmarks suffer from three limitations: limited coverage of training stages, insufficient distributional alignment between members and non-members, and lack of rigorous filtering of non-members against the training corpus. To address these limitations, we propose OLMo-Detect, a multi-stage, confounder-controlled benchmark built upon the fully open OLMo 2 pipeline. OLMo-Detect spans pre-training, mid-training, and post-training, explicitly aligns members and non-members on three key axes, and rigorously filters non-members via infini-gram. To assess robustness to distribution shifts, we further introduce OLMo-Detect (Shifted), a variant where members are misaligned with non-members. We evaluate 15 unsupervised and 3 supervised membership inference attacks (MIAs) across the OLMo 2 family, finding that: (i) overall performance is limited: the best unsupervised and supervised MIAs both reach an AUC of only 0.68, and supervised MIAs degrade under cross-domain evaluation; (ii) MIA performance peaks at mid-training and is lower at pre-training and post-training, a pattern driven by data type rather than a stage effect: curated math data is far more detectable than other types; (iii) overall scores improve from 1B to 13B but plateau at 32B; and (iv) no unsupervised MIA is robust to distribution shifts, with AUCs shifting by up to 0.42. Finally, we find that our findings on OLMo 2 generalize to OLMo 3 and non-OLMo models.

Figures & tables

Benchmark	Stage(s)	Domain(s)	Member	Non-Member	Assessments
Benchmark	Stage(s)	Domain(s)	Member	Non-Member	C	A	F
WikiMIA ( Shi et al., 2023 )	Pre-training	Wikipedia	Pre-2017 data	Post-2023 data	✗	✗	✗
StackMIA ( Ye et al., 2024 )	Pre-training	Stack Exchange	Pre-2017 data	Post-2023 data	✗	✗	✗
DETCON ( Dong et al., 2024 )	Post-training	HumanEval, GSM8K	Outputs of post-SFT LLMs	Outputs of base LLMs	✗	✗	✗
MIMIR ( Duan et al., 2024 )	Pre-training	The Pile: 7 domains	Train splits	Held-out data	✗	✗	✓ †
PatentMIA ( Zhang et al., 2024b )	Pre-training	Google Patents	Pre-2023 data	Post-2024 data	✗	✗	✗

Table 1: Comparison of existing benchmarks for membership inference on LLMs. We assess on three criteria: (i) Coverage (C) of training stages (pre-training, mid-training, and post-training); (ii) Explicit Alignment (A) of distributions between members and non-members; (iii) Rigorous Filtering (F) of non-members against the training corpus. ✓ † indicates that MIMIR uses a filter with a permissive threshold of 80%, leaving potentially high residual overlap. ✓ ‡ means that OLMoMIA aligns on semantic similarity, but most MIAs target exact wording rather than meaning.

Stage	Domain	Subsets	Split	Samples	Tokens	Quality	Temporal	Lexical
Pre-training	DCLM-Baseline		NM	150	217,117	FastText: 0.01809 $\pm$ 0.00007	2018-01-19 $\pm$ 930d	0.07
	DCLM-Baseline		M	150	217,016	FastText: 0.01811 $\pm$ 0.00000	2018-01-18 $\pm$ 940d	0.07
	peS2o		NM	268	216,981	—	2022-12-14 $\pm$ 11d	0.10
	peS2o		M	268	217,230	—	2022-12-15 $\pm$ 13d	0.10
	OpenWebMath		NM	151	217,183	—	2019-10-13 $\pm$ 853d	0.11
	OpenWebMath		M	151	217,252	—	2019-10-17 $\pm$ 864d	0.11

Table 2: Overall per-domain statistics of OLMo-Detect . Within each domain, members and non-members are aligned on up to three axes: Text Quality , Temporal Range, and Lexical Similarity. Text Quality uses OLMo 2’s metric and is enforced for quality-thresholded domains; Temporal Range is enforced when timestamps are available; and Lexical Similarity, measured by Jensen–Shannon divergence (lower is better), is enforced for all domains. “—” denotes uncontrolled axes. NM : non-member; M : member. Subsets lists constituent subsets; blanks indicate single-subset domains whose subset shares the domain’s name. † SFT and DPO are constructed per model size due to differing training data; values shown are for 1B. Each domain is split into dev/test sets at approximately 1:9 sample and token ratios; only totals are shown. Full statistics are in Appendix D .

	Pre-training				Mid-training		Post-training
	DCLM-Baseline	OpenWebMath	peS2o	StarCoder	Math Mix	Stack Exchange	SFT	DPO	RLVR	Avg
Overlap	4.07%	8.33%	3.11%	9.31%	6.65%	5.71%	6.32%	2.20%	2.06%	5.31%
BoW AUC	0.49	0.52	0.48	0.50	0.52	0.48	0.51	0.49	0.51	0.50

Table 3: Per-domain verification results, averaged across model sizes. Overlap : average 13-gram overlap of each domain’s non-members against OLMo 2’s training corpus. BoW AUC : blind detectability, measured by the AUC of a BoW classifier. Per-model-size results are in Tables 22 and 24 .

Method	1B				7B				13B				32B				Model-Avg
Method	Pre	Mid	Post	All	Pre	Mid	Post	All	Pre	Mid	Post	All	Pre	Mid	Post	All	Pre	Mid	Post	All
PPL L	0.54	0.64	0.61	0.60	0.55	0.72	0.68	0.65	0.56	0.79	0.66	0.67	0.58	0.80	0.68	0.69	0.56	0.74	0.66	0.65
Zlib L	0.57	0.67	0.66	0.63	0.59	0.76	0.66	0.67	0.59	0.83	0.67	0.70	0.61	0.85	0.69	0.72	0.59	0.78	0.67	0.68
Lower L	0.57	0.61	0.59	0.59	0.57	0.69	0.62	0.63	0.58	0.75	0.65	0.66	0.58	0.73	0.67	0.66	0.58	0.69	0.63	0.63
MinK L	0.55	0.65	0.62	0.61	0.56	0.73	0.67	0.65	0.57	0.80	0.66	0.68	0.59	0.81	0.69	0.70	0.57	0.75	0.66	0.66
MinK++ L	0.48	0.53	0.59	0.54	0.50	0.54	0.62	0.56	0.51	0.59	0.59	0.57	0.54	0.56	0.63	0.57	0.51	0.56	0.61	0.56

Table 4: AUCs of unsupervised MIAs on OLMo-Detect , grouped by family: L likelihood-based, P perturbation-based, Pr prompt-based, and O output-distribution-based. Pre / Mid / Post macro-average AUC over each stage’s domains, and All macro-averages all stages. Model-Avg averages across model sizes, and Method-Avg averages across methods. The best method per column is in bold. † SelfCrit is evaluated on post-training’s DPO and RLVR. Per-domain results are in Appendix I .

Method	Setting	1B				7B				13B				32B				Model-Avg
Method	Setting	Pre	Mid	Post	All	Pre	Mid	Post	All	Pre	Mid	Post	All	Pre	Mid	Post	All	Pre	Mid	Post	All
Sup-CAMIA	In-domain	0.56	0.72	0.61	0.63	0.54	0.78	0.72	0.68	0.55	0.86	0.72	0.71	0.55	0.84	0.67	0.69	0.55	0.80	0.68	0.68
Sup-CAMIA	LODO	0.56	0.63	0.52	0.57	0.60	0.73	0.62	0.65	0.57	0.66	0.55	0.59	0.59	0.70	0.62	0.64	0.58	0.68	0.58	0.61
MIA-Tuner	In-domain	0.54	0.60	0.53	0.56	0.53	0.61	0.55	0.56	0.54	0.60	0.53	0.56	0.54	0.53	0.51	0.52	0.54	0.59	0.53	0.55
MIA-Tuner	LODO	0.52	0.50	0.47	0.50	0.53	0.48	0.46	0.49	0.47	0.48	0.46	0.47	0.51	0.53	0.50	0.52	0.51	0.50	0.47	0.49

Table 5: Supervised MIAs on OLMo-Detect under In-domain and LODO settings. Top: AUCs of Sup-CAMIA and MIA-Tuner; the best method per column is in bold. Bottom: FSD measures the change in a base MIA’s score after fine-tuning the target model on non-members; we therefore report its AUC gain (

\Delta

AUC) over the base MIA (in parentheses), averaged across stages. Base AUC : base MIA’s AUC averaged across model sizes; positive gains are bolded. Details are in Appendix K .

	Pre-training					Mid-training			Post-training
	DCLM	peS2o	OWM	StarCoder		Math Mix	SE		SFT		DPO	RLVR
	DCLM	peS2o	OWM	Python	Java	GSM8K	Math SE	SO	Aya	WildChat	UF-WildChat	CoT-GSM8K	CoT-MATH
AUC (all MIAs)	0.56	0.52	0.54	0.56	0.59	0.71	0.59	0.60	0.57	0.60	0.50	0.70	0.63
AUC (eff. MIAs)	0.62	0.50	0.57	0.59	0.64	0.88	0.61	0.61	0.59	0.62	0.50	0.90	0.74
Dup. count	9.00	1.12	1.00	1.00	1.00	6.00	6.00	6.00	2.09	2.00	1.13	1.25	1.50

Table 6: Cross-stage analysis on OLMo-Detect . Top: Per-subset AUCs averaged across model sizes and over all MIAs (excluding FSD, which reports gain, and SelfCrit, which is evaluated on DPO/RLVR) or effective (eff.) MIAs (overall AUC

\geq 0.60

); bold means AUC

>0.70

. Dup. count : training-corpus occurrences per member in each subset. DCLM: DCLM-Baseline; OWM: OpenWebMath; SE: Stack Exchange; SO: Stack Overflow. Bottom: Stage-level AUCs with and without the three curated math subsets (GSM8K, CoT-GSM8K, CoT-MATH), and AUCs on the curated math subsets versus the others.

\Delta

: average per-MIA AUC gain on curated math subsets over the others; parentheses report the number of MIAs with positive gains and the one-sided Wilcoxon

p

-value.

PPL

Zlib

Lower

MinK

MinK++

DCPDD

ReCaLL

CAMIA

PAC

Neigh.

