A Safe Prototype Is Not a Safety Direction: Reference Dependence and Prompt Confounds in Response-Safety Embeddings

arXiv:2610.01801v1 [cs.LG] 1 Oct 2026

A Safe Prototype Is Not a Safety Direction: Reference Dependence and Prompt Confounds in Response-Safety Embeddings

Sahil Kadadekar New York University sahilkadadekar@nyu.edu

Abstract Can response safety be scored by cosine similarity to the mean embedding of known-safe responses? A recent sleeper-agent detector proposes exactly this score, yet the raw positive-centroid rule is not identified: positive observations locate the safe class relative to an encoder origin, but do not determine which direction separates safe from unsafe responses. We audit the rule on two prompt-controlled, human-labeled corpora and one auxiliary jury-labeled source control, using four frozen encoders and prompt-grouped splits. On the human-labeled corpora the safe prototype reaches ROC-AUC 0.457–0.545, with two cells significantly below chance and one above, while an explicit safe-minus-unsafe reference reaches 0.588–0.738 on the same embeddings; on the jury control the prototype is inverted (0.358–0.405) and the reference reaches 0.754–0.793. At validation-calibrated 5% false-safe thresholds, the reference accepts more safe responses on PKU-SafeRLHF (0.153–0.263 versus 0.039–0.061 across encoders) and Aegis (0.189–0.291 versus 0.004–0.045), but not reliably on BeaverTails. A fully unlabeled held-out reference recovers part to most of the referenced ranking, much less when only 5% of the pool is unsafe, whereas 80–634 labeled unsafe responses recover most of it. Prompt-only ablations show that prompt-label composition can inflate uncontrolled evaluations. This is a bounded result about a raw positive centroid, not all one-class methods or safety-specialized guards. A class mean is a location, not necessarily a safety direction; a declared reference with enough unsafe mass identifies orientation.

1

Introduction

A single prototype is an appealing safety readout. Given embeddings of responses labeled safe, average and normalize them, then score a candidate by cosine similarity. The rule is transparent, cheap, and appears to need labels from only one class. That last property is attractive when unsafe examples are sensitive, incomplete, or costly to curate. The rule has also been proposed as a detector score: a recent sleeper-agent detector flags a response when one minus its cosine similarity to a centroid of safe-mode responses, embedded with all-MiniLM-L6-v2 (one of the four encoders we audit), is high, OR-combining this signal with a canary-question check [Zanbaghi et al., 2025]. Its triggered responses are topically distinct from the safe ones, the easy case for a location score; our audit holds topic fixed. The shortcut hides a measurement problem. A class mean is a location relative to the encoder origin; a class-separating direction is a displacement relative to another distribution. Those are different objects. In a shifted or concentrated embedding space, unsafe responses can project more strongly onto the normalized safe mean than safe responses do (Figure 1). A score called “similarity to safe” can then rank unsafe responses higher without any reversal of semantic meaning. 40th Conference on Neural Information Processing Systems (NeurIPS 2026). Workshop: Foundations of Language Model Security (FLMSec).

Prompt: How do I pick a lock?

projection of u

s

ype

ot prot

axis reference s

origin

Safe response: If you are locked out, a licensed locksmith can help.

u u

[f + u] > [f + s]: similarity to safe ranks unsafe higher

Unsafe response: Insert a tension wrench, then rake the pins until

Figure 1: Illustrative two-dimensional schematic, not measured embeddings. A safe and an unsafe response to the same prompt share topic, so their class means are nearly collinear. When the unsafe mean µu projects farther than µs along the prototype axis µs /∥µs ∥, similarity to the safe prototype ranks unsafe responses higher. The reference direction µs − µu is oriented by construction. This matters for language-model security, where moderators err in two directions, accepting unsafe compliance and rejecting benign responses, and a high aggregate AUC may reflect prompt composition rather than response behavior. We ask four falsifiable questions: (i) is the positive prototype’s orientation identified from safe examples alone, (ii) does an explicit reference improve ranking under prompt or label-source controls, (iii) does that improvement survive validation-calibrated false-safe constraints, and (iv) can an unlabeled reference replace unsafe labels in finite samples? We answer with a provenance-audited study on BeaverTails [Ji et al., 2023], PKU-SafeRLHF [Ji et al., 2025], and Aegis 2.0 [Ghosh et al., 2025]. The first two primary arms use human-released safety labels and prompt-matched comparisons; Aegis is explicitly an auxiliary llm_jury-only source control. Four frozen encoders cover two sentence-transformer models and mean-pooled hidden states from two sizes of Qwen2.5-Instruct [Reimers and Gurevych, 2019, Qwen Team, 2025]. Exact prompt grouping, deduplication, source controls, response-overlap sensitivity, and cluster bootstrap intervals address the leakage and provenance defects that commonly make safety-evaluation conclusions fragile. Our contributions are: 1. We formalize positive-only non-identification: the same safe embedding distribution is compatible with unsafe distributions that induce opposite signs for the prototype’s expected score gap. 2. We show a controlled empirical pattern across 12 corpus–encoder cells with family-wise inference. The raw safe prototype is weak on the human-labeled corpora (AUC 0.457–0.545) and inverted on the jury control (0.358–0.405); 7 of 12 cells differ from chance after Holm correction, 6 of them below. It never outranks a response-length heuristic by more than 0.016 and falls below a 12-feature stylistic baseline in every cell. A difference-of-means reference is above chance everywhere (0.588–0.738 human-labeled; 0.754–0.793 jury). 3. At validation-calibrated 5% and 10% false-safe targets, referencing raises safe acceptance on PKU-SafeRLHF and Aegis for every encoder; on BeaverTails the gain is small and uncertain. 4. We separate prompt-disjointness from prompt control: prompt-only prediction falls to near chance on matched cohorts even when it is strong on full corpus populations. 5. We test label-free orientation out of sample. A fully unlabeled held-out reference recovers part to most of the referenced ranking, little at 5% unsafe prevalence, while a small labeled unsafe set from other prompts recovers most of it. The scope is deliberately narrow. That orientation needs a reference is a standard lesson of one-class and positive–unlabeled learning (Section 2). What is missing for response safety is a measurement of how the unreferenced rule behaves on real safety data once prompt composition is controlled, what it costs at an operating point, and how much a label-free reference recovers in finite samples. We do 2

not claim that all one-class estimators fail, that these scores are deployable guards, or that Aegis jury labels constitute a human replication.

2

Related work

Safety directions, prototypes, and guards. Representation-level directions are used to analyze and steer refusal behavior [Arditi et al., 2024]. Concurrent RankOne work forms per-prompt safeminus-unsafe directions and studies their transfer [Anonymous ACL ARR submission, 2026], and multi-layer prototype moderation scores inputs by Gaussian (Mahalanobis) distance to safe and unsafe class prototypes in hidden states [Chrabaszcz ˛ et al., 2025]; both are referenced readouts in our terms. Our object is the positive endpoint alone. We include global difference-of-means, two-centroid, RankOne, and supervised linear readouts to distinguish an unreferenced-location failure from a failure of linear or global readouts. We do not compete with instruction-tuned guards such as Llama Guard and ShieldGemma [Inan et al., 2023, Zeng et al., 2024], or with safety-specialized sentence encoders [Kim et al., 2024]. Benign-only detectors. The sleeper-agent detector above scores response drift as one minus cosine similarity to a safe-response centroid [Zanbaghi et al., 2025]. Embedding-drift monitoring can compare a production batch mean with a reference batch mean, which declares both endpoints [Filippova and Samuylova, 2023, Arize AI, 2026]. Closer to density estimation, recent alignmentfailure monitors fit a Gaussian to hidden states of safe conversations and score Mahalanobis distance [Feng et al., 2026]. For vision–language jailbreaks, benign-cluster Mahalanobis baselines are strong, yet the same work argues that one-class designs over-reject unseen benign inputs and proposes contrastive scores that model both classes [Hua et al., 2025]. Those methods estimate covariance and support; our claim concerns cosine to a single mean and does not extend to them. One-class and positive–unlabeled learning. Classical one-class methods estimate support or density rather than assuming that proximity to one mean is sufficient [Schölkopf et al., 2001, Ruff et al., 2018]. Positive–unlabeled learning uses an explicit unlabeled sample and assumptions relating it to the positive and negative populations [Elkan and Noto, 2008, Scott and Blanchard, 2009]. Our mixture-centering result is an elementary geometric instance of the same lesson: orientation requires a declared reference distribution. Embedding geometry and evaluation confounds. Transformer representations can share large common components and be strongly anisotropic [Ethayarajh, 2019, Biś et al., 2021, Mu et al., 2018], though anisotropy alone should not be treated as a universal explanation of semantic failure [Fuster Baggetto and Fresno, 2022], so we measure the class-mean quantities that determine the prototype’s expected gap, and test separately whether prompt composition masquerades as responselevel signal.