EMMIA

DCQ

CDD

Guided

I / D

4 / 2

2 / 2

5 / 1

2 / 1

1 / 3

2 / 3

4 / 0

4 / 1

5 / 1

3 / 2

2 / 1

3 / 0

1 / 2

Largest

\Delta

+

0.29

-

0.31

-

0.30

+

0.23

-

0.16

+

0.16

+

0.24

+

0.28

-

0.20

+

0.12

+

0.42

+

0.09

+

0.12

+

0.10

(OWM)

(SC)

(peS2o)

(OWM)

(SC)

(OWM)

(peS2o)

(OWM)

(SC)

Table 7: Effect of distribution shift on unsupervised MIAs (excluding SelfCrit), over the seven domains with shifted variants. I / D : number of domains on which the AUC increases / decreases significantly under the shift (

\Delta

= OLMo-Detect (Shifted)

-

OLMo-Detect , averaged over model sizes; 95% paired instance bootstrap). Largest

\Delta

: the largest change and the domain where it occurs. OWM: OpenWebMath; SC: StarCoder. Per-domain values are in Appendix O .

Domain	Comparison	PPL	Zlib	MinK	DCPDD	PAC	Avg
GSM8K	OLMo 2-7B / OLMo 3-7B	0.85 / 0.97	0.89 / 0.98	0.86 / 0.97	0.91 / 0.98	0.83 / 0.95	0.87 / 0.97
GSM8K	OLMo 2-32B / OLMo 3-32B	0.98 / 0.99	0.99 / 1.00	0.97 / 0.99	0.98 / 0.98	0.92 / 0.98	0.97 / 0.99
DCLM-Baseline	OLMo 2-1B / DCB-1B	0.60 / 0.63	0.59 / 0.61	0.57 / 0.60	0.57 / 0.60	0.61 / 0.63	0.59 / 0.61
DCLM-Baseline	OLMo 2-1B / SmolLM2-1.7B	0.60 / 0.62	0.59 / 0.62	0.57 / 0.59	0.57 / 0.61	0.61 / 0.64	0.59 / 0.62
OpenWebMath	OLMo 2-1B / DCB-1B	0.51 / 0.51	0.56 / 0.54	0.55 / 0.54	0.61 / 0.58	0.54 / 0.56	0.55 / 0.54
OpenWebMath	OLMo 2-7B / DCB-7B	0.51 / 0.53	0.57 / 0.56	0.55 / 0.55	0.57 / 0.59	0.56 / 0.57	0.55 / 0.56

Table 8: AUCs of the five best-performing unsupervised MIAs on OLMo 2 and other model families.

Appendix figures & tables77 assets

Supplementary material from the paper’s appendix.

Appendix

Domain	Type	Tokens	Words	Bytes	Docs
DCLM-Baseline	Web pages	3.71T	3.32T	21.32T	2.95B
StarCoder (filtered)	Code	83.0B	70.0B	459B	78.7M
peS2o	Academic papers	58.6B	51.1B	413B	38.8M
arXiv	STEM papers	20.8B	19.3B	77.2B	3.95M
OpenWebMath	Math web pages	12.2B	11.1B	47.2B	2.89M
Algebraic Stack	Math proofs/code	11.8B	10.8B	44.0B	2.83M

Appendix

Table 9: Composition of OLMo 2 Mix 1124, the pre-training corpus of the OLMo 2 suite, reproduced from Table 4 of OLMo et al. (2025) .

Domain	Type	Tokens	Words	Bytes	Docs
High-Quality Subset (five domains)
Filtered DCLM-Baseline	High-quality web	752B	670B	4.56T	606M
FLAN	Instruction data	17.0B	14.4B	98.2B	57.3M
peS2o	Academic papers	58.6B	51.1B	413B	38.8M
Wikipedia/Wikibooks	Encyclopedic	3.7B	3.16B	16.2B	6.17M
Stack Exchange	Q&A	1.26B	1.14B	7.72B	2.48M

Appendix

Table 10: Composition of Dolmino Mix 1124, the mid-training corpus of the OLMo 2 suite, reproduced from Table 5 of OLMo et al. (2025) . The High-Quality Subset contributes five domains directly; the Dolmino Math Mix is itself a single domain whose composition is given by seven subsets. “OWM-filtered” indicates that the subset is further filtered using the OpenWebMath classifier designed by OLMo et al. (2025) . † Although CodeSearchNet (OWM-filtered) is listed as part of the Dolmino Math Mix in OLMo et al. (2025) , it was not used in the final training.

Domain	Tokens	50B sample		100B sample		300B sample
Domain	Tokens	Domain %	Mix %	Domain %	Mix %	Domain %	Mix %
Filtered DCLM-Baseline	752B	3.23	47.2	6.85	50.2	20.78	51.9
FLAN	17.0B	50.0	16.6	100	16.7	200	11.3
Stack Exchange	1.26B	100	2.45	200	2.47	400	1.68
peS2o	58.6B	5.15	5.85	16.7	9.52	100	19.4
Wikipedia/Wikibooks	3.7B	100	7.11	100	3.57	400	4.86

Appendix

Table 11: Per-domain composition of the three token-budget samples (50B, 100B, 300B) drawn from Dolmino Mix 1124 for mid-training, reproduced from Table 13 of OLMo et al. (2025) . For each domain: “Domain %” is the fraction of that domain’s full token count drawn into the sample, with values above 100 indicating repetition (e.g., 400 = 4

\times

repeat); “Mix %” is the domain’s share of the sample’s total tokens (each Mix % column sums to 100%).

Subset	Count	# in SFT	Sampleable
General
Tülu 3 Hardcoded	240	240
OpenAssistant	88,838	7,132	✓
No Robots	9,500	9,500
WildChat (GPT-4 subset)	241,307	100,000	✓
Knowledge Recall

Appendix

Table 12: Subsets of OLMo 2’s SFT mix, reproduced from Table 7 of Lambert et al. (2025) . “Count” is the total number of prompts available in the upstream source corpus; “# in SFT” corresponds to tulu-3-sft-olmo-2-mixture (7B and 13B; 939,344 prompts). The 1B and 32B models use tulu-3-sft-olmo-2-mixture-0225 (866,138 prompts), which draws from the same 19 subsets but further removes date-cutoff instructions and applies majority voting over 5 completions to the † -marked subsets. The Sampleable column marks subsets with non-member candidates available for OLMo-Detect : ✓ = sampleable remainder available; blank = source corpus fully consumed (# in SFT = Count).

Stage	Domain	Subset	Prompts ∗	1B	7B	13B	32B	Sampleable
Post-training	DPO	SFT Reused	117,025	✓	✓	✓	✓	$\sim$
		SFT IF	65,792	✓	✓	✓	✓
		WildChat Unused ‡	84,105	✓	✓	✓	✓	✓
		WildChat Reused ‡	17,703	✓	✓	✓	✓	✓
		WildChat IF ‡	10,794	✓		✓	✓	✓
		UltraFeedback (cleaned)	60,816	✓	✓	✓	✓

Appendix

Table 13: Prompt subsets for OLMo 2’s DPO stage across all four model sizes. ∗ Per-subset prompt counts are reproduced from Table 27 of OLMo et al. (2025) and apply to the 7B and 13B mixes; the 1B and 32B mixes draw from the same eight subset families with comparable but not identical per-subset counts. The 7B mix omits WildChat IF; chosen responses in the 1B and 32B mixes are additionally filtered to remove date-cutoff mentions. Subsets labeled “IF” contain prompts augmented with verifiable instruction-following constraints (IFEval-style). The Sampleable column marks subsets with uncontaminated candidates available for OLMo-Detect : ✓ = sampleable remainder available; blank = source corpus fully consumed;

\sim

= unknown (SFT Reused aggregates prompts from many SFT source datasets with varying sampleability, making it impossible to determine remainder without per-source attribution). ‡ All three WildChat subsets draw from the same upstream source corpus and together count as one of the three sampleable sources ; the remaining two are DaringAnteater IF and Tülu 3 Personas IF.

Stage	Component	1B	7B	13B	32B
Pre-training	OLMo 2 Mix 1124	✓	✓	✓	✓
Mid-training	Dolmino Mix 1124, 50B sample	$\times 1$	$\times 3$
	Dolmino Mix 1124, 100B sample			$\times 3$	$\times 3$
	Dolmino Mix 1124, 300B sample			$\times 1$	$\times 1$
SFT	tulu-3-sft-olmo-2-mixture-0225	$\times 2$			$\times 2$
SFT	tulu-3-sft-olmo-2-mixture		$\times 2$	$\times 2$

Appendix

Table 14: Per-model training corpora for infini-gram indexing. Entries denote inclusion in the model’s indexed corpus, with multiplicities reflecting epoch and model-soup repetition (✓ = included once;

\times N

= included

N

times). ∗ Model-specific preference mixes: olmo-2-0425-1b-preference-mix (1B), olmo-2-1124-7b-preference-mix (7B), olmo-2-1124-13b-preference-mix (13B), olmo-2-0325-32b-preference-mix (32B). † The 1B model’s additional MATH-only RLVR pass is inferred from the OLMo 2 training documentation in the open-instruct repository ( https://github.com/allenai/open-instruct/blob/main/docs/olmo2.md ).

Stage	Domain	Subset	Split	Partition	Samples	Tokens	Quality	Temporal	Lexical
Pre-training	DCLM-Baseline		NM	Dev	16	21,745	FastText: 0.01808 $\pm$ 0.00004	2018-01-18 $\pm$ 930d	0.07
				Test	134	195,372	FastText: 0.01809 $\pm$ 0.00008	2018-01-19 $\pm$ 930d
				Total	150	217,117	FastText: 0.01809 $\pm$ 0.00007	2018-01-19 $\pm$ 930d
			M	Dev	16	21,721	FastText: 0.01811 $\pm$ 0.00000	2018-01-17 $\pm$ 933d
				Test	134	195,295	FastText: 0.01811 $\pm$ 0.00000	2018-01-18 $\pm$ 941d
				Total	150	217,016	FastText: 0.01811 $\pm$ 0.00000	2018-01-18 $\pm$ 940d

Appendix

Table 15: Detailed per-domain statistics for the pre-training stage of OLMo-Detect . NM : non-member; M : member. Dev : development set; Test : test set. The Subset column lists constituent subsets; blank entries indicate single-subset domains whose subset shares the domain’s name.

Stage	Domain	Subset	Split	Partition	Samples	Tokens	Quality	Temporal	Lexical
Mid-training	Math Mix	GSM8K	NM	Dev	103	21,755	—	—	0.04
				Test	937	195,408	—	—
				Total	1,040	217,163
			M	Dev	103	21,729	—	—
				Test	937	195,403	—	—
				Total	1,040	217,132

Appendix

Table 16: Sampling statistics for the mid-training stage of OLMo-Detect . NM : non-member; M : member. Dev : development set; Test : test set. The Subset column lists constituent subsets.

Stage	Domain	Subset	Model	Split	Partition	Samples	Tokens	Quality	Temporal	Lexical
Post-training	SFT	WildChat, Aya	1B, 32B	NM	Dev	21	21,697	—	—	0.11
					Test	204	195,360	—	—
					Total	225	217,057
				M	Dev	21	21,696	—	—
					Test	204	195,463	—	—
					Total	225	217,159

Appendix

Table 17: Detailed per-stage statistics for the post-training stage of OLMo-Detect . NM : non-member; M : member. Dev : development set; Test : test set. The Subset column lists constituent subsets; blank entries indicate single-subset domains whose subset shares the domain’s name.

Stage	Domain	Subset	Split	Partition	Samples	Tokens	Quality	Temporal	Lexical
Pre-training	StarCoder	Python	NM	Dev	10	19,364	GitHub Stars: 29.50 $\pm$ 61.41 Top-1 Freq: 0.31 $\pm$ 0.01 Top-2 Freq: 0.36 $\pm$ 0.04	—	0.16
				Test	90	175,594	GitHub Stars: 28.53 $\pm$ 59.41 Top-1 Freq: 0.30 $\pm$ 0.02 Top-2 Freq: 0.38 $\pm$ 0.06	—
				Total	100	194,958	GitHub Stars: 28.63 $\pm$ 59.62 Top-1 Freq: 0.30 $\pm$ 0.02 Top-2 Freq: 0.37 $\pm$ 0.05	—
			M	Dev	10	19,551	GitHub Stars: 28.90 $\pm$ 58.22 Top-1 Freq: 0.29 $\pm$ 0.01 Top-2 Freq: 0.35 $\pm$ 0.04	—
				Test	90	175,551	GitHub Stars: 29.23 $\pm$ 57.87 Top-1 Freq: 0.29 $\pm$ 0.01 Top-2 Freq: 0.36 $\pm$ 0.06	—
				Total	100	195,102	GitHub Stars: 29.20 $\pm$ 57.90 Top-1 Freq: 0.29 $\pm$ 0.01 Top-2 Freq: 0.36 $\pm$ 0.06	—

Appendix

Table 18: Detailed per-subset statistics for StarCoder in the pre-training stage of OLMo-Detect . NM : non-member; M : member. Dev : development set; Test : test set.

Stage	Domain	Subset	Split	Partition	Samples	Tokens	Quality	Temporal	Lexical
Mid-training	Stack Exchange	Stack Overflow	NM	Dev	37	18,489	Question Vote: 3.49 $\pm$ 2.26 Answer Vote: 5.14 $\pm$ 2.04	2015-02-06 $\pm$ 1381.39d	0.08
				Test	331	165,394	Question Vote: 3.48 $\pm$ 2.24 Answer Vote: 5.14 $\pm$ 2.05	2015-02-05 $\pm$ 1379.01d
				Total	368	183,883	Question Vote: 3.48 $\pm$ 2.25 Answer Vote: 5.14 $\pm$ 2.05	2015-02-06 $\pm$ 1379.25d
			M	Dev	37	18,489	Question Vote: 3.51 $\pm$ 2.23 Answer Vote: 5.32 $\pm$ 1.95	2015-02-06 $\pm$ 1329.25d
				Test	331	165,471	Question Vote: 3.53 $\pm$ 1.66 Answer Vote: 5.58 $\pm$ 1.99	2015-02-06 $\pm$ 1378.98d
				Total	368	183,960	Question Vote: 3.52 $\pm$ 1.72 Answer Vote: 5.55 $\pm$ 1.98	2015-02-06 $\pm$ 1374.07d

Appendix

Table 19: Detailed per-subset statistics for Stack Exchange in the mid-training stage of OLMo-Detect . NM : non-member; M : member. Dev : development set; Test : test set.

Stage	Domain	Model	Subset	Split	Partition	Samples	Tokens	Quality	Temporal	Lexical
Post-training	SFT	1B, 32B	Wildchat	NM	Dev	7	16,404	—	—	0.14
					Test	64	148,039	—	—
					Total	71	164,443
				M	Dev	7	16,438	—	—
					Test	64	148,115	—	—
					Total	71	164,553

Appendix

Table 20: Detailed per-subset statistics for SFT in the post-training stage of OLMo-Detect . NM : non-member; M : member. Dev : development set; Test : test set.

Stage	Domain	Model	Subset	Split	Partition	Samples	Tokens	Quality	Temporal	Lexical
Post-training	RLVR	1B, 7B, 13B, 32B	CoT-GSM8K	NM	Dev	14	11,835	—	—	0.01
					Test	128	107,609	—	—
					Total	142	119,444
				M	Dev	14	11,796	—	—
					Test	128	107,563	—	—
					Total	142	119,359

Appendix

Table 21: Detailed per-subset statistics for RLVR in the post-training stage of OLMo-Detect . NM : non-member; M : member. Dev : development set; Test : test set.

	Pre-training				Mid-training		Post-training
	DCLM-Baseline	OpenWebMath	peS2o	StarCoder	Math Mix	Stack Exchange	SFT	DPO	RLVR	Avg
1B	4.07 ±4.87	8.33 ±5.69	3.11 ±4.01	9.31 ±5.24	6.65 ±4.77	5.71 ±5.34	6.08 ±5.24	2.12 ±3.01	2.06 ±4.55	5.27
7B	4.07 ±4.87	8.33 ±5.69	3.11 ±4.01	9.31 ±5.24	6.66 ±4.75	5.71 ±5.34	6.54 ±5.29	1.98 ±3.05	2.06 ±4.55	5.31
13B	4.07 ±4.87	8.33 ±5.69	3.11 ±4.01	9.31 ±5.24	6.65 ±4.75	5.71 ±5.34	6.55 ±5.30	2.52 ±3.37	2.06 ±4.55	5.37
32B	4.07 ±4.87	8.33 ±5.69	3.11 ±4.01	9.31 ±5.24	6.64 ±4.75	5.71 ±5.35	6.12 ±5.31	2.20 ±3.15	2.06 ±4.55	5.28
Avg	4.07	8.33	3.11	9.31	6.65	5.71	6.32	2.20	2.06	5.31

Appendix

Table 22: Per-model-size 13-gram overlap

\eta

(%; mean

{}_{\pm\text{std}}

over non-members) for each domain against the training corpus of the corresponding OLMo 2 model size. Multi-subset domains are macro-averaged across subsets (Table 23 ), with the domain-level standard deviation computed as the root mean square of the subset-level standard deviations.

Domain	Subset	1B	7B	13B	32B	Avg
StarCoder	Python	7.17 ±5.28	7.17 ±5.28	7.17 ±5.28	7.17 ±5.28	7.17
StarCoder	Java	11.45 ±5.20	11.45 ±5.20	11.45 ±5.20	11.45 ±5.20	11.45
Stack Exchange	Math Stack Exchange	5.67 ±4.91	5.67 ±4.91	5.67 ±4.91	5.68 ±4.92	5.67
Stack Exchange	Stack Overflow	5.74 ±5.74	5.74 ±5.74	5.74 ±5.75	5.75 ±5.74	5.74
SFT	WildChat	5.16 ±4.49	4.53 ±4.53	4.55 ±4.53	5.14 ±4.59	4.84
SFT	Aya	7.01 ±5.89	8.55 ±5.95	8.55 ±5.96	7.10 ±5.95	7.80

Appendix

Table 23: Per-subset 13-gram overlap

\eta

(%; mean

{}_{\pm\text{std}}

over non-members) for multi-subset domains. Domain-level values are macro-averaged across subsets; for DPO, they are averaged across the prompt, chosen, and rejected fields.

	Pre-training				Mid-training		Post-training
	DCLM-Baseline	OpenWebMath	peS2o	StarCoder	Math Mix	Stack Exchange	SFT	DPO	RLVR	Avg
1B	0.49	0.52	0.48	0.50	0.52	0.48	0.51	0.47	0.51	0.50
7B	0.49	0.52	0.48	0.50	0.52	0.48	0.52	0.51	0.51	0.50
13B	0.49	0.52	0.48	0.50	0.52	0.48	0.52	0.49	0.51	0.50
32B	0.49	0.52	0.48	0.50	0.52	0.48	0.51	0.48	0.51	0.50
Avg	0.49	0.52	0.48	0.50	0.52	0.48	0.51	0.49	0.51	0.50

Appendix

Table 24: Per-model-size blind detectability, measured by BoW classifier AUC. Multi-subset domains are macro-averaged across subsets, with per-subset AUCs reported in Table 25 .

Domain	Subset	1B	7B	13B	32B	Avg
StarCoder	Python	0.48	0.48	0.48	0.48	0.48
StarCoder	Java	0.51	0.51	0.51	0.51	0.51
Stack Exchange	Math Stack Exchange	0.47	0.47	0.47	0.47	0.47
Stack Exchange	Stack Overflow	0.49	0.49	0.49	0.49	0.49
SFT	WildChat	0.52	0.54	0.54	0.52	0.53
SFT	Aya	0.50	0.51	0.51	0.50	0.50

Appendix

Table 25: Per-subset blind detectability for multi-subset domains, measured by BoW classifier AUC.

Method	Reference	Repository
PPL	Yeom et al. (2018)	— (standard baseline)
Zlib	Carlini et al. (2021)	— (standard baseline)
Lower	Carlini et al. (2021)	— (standard baseline)
MinK	Shi et al. (2023)	https://github.com/swj0419/detect-pretrain-code
MinK++	Zhang et al. (2024a)	https://github.com/zjysteven/mink-plus-plus
DCPDD	Zhang et al. (2024b)	https://github.com/zhang-wei-chao/DC-PDD

Appendix

Table 26: Public repositories followed by our implementations of the compared MIAs. The final three rows are the supervised methods; all others are unsupervised.