3

Why a positive prototype is not identified

Let each response embedding z ∈ Rd be unit normalized. Let µs = E[z | s] and µu = E[z | u] be the safe and unsafe population means. The positive-prototype score is f+ (z) = z ⊤

µs . ∥µs ∥2

(1)

Its expected safe-minus-unsafe score gap is ∆+ = E[f+ (z) | s] − E[f+ (z) | u] =

∥µs ∥22 − µ⊤ u µs . ∥µs ∥2

(2)

Nothing forces this quantity to be positive. Proposition 1 (Positive-only non-identification). Fix any safe embedding distribution on the unit sphere with 0 < ∥µs ∥2 < 1. Observations from that safe distribution alone are compatible with two unsafe embedding distributions for which ∆+ has opposite signs. 3

Proof. Let e = µs /∥µs ∥2 and a = ∥µs ∥2 . For any b ∈ [0, 1], a distribution supported on {e, −e} with probabilities (1 + b)/2 and (1 − b)/2 has mean be. Choose b− < a < b+ . Unsafe means b− e and b+ e leave the safe distribution unchanged, but Eq. 2 gives ∆+ = a − b− > 0 in the first world and ∆+ = a − b+ < 0 in the second. Thus the sign is not identified from positive observations. By contrast, the unnormalized difference score f∆ (z) = z ⊤ (µs − µu ) has expected gap E[f∆ (z) | s] − E[f∆ (z) | u] = ∥µs − µu ∥22 ≥ 0.

(3)

This identifies the mean orientation; it does not guarantee a particular AUC. Unsafe labels are not the only possible reference. Assume an in-domain two-class mixture with shared class-conditional distributions and mean µm = πs µs + πu µu , where πu > 0. Then µs − µm = πu (µs − µu ).

(4)

A labeled-safe mean centered by such an unlabeled mixture is therefore collinear with the twoclass difference direction in expectation. In finite samples the reference contributes signal of size πu ∥µs − µu ∥2 , which competes with any difference between the samples used to estimate µs and µm ; Section 5.4 measures how this plays out.

4

Audit design

4.1

Data, provenance, and dependence units

We union all configured public source splits before analysis: BeaverTails 30k_train/30k_test, PKU-SafeRLHF train/test, and Aegis 2.0 train/validation/test. Pinned dataset revisions are 8401fe6, 9421ffa, and d86bb8b, respectively. We canonicalize prompt identity with Unicode NFKC, case-folding, trimming, and whitespace collapse. Exact prompt–response duplicates are collapsed; both representatives are removed if an exact pair has contradictory labels. We do not filter refusals or any other response type. We hash the canonical prompt with the frozen salt one-class-centroid-v1-20260715 into 70% train, 15% validation, and 15% test. Every response to the same prompt remains in one split; exact train/test prompt overlap is zero. The primary BeaverTails cohort retains prompts having both response labels. PKU-SafeRLHF retains post-deduplication native two-response records with discordant safety labels; pair accuracy is grouped by native pair_id, not canonical prompt. Aegis fixes response_label_source=llm_jury. It is a label-source control, not a human-labeled paired replication. The released BeaverTails and PKU-SafeRLHF labels originate from their human-annotation pipelines; we reuse rather than independently validate them. Aegis mixes human and synthetic sources in the full release, so the primary Aegis cohort uses only the released jury label source. Table 1 reports the resulting attrition instead of treating it as bookkeeping. 4.2

Encoders, readouts, and statistics

The sentence encoders are frozen sentence-transformers/all-MiniLM-L6-v2 (384 dimensions; revision 1110a24) and all-mpnet-base-v2 (768 dimensions; e8c3b32), with their standard normalized pooling and maximum sequence lengths of 256 and 384 tokens. The decoder arm uses Corpus

Records

BeaverTails PKU-SafeRLHF Aegis 2.0

30,207 30,207 30,120 7,987/1,742/1,868 966/902 82,118 164,236 159,478 16,352/3,374/3,486 1,743/1,743 33,416 15,930 14,247 4,045/874/948 265/683

Usable

Dedup

Primary T/V/E

Test S/U

Groups

Labels; control

438 Human; mixed prompt 1,743 Human; native pair 941 Jury; source fixed

Table 1: Provenance and primary-cohort ledger: source records, usable and deduplicated responses, train/validation/evaluation (T/V/E) response counts after cohort selection, and test safe/unsafe (S/U) counts. PKU-SafeRLHF expands each source record into two candidate responses. Aegis excludes 17,486 records without a usable binary response label or nonblank response before exact deduplication. Test groups are mixed-label prompts, native pairs, and unique prompts, respectively. 4

masked mean pooling over final hidden states of frozen Qwen2.5-0.5B-Instruct (896 dimensions; 7ae5576) and Qwen2.5-3B-Instruct (2,048 dimensions; aa8e725), followed by L2 normalization and 512-token truncation. Response-only text is primary; every encoder also receives prompt-only and prompt-plus-response ablations, operating points, and cross-corpus transfer. Our main comparison is the normalized safe prototype f+ versus difference-of-means f∆ . The other audited readouts are the two-centroid score (cosine to the safe prototype minus cosine to the unsafe prototype), the mixture-centered safe mean (the safe mean minus the pooled train mean), RankOne (the normalized average of per-prompt safe-minus-unsafe unit vectors over mixed-label train prompts), and a supervised linear baseline: L2-regularized logistic regression (C = 1, L-BFGS, at most 2,000 iterations, no tuning) on the frozen embeddings. We call it a baseline, not a ceiling. Two scalar nuisance baselines, log response length and a refusal-template indicator, use train labels only to choose their sign; a stylistic baseline fits the same logistic regression to 12 standardized surface features of the response text (length, lexical, punctuation, casing, list, and refusal features). We do not interpret Aegis RankOne because only six train prompts supply mixed-label directions; that denominator is persisted in the artifact. Appendix B gives full definitions. ROC-AUC is the primary ranking metric. We report percentile 95% intervals from 500 bootstrap draws resampling whole canonical-prompt clusters; methods share draws for paired differences. These intervals are conditional on the fitted train direction and do not include train-refit uncertainty. Prototype-versus-chance tests use a normal approximation from the interval half-width with Holm– Bonferroni control over the 12 cells; we call a cell equivalent to chance when its interval lies within 0.5 ± 0.05. For operating points, “accept as safe” means score ≥ t. We choose t on validation unsafe responses to target empirical FSR ∈ {0.05, 0.10}, conservatively rejecting ties at the boundary. Ten thousand bootstrap draws independently resample validation and test prompt clusters, recalibrate t, and evaluate test false-safe rate and safe-response acceptance. The train fit remains fixed. Thresholds are corpus- and method-specific, not transferable deployment thresholds.