Method	Hyperparameter	Search space	Selected value
			1B	7B	13B	32B
MinK	$k$	$\{0.05,\dots,1.0\}$	$0.2$
MinK++	$k$	$\{0.05,\dots,1.0\}$	$0.2$
DCPDD	$\alpha$	$\{0.001,\dots,0.5\}$	$0.001$	$0.2$	$0.05$	$0.2$
ReCaLL	# prefix shots $n$	$\{1,\dots,12\}$	$10$	$3$	$7$	$12$
CAMIA	$p$ -value composition	{Edgington, Fisher, George}	George	Fisher	George	George

Appendix

Table 27: Tunable hyperparameters, search spaces, and the values selected by development-set AUC on OLMo-Detect .

Method	AUC	95% CI
PPL	0.65	[0.64, 0.67]
Zlib	0.68	[0.67, 0.70]
Lower	0.63	[0.62, 0.65]
MinK	0.66	[0.64, 0.67]
MinK++	0.56	[0.54, 0.57]
DCPDD	0.67	[0.65, 0.68]

Appendix

Table 28: Bootstrap

95\%

confidence intervals for the overall AUC of each unsupervised MIA on OLMo-Detect , i.e. the All column of Table 4 averaged over model sizes. Members and non-members are resampled with replacement within every subset and the full subset-to-domain-to-stage aggregation is recomputed on each of

2{,}000

resamples, so the interval applies to the aggregate rather than to any single evaluation. SelfCrit is omitted because it covers only post-training. Point estimates match Table 4 .

Method	Setting	AUC	95% CI
Sup-CAMIA	In-domain	0.68	[0.67, 0.68]
Sup-CAMIA	LODO	0.61	[0.60, 0.62]
MIA-Tuner	In-domain	0.55	[0.54, 0.56]
MIA-Tuner	LODO	0.49	[0.48, 0.50]

Appendix

Table 29: Bootstrap

95\%

confidence intervals for the overall AUC of the supervised MIAs on OLMo-Detect , i.e. the All column of Table 5 averaged over model sizes, computed as in Table 28 . FSD is omitted because it is reported as a gain over its base detector rather than as an absolute AUC. Point estimates match Table 5 .

Stage	Domain	Subsets	Split	Samples	Tokens	Quality	Temporal	Lexical
Pre-training	DCLM-Baseline		Non-member	150	217,117	FastText: 0.01809 $\pm$ 0.00007	2018-01-19 $\pm$ 930d	0.08
	DCLM-Baseline		Member	150	217,295	FastText: 0.13129 $\pm$ 0.18279	2017-02-21 $\pm$ 1208d	0.08
	peS2o		Non-member	268	216,981	—	2022-12-14 $\pm$ 11d	0.13
	peS2o		Member	268	217,039	—	2014-02-03 $\pm$ 2657d	0.13
	OpenWebMath		Non-member	151	217,183	—	2019-10-13 $\pm$ 853d	0.32
	OpenWebMath		Member	151	217,379	—	2011-10-01 $\pm$ 2936d	0.32

Appendix

Table 30: Overall statistics of OLMo-Detect (Shifted) , spanning seven of the nine domains of OLMo-Detect (GSM8K and RLVR are excluded, as neither has any shiftable axis). Non-members are unchanged from OLMo-Detect , while members are randomly sampled subject only to matched instance and token counts, leaving Text Quality , Temporal Range, and Lexical Similarity unaligned. “—” denotes an axis that does not apply to a given domain, i.e., no quality thresholding is applied, or no timestamp metadata exists. NM : non-member; M : member. The Subsets column lists constituent subsets; blank entries indicate single-subset domains whose subset shares the domain’s name. † SFT and DPO are constructed separately for each model size because their training data differ across sizes; the reported values correspond to the 1B model.

Stage	Domain	Subset	Split	Partition	Samples	Tokens	Quality	Temporal	Lexical
Pre-training	DCLM-Baseline		NM	Dev	16	21,745	FastText: 0.01808 $\pm$ 0.00004	2018-01-18 $\pm$ 930.40d	0.08
				Test	134	195,372	FastText: 0.01809 $\pm$ 0.00008	2018-01-19 $\pm$ 930.19d
				Total	150	217,117	FastText: 0.01809 $\pm$ 0.00007	2018-01-19 $\pm$ 930.21d
			M	Dev	16	21,745	FastText: 0.13136 $\pm$ 0.19309	2017-02-21 $\pm$ 1204.63d
				Test	134	195,550	FastText: 0.13128 $\pm$ 0.18152	2017-02-21 $\pm$ 1208.34d
				Total	150	217,295	FastText: 0.13129 $\pm$ 0.18279	2017-02-21 $\pm$ 1207.94d

Appendix

Table 31: Detailed per-domain statistics for the pre-training stage of OLMo-Detect (Shifted) . NM : non-member; M : member. Dev : development set; Test : test set. The Subset column lists constituent subsets; blank entries indicate single-subset domains whose subset shares the domain’s name.

Stage	Domain	Subset	Split	Partition	Samples	Tokens	Quality	Temporal	Lexical
Mid-training	Stack Exchange	Stack Overflow, Math Stack Exchange	NM	Dev	43	21,760	Question Vote: 3.47 $\pm$ 2.20 Answer Vote: 5.12 $\pm$ 1.94	2015-03-27 $\pm$ 1378.74d	0.08
				Test	387	195,448	Question Vote: 3.45 $\pm$ 2.19 Answer Vote: 5.12 $\pm$ 2.00	2015-03-31 $\pm$ 1378.12d
				Total	430	217,208	Question Vote: 3.45 $\pm$ 2.19 Answer Vote: 5.12 $\pm$ 1.99	2015-03-31 $\pm$ 1378.18d
			M	Dev	43	21,750	Question Vote: 8.16 $\pm$ 6.92 Answer Vote: 10.02 $\pm$ 6.41	2013-06-05 $\pm$ 1206.73d
				Test	387	195,459	Question Vote: 8.12 $\pm$ 7.10 Answer Vote: 10.02 $\pm$ 6.37	2013-05-31 $\pm$ 1214.10d
				Total	430	217,209	Question Vote: 8.12 $\pm$ 7.08 Answer Vote: 10.02 $\pm$ 6.37	2013-05-31 $\pm$ 1213.37d

Appendix

Table 32: Detailed per-domain statistics for the mid-training stage of OLMo-Detect (Shifted) . NM : non-member; M : member. Dev : development set; Test : test set. The Subset column lists constituent subsets.

Stage	Domain	Subset	Model	Split	Partition	Samples	Tokens	Quality	Temporal	Lexical
Post-training	SFT	WildChat, Aya	1B, 32B	NM	Dev	21	21,697	—	—	0.34
					Test	204	195,360	—	—
					Total	225	217,057
				M	Dev	21	21,727	—	—
					Test	204	195,511	—	—
					Total	225	217,238

Appendix

Table 33: Detailed per-domain statistics for the post-training stage of OLMo-Detect (Shifted) . NM : non-member; M : member. Dev : development set; Test : test set. The Subset column lists constituent subsets.

Stage	Domain	Subset	Split	Partition	Samples	Tokens	Quality	Temporal	Lexical
Pre-training	StarCoder	Python	NM	Dev	10	19,364	GitHub Stars: 29.50 $\pm$ 61.41 Top-1 Freq: 0.31 $\pm$ 0.01 Top-2 Freq: 0.36 $\pm$ 0.04	—	0.37
				Test	90	175,594	GitHub Stars: 28.53 $\pm$ 59.41 Top-1 Freq: 0.30 $\pm$ 0.02 Top-2 Freq: 0.38 $\pm$ 0.06	—
				Total	100	194,958	GitHub Stars: 28.63 $\pm$ 59.62 Top-1 Freq: 0.30 $\pm$ 0.02 Top-2 Freq: 0.37 $\pm$ 0.05	—
			M	Dev	10	19,295	GitHub Stars: 8.60 $\pm$ 17.62 Top-1 Freq: 0.08 $\pm$ 0.02 Top-2 Freq: 0.14 $\pm$ 0.03	—
				Test	90	175,746	GitHub Stars: 9.02 $\pm$ 18.29 Top-1 Freq: 0.09 $\pm$ 0.03 Top-2 Freq: 0.15 $\pm$ 0.04	—
				Total	100	195,041	GitHub Stars: 8.98 $\pm$ 18.23 Top-1 Freq: 0.09 $\pm$ 0.03 Top-2 Freq: 0.15 $\pm$ 0.04	—

Appendix

Table 34: Detailed per-subset statistics for StarCoder in OLMo-Detect (Shifted) . NM : non-member; M : member. Dev : development set; Test : test set.

Stage	Domain	Subset	Split	Partition	Samples	Tokens	Quality	Temporal	Lexical
Mid-training	Stack Exchange	Stack Overflow	NM	Dev	37	18,489	Question Vote: 3.49 $\pm$ 2.26 Answer Vote: 5.14 $\pm$ 2.04	2015-02-06 $\pm$ 1381.39d	0.09
				Test	331	165,394	Question Vote: 3.48 $\pm$ 2.24 Answer Vote: 5.14 $\pm$ 2.05	2015-02-05 $\pm$ 1379.01d
				Total	368	183,883	Question Vote: 3.48 $\pm$ 2.25 Answer Vote: 5.14 $\pm$ 2.05	2015-02-06 $\pm$ 1379.25d
			M	Dev	37	18,488	Question Vote: 8.00 $\pm$ 6.70 Answer Vote: 10.00 $\pm$ 6.58	2013-07-30 $\pm$ 1269.85d
				Test	331	165,394	Question Vote: 8.00 $\pm$ 6.98 Answer Vote: 10.00 $\pm$ 6.55	2013-07-25 $\pm$ 1281.27d
				Total	368	183,882	Question Vote: 8.00 $\pm$ 6.95 Answer Vote: 10.00 $\pm$ 6.55	2013-07-26 $\pm$ 1280.13d

Appendix

Table 35: Detailed per-subset statistics for Stack Exchange in OLMo-Detect (Shifted) . NM : non-member; M : member. Dev : development set; Test : test set.