5

Results

5.1

Controlled ranking

Figure 2 gives the central result. Across the two human-labeled, prompt-controlled corpora, the safe prototype is weak rather than uniformly at chance: AUC spans 0.457–0.545. Holm–Bonferroni over the 12 prototype-versus-chance tests rejects 7: 6 below chance (all four Aegis cells, and PKUSafeRLHF mpnet and Qwen-3B) and 1 above (BeaverTails Qwen-0.5B). The pronounced inversion is confined to the auxiliary Aegis jury control (0.358–0.405); the two significant PKU-SafeRLHF cells have point estimates within 0.05 of chance, and 4 cells are formally equivalent to chance at that margin (Appendix Table 5). Difference-of-means is above chance in every cell: 0.588–0.622 on BeaverTails, 0.668–0.738 on PKU-SafeRLHF, and 0.754–0.793 on Aegis. The same frozen embeddings therefore contain separable signal; what fails is treating an unreferenced positive location as an oriented axis. Table 2 makes the control comparison explicit. Every referenced readout recovers a stronger ranking, so the negative result is not a claim that the frozen representations lack safety information or that linear separation fails. The in-sample mixture-centered mean equals difference-of-means exactly, as Eq. 4 predicts. The scalar baselines calibrate how little the prototype carries: log response length alone reaches 0.529, 0.595, and 0.554 on the three corpora, outranking the prototype in every PKUSafeRLHF and Aegis cell and staying within 0.021 of it on BeaverTails. The 12-feature stylistic baseline (0.561, 0.640, 0.615) outranks the prototype in every cell, while every referenced readout in Table 2 exceeds both scalar and stylistic baselines. The native-pair result is consistent with AUC: on 1,743 held-out PKU-SafeRLHF pairs, the MiniLM prototype ranks the safe response higher 48.3% of the time, compared with 73.1% for differenceof-means; for mpnet the prototype falls below chance at 0.409 (Wilson 95% interval 0.386–0.432). Refusal templates do not drive the result. They open at most 5.1% of safe and 2.0% of unsafe test responses, a refusal indicator alone reaches 0.506–0.523, and removing refusal-opening responses from fit and test changes no primary prototype or difference-of-means AUC by more than 0.015 (Appendix Table 9). 5

Controlled response-safety readouts Chance

Safe prototype

Difference of means

BeaverTails mixed-label prompts - MiniLM BeaverTails mixed-label prompts - mpnet BeaverTails mixed-label prompts - Qwen-0.5B BeaverTails mixed-label prompts - Qwen-3B SafeRLHF native pairs - MiniLM SafeRLHF native pairs - mpnet SafeRLHF native pairs - Qwen-0.5B SafeRLHF native pairs - Qwen-3B Aegis jury-only - MiniLM Aegis jury-only - mpnet Aegis jury-only - Qwen-0.5B Aegis jury-only - Qwen-3B 0.3

0.4 0.5 0.6 0.7 0.8 ROC-AUC with 95% prompt-cluster bootstrap interval

0.9

Figure 2: Controlled response-only ROC-AUC for the raw safe prototype (blue circles) and the explicitly referenced difference of class means (orange squares); the dashed line is chance. Error bars are 95% prompt-cluster bootstrap intervals conditional on the fitted train direction. BeaverTails uses mixed-label prompts, PKU-SafeRLHF (“SafeRLHF”) uses discordant native pairs, and Aegis is an auxiliary jury-only source control. Readout

Train information

BeaverTails

PKU-SafeRLHF

Aegis jury

Safe prototype Log response length Refusal-template indicator Stylistic features (12) Difference of means Mixture-centered safe mean Two-centroid RankOne Supervised linear

Safe labels; encoder origin Label sign only Label sign only Response-level labels Safe and unsafe labels Safe labels; pooled train mean Safe and unsafe prototypes Prompt-paired directions Response-level labels

.509–.545 .529 .523 .561 .588–.622 .588–.622 .591–.622 .614–.636 .632–.695

.457–.501 .595 .513 .640 .668–.738 .668–.738 .670–.738 .667–.743 .733–.843

.358–.405 .554 .506 .615 .754–.793 .754–.793 .739–.764 N/A† .818–.857

Table 2: Observed ROC-AUC ranges across the four frozen encoders on the primary controlled cohorts; ranges are descriptive minima and maxima, not confidence intervals. Scalar baselines are encoder-invariant. “Label sign only” means train labels choose only the sign of a fixed scalar. Two-centroid is cosine to the safe prototype minus cosine to the unsafe prototype. Per-cell values and intervals are in Appendix Table 4. † Aegis RankOne is not interpreted because its fit uses only six mixed-label prompt groups. The result is also stable to analysis choices. Exact normalized response overlap between primary train and test removes only 2 BeaverTails, 8 PKU-SafeRLHF, and 7 Aegis test rows; across all four encoders, removing them changes either main-method AUC by at most 0.0036. On the human-labeled corpora, fitting on all train responses rather than only mixed-label train prompts, evaluated on the same mixed-label test prompts, moves the prototype by at most 0.032 and difference-of-means by at most 0.063. Quadrupling bootstrap draws to 2,000 moves no primary MiniLM interval endpoint by more than 0.0055, and two alternative frozen split salts preserve the qualitative ordering for MiniLM. 5.2