Stage	Domain	Model	Subset	Split	Partition	Samples	Tokens	Quality	Temporal	Lexical
Post-training	SFT	1B, 32B	Wildchat	NM	Dev	7	16,404	—	—	0.43
					Test	64	148,039	—	—
					Total	71	164,443
				M	Dev	7	16,388	—	—
					Test	64	148,120	—	—
					Total	71	164,508

Appendix

Table 36: Detailed per-subset statistics for SFT in OLMo-Detect (Shifted) . NM : non-member; M : member. Dev : development set; Test : test set.

Model	Likelihood-based										Pert.	Prompt		Out.-Dist.	Method- Avg
Model	PPL	Zlib	Lower	MinK	MinK++	DCPDD	PAC	ReCaLL	EMMIA	CAMIA	Neigh.	Guided	DCQ	CDD	Method- Avg
1B	0.60	0.59	0.60	0.57	0.46	0.57	0.61	0.46	0.52	0.60	0.64	0.54	0.50	0.50	0.55
7B	0.64	0.64	0.62	0.61	0.53	0.64	0.65	0.50	0.54	0.65	0.61	0.49	0.43	0.49	0.57
13B	0.65	0.65	0.63	0.63	0.52	0.64	0.68	0.62	0.53	0.66	0.62	0.47	0.47	0.51	0.59
32B	0.66	0.67	0.66	0.64	0.61	0.65	0.69	0.53	0.50	0.64	0.61	0.47	0.64	0.51	0.61
Model-Avg	0.64	0.64	0.63	0.61	0.53	0.62	0.66	0.53	0.52	0.64	0.62	0.49	0.51	0.50	0.58

Appendix

Table 37: Comparison of unsupervised MIAs on the DCLM-Baseline domain of OLMo-Detect , evaluated via AUC. Methods are grouped by family as in Table 4 . Model-Avg averages across model sizes, while Method-Avg averages the methods with a value in that row. The best-performing method in each row is highlighted in bold.

Model	Likelihood-based										Pert.	Prompt		Out.-Dist.	Method- Avg
Model	PPL	Zlib	Lower	MinK	MinK++	DCPDD	PAC	ReCaLL	EMMIA	CAMIA	Neigh.	Guided	DCQ	CDD	Method- Avg
1B	0.47	0.49	0.48	0.50	0.51	0.52	0.48	0.51	0.63	0.50	0.49	0.44	0.49	0.50	0.50
7B	0.47	0.49	0.48	0.48	0.49	0.51	0.47	0.55	0.70	0.47	0.51	0.52	0.52	0.50	0.51
13B	0.48	0.50	0.50	0.49	0.50	0.51	0.51	0.51	0.70	0.47	0.51	0.51	0.54	0.50	0.52
32B	0.49	0.51	0.50	0.51	0.48	0.52	0.51	0.52	0.71	0.47	0.53	0.44	0.64	0.49	0.52
Model-Avg	0.48	0.50	0.49	0.50	0.50	0.51	0.49	0.52	0.69	0.48	0.51	0.48	0.55	0.50	0.51

Appendix

Table 38: Comparison of unsupervised MIAs on the peS2o domain of OLMo-Detect , evaluated via AUC. Methods are grouped by family as in Table 4 . Model-Avg averages across model sizes, while Method-Avg averages the methods with a value in that row. The best-performing method in each row is highlighted in bold.

Model	Likelihood-based										Pert.	Prompt		Out.-Dist.	Method- Avg
Model	PPL	Zlib	Lower	MinK	MinK++	DCPDD	PAC	ReCaLL	EMMIA	CAMIA	Neigh.	Guided	DCQ	CDD	Method- Avg
1B	0.58	0.65	0.60	0.60	0.49	0.65	0.69	0.60	0.53	0.55	0.53	0.43	0.59	0.52	0.57
7B	0.60	0.65	0.62	0.61	0.50	0.67	0.68	0.60	0.53	0.54	0.53	0.55	0.46	0.54	0.58
13B	0.60	0.64	0.59	0.60	0.50	0.68	0.70	0.60	0.52	0.60	0.52	0.45	0.54	0.56	0.58
32B	0.60	0.63	0.58	0.62	0.48	0.69	0.70	0.56	0.64	0.61	0.52	0.58	0.45	0.54	0.59
Model-Avg	0.59	0.64	0.60	0.61	0.49	0.67	0.69	0.59	0.56	0.58	0.53	0.50	0.51	0.54	0.58

Appendix

Table 39: Comparison of unsupervised MIAs on the StarCoder domain of OLMo-Detect , evaluated via AUC (macro-averaged over its subsets). Methods are grouped by family as in Table 4 . Model-Avg averages across model sizes, while Method-Avg averages the methods with a value in that row. The best-performing method in each row is highlighted in bold.

Model	Likelihood-based										Pert.	Prompt		Out.-Dist.	Method- Avg
Model	PPL	Zlib	Lower	MinK	MinK++	DCPDD	PAC	ReCaLL	EMMIA	CAMIA	Neigh.	Guided	DCQ	CDD	Method- Avg
1B	0.51	0.56	0.61	0.55	0.48	0.61	0.54	0.44	0.54	0.56	0.54	0.47	0.52	0.51	0.53
7B	0.51	0.57	0.59	0.55	0.50	0.57	0.56	0.49	0.53	0.46	0.52	0.42	0.24	0.48	0.50
13B	0.52	0.58	0.61	0.56	0.53	0.63	0.58	0.48	0.52	0.45	0.55	0.44	0.42	0.49	0.53
32B	0.57	0.64	0.59	0.60	0.59	0.65	0.60	0.44	0.60	0.43	0.55	0.43	0.51	0.48	0.55
Model-Avg	0.53	0.59	0.60	0.56	0.52	0.61	0.57	0.46	0.55	0.47	0.54	0.44	0.42	0.49	0.53

Appendix

Table 40: Comparison of unsupervised MIAs on the OpenWebMath domain of OLMo-Detect , evaluated via AUC. Methods are grouped by family as in Table 4 . Model-Avg averages across model sizes, while Method-Avg averages the methods with a value in that row. The best-performing method in each row is highlighted in bold.

Model	Likelihood-based										Pert.	Prompt		Out.-Dist.	Method- Avg
Model	PPL	Zlib	Lower	MinK	MinK++	DCPDD	PAC	ReCaLL	EMMIA	CAMIA	Neigh.	Guided	DCQ	CDD	Method- Avg
1B	0.73	0.76	0.72	0.76	0.57	0.69	0.72	0.32	0.50	0.75	0.64	0.49	0.46	0.52	0.62
7B	0.85	0.89	0.83	0.86	0.52	0.91	0.83	0.05	0.51	0.88	0.72	0.50	0.51	0.55	0.67
13B	0.98	0.99	0.93	0.99	0.58	0.99	0.96	0.01	0.48	0.99	0.89	0.48	0.53	0.68	0.75
32B	0.98	0.99	0.93	0.97	0.51	0.98	0.92	0.02	0.50	0.99	0.91	0.55	0.51	0.74	0.75
Model-Avg	0.89	0.91	0.85	0.89	0.55	0.89	0.86	0.10	0.50	0.90	0.79	0.51	0.50	0.62	0.70

Appendix

Table 41: Comparison of unsupervised MIAs on the GSM8K subset of OLMo-Detect ’s Math Mix domain, evaluated via AUC. Methods are grouped by family as in Table 4 . Model-Avg averages across model sizes, while Method-Avg averages the methods with a value in that row. The best-performing method in each row is highlighted in bold.

Model	Likelihood-based										Pert.	Prompt		Out.-Dist.	Method- Avg
Model	PPL	Zlib	Lower	MinK	MinK++	DCPDD	PAC	ReCaLL	EMMIA	CAMIA	Neigh.	Guided	DCQ	CDD	Method- Avg
1B	0.55	0.59	0.50	0.54	0.49	0.53	0.59	0.54	0.56	0.58	0.55	0.54	0.54	0.51	0.54
7B	0.58	0.64	0.55	0.60	0.56	0.61	0.63	0.53	0.57	0.59	0.56	0.45	0.40	0.53	0.56
13B	0.60	0.67	0.56	0.62	0.61	0.67	0.66	0.66	0.65	0.61	0.58	0.49	0.64	0.52	0.61
32B	0.63	0.70	0.53	0.65	0.61	0.68	0.69	0.73	0.69	0.64	0.60	0.54	0.64	0.50	0.63
Model-Avg	0.59	0.65	0.53	0.60	0.57	0.62	0.64	0.61	0.62	0.61	0.57	0.51	0.55	0.51	0.59

Appendix

Table 42: Comparison of unsupervised MIAs on the Stack Exchange domain of OLMo-Detect , evaluated via AUC (macro-averaged over its subsets). Methods are grouped by family as in Table 4 . Model-Avg averages across model sizes, while Method-Avg averages the methods with a value in that row. The best-performing method in each row is highlighted in bold.

Model	Likelihood-based										Pert.	Prompt		Out.-Dist.	Method- Avg
Model	PPL	Zlib	Lower	MinK	MinK++	DCPDD	PAC	ReCaLL	EMMIA	CAMIA	Neigh.	Guided	DCQ	CDD	Method- Avg
1B	0.62	0.64	0.49	0.63	0.73	0.56	0.51	0.61	0.57	0.49	0.54	0.48	0.51	0.51	0.56
7B	0.73	0.70	0.55	0.71	0.77	0.70	0.59	0.74	0.59	0.74	0.60	0.51	0.43	0.50	0.63
13B	0.65	0.61	0.50	0.64	0.70	0.60	0.55	0.65	0.55	0.57	0.51	0.54	0.44	0.51	0.57
32B	0.64	0.64	0.50	0.65	0.69	0.60	0.51	0.69	0.55	0.54	0.52	0.44	0.45	0.50	0.57
Model-Avg	0.66	0.65	0.51	0.66	0.72	0.61	0.54	0.67	0.56	0.58	0.54	0.49	0.46	0.51	0.58

Appendix

Table 43: Comparison of unsupervised MIAs on the SFT domain of OLMo-Detect , evaluated via AUC (macro-averaged over its subsets). Methods are grouped by family as in Table 4 . Model-Avg averages across model sizes, while Method-Avg averages the methods with a value in that row. The best-performing method in each row is highlighted in bold.

Model	Likelihood-based										Pert.	Prompt		Out.-Dist.		Method- Avg
Model	PPL	Zlib	Lower	MinK	MinK++	DCPDD	PAC	ReCaLL	EMMIA	CAMIA	Neigh.	Guided	DCQ	CDD	SelfCrit †	Method- Avg
1B	0.44	0.55	0.64	0.44	0.45	0.47	0.62	0.54	0.60	0.59	0.54	0.53	0.45	0.53	0.43	0.52
7B	0.41	0.39	0.50	0.40	0.40	0.40	0.43	0.48	0.50	0.60	0.46	0.48	0.30	0.53	0.53	0.45
13B	0.38	0.47	0.64	0.38	0.45	0.39	0.53	0.59	0.49	0.57	0.49	0.45	0.50	0.53	0.43	0.49
32B	0.46	0.53	0.62	0.48	0.47	0.48	0.62	0.65	0.39	0.55	0.60	0.47	0.47	0.48	0.55	0.52
Model-Avg	0.42	0.48	0.60	0.43	0.44	0.43	0.55	0.57	0.49	0.58	0.52	0.48	0.43	0.52	0.48	0.50

Appendix

Table 44: Comparison of unsupervised MIAs on the UF-Wildchat subset of OLMo-Detect ’s DPO domain, evaluated via AUC. Methods are grouped by family as in Table 4 . Model-Avg averages across model sizes, while Method-Avg averages the methods with a value in that row. The best-performing method in each row is highlighted in bold. † SelfCrit is evaluated only on DPO and RLVR.

Model	Likelihood-based										Pert.	Prompt		Out.-Dist.		Method- Avg
Model	PPL	Zlib	Lower	MinK	MinK++	DCPDD	PAC	ReCaLL	EMMIA	CAMIA	Neigh.	Guided	DCQ	CDD	SelfCrit †	Method- Avg
1B	0.77	0.79	0.64	0.79	0.60	0.74	0.69	0.36	0.66	0.68	0.51	0.50	0.43	0.48	0.50	0.61
7B	0.89	0.88	0.80	0.90	0.69	0.87	0.77	0.25	0.73	0.82	0.60	0.53	0.48	0.48	0.48	0.68
13B	0.95	0.94	0.81	0.95	0.62	0.92	0.75	0.18	0.76	0.85	0.58	0.47	0.50	0.46	0.46	0.68
32B	0.94	0.91	0.90	0.94	0.72	0.92	0.77	0.28	0.47	0.89	0.60	0.47	0.50	0.49	0.41	0.68
Model-Avg	0.89	0.88	0.79	0.90	0.66	0.86	0.75	0.27	0.65	0.81	0.57	0.49	0.48	0.48	0.46	0.66

Appendix

Table 45: Comparison of unsupervised MIAs on the RLVR domain of OLMo-Detect , evaluated via AUC (macro-averaged over its subsets). Methods are grouped by family as in Table 4 . Model-Avg averages across model sizes, while Method-Avg averages the methods with a value in that row. The best-performing method in each row is highlighted in bold. † SelfCrit is evaluated only on DPO and RLVR.

Subset	Model	Likelihood-based										Pert.	Prompt		Out.-Dist.	Method- Avg
Subset	Model	PPL	Zlib	Lower	MinK	MinK++	DCPDD	PAC	ReCaLL	EMMIA	CAMIA	Neigh.	Guided	DCQ	CDD	Method- Avg
Python	1B	0.54	0.61	0.58	0.55	0.50	0.61	0.69	0.52	0.49	0.58	0.52	0.38	0.57	0.52	0.55
	7B	0.55	0.62	0.60	0.56	0.53	0.61	0.68	0.51	0.50	0.58	0.52	0.48	0.51	0.51	0.56
	13B	0.55	0.62	0.58	0.56	0.52	0.62	0.67	0.56	0.51	0.62	0.51	0.48	0.54	0.52	0.56
	32B	0.54	0.60	0.55	0.55	0.53	0.61	0.66	0.53	0.62	0.60	0.53	0.56	0.49	0.56	0.57
	Model-Avg	0.54	0.62	0.58	0.55	0.52	0.61	0.68	0.53	0.53	0.60	0.52	0.48	0.53	0.53	0.56

Appendix

Table 46: Comparison of unsupervised MIAs on the subsets of the StarCoder domain of OLMo-Detect , evaluated via AUC. Methods are grouped by family as in Table 4 . Model-Avg averages across model sizes, while Method-Avg averages the methods with a value in that row. The best-performing method in each row is highlighted in bold.

Subset	Model	Likelihood-based										Pert.	Prompt		Out.-Dist.	Method- Avg
Subset	Model	PPL	Zlib	Lower	MinK	MinK++	DCPDD	PAC	ReCaLL	EMMIA	CAMIA	Neigh.	Guided	DCQ	CDD	Method- Avg
Math Stack Exchange	1B	0.55	0.60	0.49	0.54	0.49	0.55	0.62	0.57	0.58	0.60	0.57	0.60	0.59	0.52	0.56
	7B	0.57	0.63	0.53	0.58	0.55	0.59	0.67	0.51	0.62	0.61	0.57	0.41	0.36	0.54	0.55
	13B	0.60	0.67	0.55	0.62	0.62	0.68	0.71	0.63	0.69	0.64	0.60	0.45	0.63	0.51	0.61
	32B	0.62	0.71	0.51	0.65	0.61	0.70	0.71	0.79	0.74	0.66	0.61	0.57	0.59	0.50	0.64
	Model-Avg	0.59	0.65	0.52	0.60	0.57	0.63	0.68	0.63	0.66	0.63	0.59	0.51	0.54	0.52	0.59

Appendix

Table 47: Comparison of unsupervised MIAs on the subsets of the Stack Exchange domain of OLMo-Detect , evaluated via AUC. Methods are grouped by family as in Table 4 . Model-Avg averages across model sizes, while Method-Avg averages the methods with a value in that row. The best-performing method in each row is highlighted in bold.

Subset	Model	Likelihood-based										Pert.	Prompt		Out.-Dist.	Method- Avg
Subset	Model	PPL	Zlib	Lower	MinK	MinK++	DCPDD	PAC	ReCaLL	EMMIA	CAMIA	Neigh.	Guided	DCQ	CDD	Method- Avg
Aya	1B	0.56	0.58	0.50	0.54	0.67	0.54	0.50	0.48	0.58	0.54	0.54	0.49	0.48	0.50	0.53
	7B	0.77	0.70	0.53	0.72	0.76	0.72	0.67	0.69	0.59	0.76	0.69	0.52	0.47	0.53	0.65
	13B	0.69	0.60	0.49	0.66	0.64	0.62	0.60	0.56	0.51	0.67	0.59	0.51	0.49	0.55	0.59
	32B	0.55	0.56	0.49	0.54	0.59	0.55	0.49	0.60	0.44	0.50	0.51	0.38	0.51	0.51	0.52
	Model-Avg	0.64	0.61	0.51	0.61	0.66	0.61	0.57	0.58	0.53	0.62	0.58	0.47	0.49	0.52	0.57

Appendix

Table 48: Comparison of unsupervised MIAs on the subsets of the SFT domain of OLMo-Detect , evaluated via AUC. Methods are grouped by family as in Table 4 . Model-Avg averages across model sizes, while Method-Avg averages the methods with a value in that row. The best-performing method in each row is highlighted in bold.

Subset	Model	Likelihood-based										Pert.	Prompt		Out.-Dist.		Method- Avg
Subset	Model	PPL	Zlib	Lower	MinK	MinK++	DCPDD	PAC	ReCaLL	EMMIA	CAMIA	Neigh.	Guided	DCQ	CDD	SelfCrit †	Method- Avg
CoT-GSM8K	1B	0.85	0.89	0.73	0.88	0.62	0.80	0.78	0.21	0.80	0.75	0.49	0.51	0.42	0.51	0.47	0.65
	7B	0.98	0.99	0.87	0.99	0.78	0.98	0.89	0.10	0.97	0.98	0.62	0.51	0.50	0.53	0.50	0.75
	13B	1.00	1.00	0.90	1.00	0.64	0.99	0.78	0.01	1.00	0.98	0.56	0.48	0.41	0.49	0.39	0.71
	32B	1.00	1.00	0.95	1.00	0.79	1.00	0.87	0.04	0.50	0.99	0.61	0.49	0.51	0.50	0.35	0.71
	Model-Avg	0.96	0.97	0.86	0.97	0.71	0.94	0.83	0.09	0.82	0.93	0.57	0.50	0.46	0.51	0.43	0.70

Appendix

Table 49: Comparison of unsupervised MIAs on the subsets of the RLVR domain of OLMo-Detect , evaluated via AUC. Methods are grouped by family as in Table 4 . Model-Avg averages across model sizes, while Method-Avg averages the methods with a value in that row. The best-performing method in each row is highlighted in bold. † SelfCrit is evaluated only on DPO and RLVR.

Model	Stage	Likelihood-based										Pert.	Prompt		Out.-Dist.		Method- Avg
Model	Stage	PPL	Zlib	Lower	MinK	MinK++	DCPDD	PAC	ReCaLL	EMMIA	CAMIA	Neigh.	Guided	DCQ	CDD	SelfCrit †	Method- Avg
1B	Pre	0.07	0.09	0.08	0.09	0.07	0.12	0.12	0.07	0.10	0.09	0.05	0.03	0.07	0.06	—	0.08
	Mid	0.14	0.17	0.15	0.15	0.09	0.10	0.14	0.07	0.09	0.15	0.10	0.06	0.07	0.06	—	0.11
	Post	0.20	0.18	0.12	0.20	0.15	0.12	0.13	0.10	0.09	0.17	0.05	0.05	0.04	0.07	0.07	0.12
	All	0.13	0.15	0.12	0.15	0.10	0.11	0.13	0.08	0.09	0.14	0.07	0.05	0.06	0.06	0.07	0.10
7B	Pre	0.08	0.13	0.10	0.11	0.09	0.15	0.13	0.08	0.18	0.12	0.06	0.05	0.05	0.06	—	0.10

Appendix

Table 50: Comparison of unsupervised MIAs on OLMo-Detect , evaluated via TPR@5% FPR. Methods are grouped by family: likelihood-based, perturbation-based ( Pert. ), prompt-based and output-distribution-based ( Out.-Dist. ). Pre / Mid / Post report macro-averaged TPRs over the domains of each stage, while All macro-averages the three stages. Model-Avg averages across model sizes, while Method-Avg averages the methods with a value in that row. The best-performing method in each row is highlighted in bold. † SelfCrit is evaluated only on DPO and RLVR and thus has only Post and All values, averaged over these two domains. Per-domain results are provided in Tables 51 – 63 .