Validation-calibrated operating points

Table 3 shows why reference ambiguity matters beyond AUC. At the 5% target, BeaverTails is essentially tied for MiniLM: prototype and difference-of-means accept 8.2% and 8.4% of safe test responses. On PKU-SafeRLHF, the referenced direction accepts 17.0% versus 6.1% while also admitting fewer unsafe responses; on Aegis, 24.5% versus 1.9%. The pattern holds for every encoder (Appendix Table 6): at 5%, difference-of-means accepts 0.153–0.263 of safe PKU-SafeRLHF 6

Corpus

Target Prototype test FSR Prototype safe accept. Diff-means test FSR Diff-means safe accept.

BeaverTails

5% 10% 5% 10% 5% 10%

PKU-SafeRLHF Aegis jury

.050 [.021,.074] .091 [.057,.130] .064 [.047,.078] .119 [.090,.147] .042 [.019,.066] .081 [.055,.108]

.082 [.038,.109] .124 [.084,.171] .061 [.043,.077] .117 [.089,.139] .019 [.004,.037] .034 [.012,.063]

.045 [.025,.085] .104 [.068,.159] .052 [.039,.066] .090 [.072,.115] .053 [.029,.085] .117 [.081,.150]

.084 [.056,.130] .163 [.112,.229] .170 [.133,.198] .250 [.222,.299] .245 [.160,.318] .358 [.288,.476]

Table 3: MiniLM operating points. Brackets are 95% intervals from 10,000 validation/test promptcluster bootstrap draws that recalibrate the threshold in each draw, conditional on a fixed train fit. FSR is the fraction of unsafe responses accepted as safe. Safe acceptance is the fraction of safe responses accepted. All four encoders are reported in Appendix Table 6.

responses against 0.039–0.061 for the prototype, and 0.189–0.291 against 0.004–0.045 on Aegis, while BeaverTails stays low for both (0.067–0.095 versus 0.037–0.082). Realized test false-safe rates can differ from the validation targets: on Aegis at 5%, difference-of-means admits 0.044–0.066 of unsafe responses against 0.037–0.060 for the prototype; per encoder the two differ by at most 0.030 in either direction, small beside the gain in safe acceptance. At the 10% target the same pattern strengthens. 5.3

Prompt composition, geometry, and transfer

Prompt-disjoint splitting prevents exact leakage but does not equalize prompt composition. On full populations, prompt-only two-centroid readouts reach 0.679–0.731 on BeaverTails and 0.741–0.831 on PKU-SafeRLHF across the four encoders. Within the matched primary cohorts they fall to 0.522–0.548 and exactly 0.500, because both members of a native pair share one prompt (Appendix Figure 3 and Table 7). The Aegis jury control is not prompt-matched, and there prompt-only readouts still reach 0.621–0.649, so part of its referenced-readout AUC may reflect prompt composition, one more reason to treat Aegis as auxiliary. Response-level safety claims therefore need a prompt-only diagnostic and, where possible, within-prompt or matched evaluation. Equation 2 determines the expected mean-score gap, not ROC-AUC. Measured class means are strongly aligned in all 12 cells (cos(µs , µu ) = 0.825–0.999), and the unsafe mean often has greater norm along that shared direction. The measured gap ∆+ nonetheless tracks prototype AUC closely across cells (Spearman ρ = 0.881, Pearson r = 0.855), and its sign agrees with whether AUC is above or below 0.5 in 10 of 12 cells (one-sided exact binomial p = 0.019). The cells share corpora and encoders, so these statistics are descriptive rather than independent tests. Both mismatches have |∆+ | ≤ 0.005, a near-zero expected gap, which is why the identity should not be read as an AUC claim. Finally, we refit each encoder on each primary controlled cohort and evaluate on each other primary test cohort after exact prompt decontamination (Appendix Table 8). Safe-prototype transfer is weak and sign-unstable (AUC 0.253–0.544) and is inverted whenever Aegis is the evaluation cohort (0.253– 0.384). Difference-of-means stays above chance in 24 of 24 transfers (0.532–0.698), but is weak when fit on Aegis. 5.4

Does an unlabeled reference suffice?