Model	Likelihood-based										Pert.	Prompt		Out.-Dist.	Method- Avg
Model	PPL	Zlib	Lower	MinK	MinK++	DCPDD	PAC	ReCaLL	EMMIA	CAMIA	Neigh.	Guided	DCQ	CDD	Method- Avg
1B	0.09	0.06	0.14	0.13	0.01	0.12	0.16	0.03	0.06	0.13	0.09	0.04	0.03	0.06	0.08
7B	0.15	0.11	0.16	0.21	0.06	0.18	0.20	0.03	0.07	0.22	0.08	0.06	0.04	0.04	0.12
13B	0.16	0.13	0.14	0.20	0.05	0.15	0.26	0.06	0.08	0.23	0.10	0.04	0.03	0.06	0.12
32B	0.21	0.18	0.13	0.22	0.11	0.18	0.34	0.06	0.12	0.26	0.11	0.04	0.07	0.07	0.15
Model-Avg	0.15	0.12	0.14	0.19	0.06	0.16	0.24	0.04	0.08	0.21	0.10	0.05	0.04	0.06	0.12

Appendix

Table 51: Comparison of unsupervised MIAs on the DCLM-Baseline domain of OLMo-Detect , evaluated via TPR@5% FPR. Methods are grouped by family as in Table 50 . Model-Avg averages across model sizes, while Method-Avg averages the methods with a value in that row. The best-performing method in each row is highlighted in bold.

Model	Likelihood-based										Pert.	Prompt		Out.-Dist.	Method- Avg
Model	PPL	Zlib	Lower	MinK	MinK++	DCPDD	PAC	ReCaLL	EMMIA	CAMIA	Neigh.	Guided	DCQ	CDD	Method- Avg
1B	0.06	0.07	0.05	0.09	0.07	0.07	0.06	0.05	0.18	0.06	0.04	0.05	0.04	0.05	0.07
7B	0.07	0.07	0.06	0.07	0.07	0.07	0.07	0.05	0.47	0.09	0.05	0.03	0.10	0.05	0.09
13B	0.07	0.07	0.08	0.07	0.05	0.09	0.10	0.05	0.44	0.05	0.07	0.05	0.07	0.05	0.09
32B	0.08	0.09	0.08	0.10	0.08	0.10	0.09	0.07	0.48	0.05	0.06	0.05	0.11	0.04	0.10
Model-Avg	0.07	0.07	0.07	0.08	0.07	0.08	0.08	0.05	0.39	0.06	0.05	0.05	0.08	0.05	0.09

Appendix

Table 52: Comparison of unsupervised MIAs on the peS2o domain of OLMo-Detect , evaluated via TPR@5% FPR. Methods are grouped by family as in Table 50 . Model-Avg averages across model sizes, while Method-Avg averages the methods with a value in that row. The best-performing method in each row is highlighted in bold.

Model	Likelihood-based										Pert.	Prompt		Out.-Dist.	Method- Avg
Model	PPL	Zlib	Lower	MinK	MinK++	DCPDD	PAC	ReCaLL	EMMIA	CAMIA	Neigh.	Guided	DCQ	CDD	Method- Avg
1B	0.08	0.17	0.07	0.08	0.13	0.16	0.17	0.17	0.09	0.11	0.05	0.01	0.16	0.07	0.11
7B	0.08	0.27	0.10	0.08	0.08	0.23	0.22	0.22	0.10	0.11	0.04	0.05	0.06	0.12	0.13
13B	0.09	0.24	0.08	0.09	0.07	0.20	0.27	0.09	0.11	0.10	0.07	0.03	0.01	0.07	0.11
32B	0.08	0.19	0.04	0.08	0.03	0.24	0.26	0.08	0.10	0.12	0.06	0.04	0.06	0.10	0.11
Model-Avg	0.08	0.22	0.07	0.08	0.08	0.21	0.23	0.14	0.10	0.11	0.06	0.03	0.07	0.09	0.11

Appendix

Table 53: Comparison of unsupervised MIAs on the StarCoder domain of OLMo-Detect , evaluated via TPR@5% FPR (macro-averaged over its subsets). Methods are grouped by family as in Table 50 . Model-Avg averages across model sizes, while Method-Avg averages the methods with a value in that row. The best-performing method in each row is highlighted in bold.

Model	Likelihood-based										Pert.	Prompt		Out.-Dist.	Method- Avg
Model	PPL	Zlib	Lower	MinK	MinK++	DCPDD	PAC	ReCaLL	EMMIA	CAMIA	Neigh.	Guided	DCQ	CDD	Method- Avg
1B	0.04	0.07	0.08	0.06	0.08	0.12	0.07	0.01	0.09	0.07	0.04	0.03	0.05	0.07	0.06
7B	0.04	0.07	0.07	0.06	0.14	0.12	0.02	0.01	0.09	0.06	0.07	0.04	0.00	0.04	0.06
13B	0.06	0.10	0.04	0.06	0.11	0.10	0.04	0.04	0.15	0.04	0.07	0.03	0.08	0.03	0.07
32B	0.10	0.17	0.04	0.07	0.15	0.13	0.11	0.03	0.10	0.04	0.07	0.02	0.04	0.02	0.08
Model-Avg	0.06	0.10	0.06	0.06	0.12	0.12	0.06	0.03	0.11	0.05	0.06	0.03	0.04	0.04	0.07

Appendix

Table 54: Comparison of unsupervised MIAs on the OpenWebMath domain of OLMo-Detect , evaluated via TPR@5% FPR. Methods are grouped by family as in Table 50 . Model-Avg averages across model sizes, while Method-Avg averages the methods with a value in that row. The best-performing method in each row is highlighted in bold.

Model	Likelihood-based										Pert.	Prompt		Out.-Dist.	Method- Avg
Model	PPL	Zlib	Lower	MinK	MinK++	DCPDD	PAC	ReCaLL	EMMIA	CAMIA	Neigh.	Guided	DCQ	CDD	Method- Avg
1B	0.21	0.25	0.17	0.25	0.14	0.12	0.16	0.03	0.04	0.22	0.11	0.04	0.04	0.07	0.13
7B	0.43	0.54	0.21	0.48	0.13	0.60	0.37	0.00	0.05	0.49	0.22	0.05	0.06	0.07	0.26
13B	0.92	0.97	0.54	0.93	0.21	0.94	0.78	0.00	0.03	0.95	0.53	0.05	0.04	0.17	0.50
32B	0.89	0.96	0.61	0.84	0.14	0.92	0.67	0.00	0.06	0.96	0.63	0.12	0.06	0.24	0.51
Model-Avg	0.61	0.68	0.38	0.63	0.16	0.65	0.49	0.01	0.05	0.66	0.37	0.06	0.05	0.14	0.35

Appendix

Table 55: Comparison of unsupervised MIAs on the GSM8K subset of OLMo-Detect ’s Math Mix domain, evaluated via TPR@5% FPR. Methods are grouped by family as in Table 50 . Model-Avg averages across model sizes, while Method-Avg averages the methods with a value in that row. The best-performing method in each row is highlighted in bold.

Model	Likelihood-based										Pert.	Prompt		Out.-Dist.	Method- Avg
Model	PPL	Zlib	Lower	MinK	MinK++	DCPDD	PAC	ReCaLL	EMMIA	CAMIA	Neigh.	Guided	DCQ	CDD	Method- Avg
1B	0.06	0.08	0.12	0.05	0.03	0.08	0.12	0.10	0.13	0.07	0.10	0.07	0.10	0.06	0.08
7B	0.06	0.12	0.09	0.08	0.06	0.18	0.12	0.03	0.09	0.06	0.10	0.05	0.05	0.06	0.08
13B	0.07	0.17	0.13	0.08	0.07	0.16	0.19	0.10	0.10	0.05	0.10	0.07	0.06	0.05	0.10
32B	0.09	0.20	0.17	0.13	0.12	0.21	0.25	0.16	0.17	0.07	0.10	0.10	0.14	0.05	0.14
Model-Avg	0.07	0.14	0.13	0.08	0.07	0.16	0.17	0.10	0.12	0.06	0.10	0.07	0.09	0.05	0.10

Appendix

Table 56: Comparison of unsupervised MIAs on the Stack Exchange domain of OLMo-Detect , evaluated via TPR@5% FPR (macro-averaged over its subsets). Methods are grouped by family as in Table 50 . Model-Avg averages across model sizes, while Method-Avg averages the methods with a value in that row. The best-performing method in each row is highlighted in bold.

Model	Likelihood-based										Pert.	Prompt		Out.-Dist.	Method- Avg
Model	PPL	Zlib	Lower	MinK	MinK++	DCPDD	PAC	ReCaLL	EMMIA	CAMIA	Neigh.	Guided	DCQ	CDD	Method- Avg
1B	0.22	0.14	0.09	0.21	0.33	0.12	0.08	0.12	0.04	0.15	0.07	0.05	0.05	0.05	0.12
7B	0.40	0.29	0.13	0.36	0.50	0.28	0.17	0.17	0.07	0.22	0.06	0.06	0.02	0.06	0.20
13B	0.19	0.14	0.07	0.18	0.26	0.10	0.06	0.11	0.06	0.14	0.09	0.10	0.07	0.08	0.12
32B	0.28	0.15	0.07	0.32	0.33	0.19	0.05	0.17	0.07	0.21	0.07	0.08	0.00	0.08	0.15
Model-Avg	0.27	0.18	0.09	0.27	0.36	0.17	0.09	0.14	0.06	0.18	0.07	0.07	0.04	0.07	0.15

Appendix

Table 57: Comparison of unsupervised MIAs on the SFT domain of OLMo-Detect , evaluated via TPR@5% FPR (macro-averaged over its subsets). Methods are grouped by family as in Table 50 . Model-Avg averages across model sizes, while Method-Avg averages the methods with a value in that row. The best-performing method in each row is highlighted in bold.

Model	Likelihood-based										Pert.	Prompt		Out.-Dist.		Method- Avg
Model	PPL	Zlib	Lower	MinK	MinK++	DCPDD	PAC	ReCaLL	EMMIA	CAMIA	Neigh.	Guided	DCQ	CDD	SelfCrit †	Method- Avg
1B	0.07	0.06	0.14	0.08	0.04	0.07	0.12	0.16	0.08	0.22	0.04	0.04	0.03	0.10	0.12	0.09
7B	0.02	0.03	0.07	0.01	0.02	0.01	0.01	0.07	0.09	0.07	0.04	0.05	0.00	0.10	0.04	0.04
13B	0.03	0.06	0.28	0.04	0.04	0.03	0.06	0.33	0.10	0.08	0.03	0.03	0.06	0.11	0.06	0.09
32B	0.04	0.09	0.09	0.06	0.07	0.04	0.13	0.19	0.01	0.06	0.03	0.03	0.07	0.07	0.11	0.07
Model-Avg	0.04	0.06	0.15	0.05	0.04	0.04	0.08	0.19	0.07	0.11	0.03	0.04	0.04	0.09	0.08	0.07

Appendix

Table 58: Comparison of unsupervised MIAs on the UF-Wildchat subset of OLMo-Detect ’s DPO domain, evaluated via TPR@5% FPR. Methods are grouped by family as in Table 50 . Model-Avg averages across model sizes, while Method-Avg averages the methods with a value in that row. The best-performing method in each row is highlighted in bold. † SelfCrit is evaluated only on DPO and RLVR.

Model	Likelihood-based										Pert.	Prompt		Out.-Dist.		Method- Avg
Model	PPL	Zlib	Lower	MinK	MinK++	DCPDD	PAC	ReCaLL	EMMIA	CAMIA	Neigh.	Guided	DCQ	CDD	SelfCrit †	Method- Avg
1B	0.29	0.35	0.12	0.33	0.08	0.16	0.19	0.02	0.15	0.14	0.03	0.06	0.04	0.04	0.02	0.14
7B	0.66	0.65	0.33	0.66	0.16	0.60	0.25	0.02	0.51	0.53	0.11	0.04	0.05	0.03	0.05	0.31
13B	0.82	0.81	0.41	0.78	0.06	0.71	0.30	0.00	0.52	0.62	0.11	0.02	0.05	0.05	0.05	0.36
32B	0.71	0.68	0.43	0.74	0.15	0.71	0.34	0.03	0.04	0.67	0.17	0.03	0.06	0.05	0.02	0.32
Model-Avg	0.62	0.62	0.32	0.63	0.11	0.54	0.27	0.02	0.30	0.49	0.10	0.04	0.05	0.05	0.04	0.28

Appendix

Table 59: Comparison of unsupervised MIAs on the RLVR domain of OLMo-Detect , evaluated via TPR@5% FPR (macro-averaged over its subsets). Methods are grouped by family as in Table 50 . Model-Avg averages across model sizes, while Method-Avg averages the methods with a value in that row. The best-performing method in each row is highlighted in bold. † SelfCrit is evaluated only on DPO and RLVR.

Subset	Model	Likelihood-based										Pert.	Prompt		Out.-Dist.	Method- Avg
Subset	Model	PPL	Zlib	Lower	MinK	MinK++	DCPDD	PAC	ReCaLL	EMMIA	CAMIA	Neigh.	Guided	DCQ	CDD	Method- Avg
Python	1B	0.10	0.23	0.10	0.10	0.12	0.20	0.16	0.09	0.06	0.17	0.06	0.00	0.14	0.08	0.11
	7B	0.10	0.22	0.12	0.10	0.12	0.19	0.23	0.09	0.08	0.13	0.06	0.07	0.05	0.02	0.11
	13B	0.11	0.22	0.10	0.12	0.07	0.18	0.26	0.06	0.08	0.16	0.04	0.06	0.01	0.07	0.11
	32B	0.10	0.14	0.03	0.10	0.07	0.17	0.22	0.09	0.10	0.16	0.04	0.04	0.06	0.13	0.10
	Model-Avg	0.10	0.21	0.09	0.10	0.09	0.18	0.22	0.08	0.08	0.15	0.05	0.04	0.06	0.07	0.11

Appendix

Table 60: Comparison of unsupervised MIAs on the subsets of the StarCoder domain of OLMo-Detect , evaluated via TPR@5% FPR. Methods are grouped by family as in Table 50 . Model-Avg averages across model sizes, while Method-Avg averages the methods with a value in that row. The best-performing method in each row is highlighted in bold.

Subset	Model	Likelihood-based										Pert.	Prompt		Out.-Dist.	Method- Avg
Subset	Model	PPL	Zlib	Lower	MinK	MinK++	DCPDD	PAC	ReCaLL	EMMIA	CAMIA	Neigh.	Guided	DCQ	CDD	Method- Avg
Math Stack Exchange	1B	0.07	0.07	0.16	0.04	0.04	0.11	0.20	0.14	0.20	0.11	0.11	0.09	0.16	0.08	0.11
	7B	0.05	0.07	0.07	0.07	0.02	0.25	0.16	0.04	0.14	0.08	0.11	0.02	0.02	0.05	0.08
	13B	0.07	0.16	0.15	0.07	0.04	0.20	0.27	0.11	0.11	0.02	0.12	0.09	0.07	0.04	0.11
	32B	0.11	0.25	0.21	0.14	0.11	0.25	0.39	0.23	0.20	0.05	0.11	0.11	0.12	0.05	0.17
	Model-Avg	0.08	0.14	0.15	0.08	0.05	0.20	0.25	0.13	0.16	0.06	0.11	0.08	0.09	0.06	0.12

Appendix

Table 61: Comparison of unsupervised MIAs on the subsets of the Stack Exchange domain of OLMo-Detect , evaluated via TPR@5% FPR. Methods are grouped by family as in Table 50 . Model-Avg averages across model sizes, while Method-Avg averages the methods with a value in that row. The best-performing method in each row is highlighted in bold.

Subset	Model	Likelihood-based										Pert.	Prompt		Out.-Dist.	Method- Avg
Subset	Model	PPL	Zlib	Lower	MinK	MinK++	DCPDD	PAC	ReCaLL	EMMIA	CAMIA	Neigh.	Guided	DCQ	CDD	Method- Avg
Aya	1B	0.12	0.02	0.16	0.16	0.24	0.09	0.04	0.09	0.06	0.14	0.08	0.06	0.04	0.05	0.10
	7B	0.48	0.27	0.12	0.40	0.35	0.26	0.20	0.18	0.09	0.41	0.07	0.10	0.05	0.11	0.22
	13B	0.28	0.15	0.06	0.28	0.23	0.15	0.10	0.09	0.04	0.26	0.09	0.13	0.11	0.13	0.15
	32B	0.17	0.04	0.11	0.14	0.10	0.06	0.04	0.22	0.07	0.08	0.10	0.04	0.01	0.14	0.09
	Model-Avg	0.26	0.12	0.11	0.25	0.23	0.14	0.09	0.15	0.06	0.22	0.08	0.08	0.05	0.11	0.14

Appendix

Table 62: Comparison of unsupervised MIAs on the subsets of the SFT domain of OLMo-Detect , evaluated via TPR@5% FPR. Methods are grouped by family as in Table 50 . Model-Avg averages across model sizes, while Method-Avg averages the methods with a value in that row. The best-performing method in each row is highlighted in bold.

Subset	Model	Likelihood-based										Pert.	Prompt		Out.-Dist.		Method- Avg
Subset	Model	PPL	Zlib	Lower	MinK	MinK++	DCPDD	PAC	ReCaLL	EMMIA	CAMIA	Neigh.	Guided	DCQ	CDD	SelfCrit †	Method- Avg
CoT-GSM8K	1B	0.45	0.55	0.22	0.43	0.10	0.19	0.30	0.00	0.25	0.14	0.01	0.06	0.04	0.03	0.02	0.19
	7B	0.94	0.96	0.46	0.97	0.24	0.91	0.38	0.00	0.97	0.95	0.11	0.02	0.07	0.04	0.03	0.47
	13B	1.00	1.00	0.59	1.00	0.09	0.96	0.41	0.00	1.00	0.97	0.06	0.03	0.02	0.05	0.02	0.48
	32B	1.00	1.00	0.63	1.00	0.21	0.98	0.52	0.00	0.05	0.95	0.16	0.03	0.09	0.06	0.01	0.45
	Model-Avg	0.85	0.88	0.48	0.85	0.16	0.76	0.41	0.00	0.57	0.75	0.09	0.03	0.05	0.04	0.02	0.40

Appendix

Table 63: Comparison of unsupervised MIAs on the subsets of the RLVR domain of OLMo-Detect , evaluated via TPR@5% FPR. Methods are grouped by family as in Table 50 . Model-Avg averages across model sizes, while Method-Avg averages the methods with a value in that row. The best-performing method in each row is highlighted in bold. † SelfCrit is evaluated only on DPO and RLVR.

Method	Setting	1B	7B	13B	32B	Model-Avg
Zlib (unsup.)	—	0.59	0.64	0.65	0.67	0.64
Sup-CAMIA	In-domain	0.51	0.55	0.54	0.56	0.54
	LODO	0.55	0.64	0.58	0.57	0.58
MIA-Tuner	In-domain	0.45	0.45	0.53	0.55	0.50
	LODO	0.47	0.51	0.49	0.47	0.49

Appendix

Table 64: Supervised MIAs on the DCLM-Baseline domain of OLMo-Detect , evaluated via AUC. Top: AUCs of Sup-CAMIA and MIA-Tuner under the In-domain setting (trained on this domain’s dev set) and the LODO setting (trained on the other eight domains’ dev sets); Zlib, the strongest unsupervised MIA, is repeated as a reference and is excluded from the bold, which marks the best supervised entry per column. Bottom: FSD measures the change in a base MIA’s score after fine-tuning the target model on non-members, so we report its AUC gain (

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