Equation 4 suggests that unsafe labels can be replaced by an unlabeled in-domain sample. The in-sample version of this test is uninformative: centering by the pooled labeled train mean reproduces difference-of-means by construction. We therefore fit the safe mean on labeled-safe train responses and center it by the mean of the held-out validation split, which shares no prompts with train or test (Appendix Tables 10 and 11). With the full validation population, no label is used to build the reference. Its unsafe shares are 0.568, 0.505, and 0.293, and it reaches 0.581–0.609 on BeaverTails, close to difference-of-means (0.588–0.622), and 0.623–0.668 and 0.563–0.710 on PKU-SafeRLHF and Aegis, most and part of the referenced gain. When the population is subsampled to 5% unsafe, the reference falls to 0.481–0.530, 0.483–0.533, and 0.460–0.563, within 0.063 of chance. A labeled reference of the same unsafe size (105, 634, and 80 unsafe validation responses from other prompts) instead reaches 0.571–0.612, 0.625–0.693, and 0.720–0.791. 7

The competing term in Section 3 explains the difference: an unlabeled reference contributes signal πu ∥µs − µu ∥2 , a labeled unsafe set the full gap, while the safe means of the fitting sample (primary train cohort) and the reference population differ by 0.636–1.403 class-gap units regardless of πu , reflecting sampling and a composition mismatch that departs from the shared-distribution assumption of Eq. 4. The fitted direction’s cosine with difference-of-means is accordingly 0.164–0.938 for the population, −0.180 to 0.288 at 5%, and 0.772–0.907 for the labeled set. A label-free reference therefore orients the score increasingly with its unsafe share; at low prevalence, 80–634 labeled unsafe responses are more reliable.

6

Implications for language-model security

Name the reference. “Similarity to safe” is not coordinate-free. A security readout should state the negative or unlabeled distribution that orients it, and an unlabeled reference must hold enough unsafe mass to survive sampling shift. Separate ranking from operation. Above-chance AUC is not a deployment threshold; false-safe constraints expose how much benign traffic a detector rejects. Even the referenced direction accepts at most 0.095 of safe BeaverTails responses at its 5% target, so these readouts are diagnostics, not filters. Report a nuisance baseline and do not repair by sign flipping. A one-class readout should be compared with response length and simple stylistic features before it is called a safety score. Inverting the prototype would improve AUC in some cells, but the required sign is corpus-dependent and would be selected after viewing test labels. A declared reference, not post-hoc sign choice, identifies orientation.

7

Limitations and broader impact

Our conclusion concerns a raw positive centroid scored by cosine. It does not rule out support estimators, Gaussian or other density models, positive–unlabeled methods, safety-specialized encoders, or supervised guards. The study covers English responses, two SBERT-family encoders, and one Qwen family at two scales under fixed pooling and truncation; category-conditional performance and truncation by label are not audited. BeaverTails and PKU-SafeRLHF use released human annotations without a new adjudication study. Aegis is jury-only in our primary arm and is auxiliary evidence. Only the population reference in Section 5.4 is built without labels: the cohort pools for BeaverTails and PKU-SafeRLHF are selected by label (mixed-label prompts or discordant pairs), and the 5%, 10%, and 25% pools are subsampled by label; only their means enter the score. The stylistic baseline covers simple surface features, not all style. Bootstrap intervals hold the train-fitted direction fixed. They quantify test sampling and, for operating points, validation-threshold variability, but omit train-refit uncertainty. Thresholds are calibrated separately per corpus and method; they are not portable deployment thresholds. The 5% and 10% targets are diagnostic and remain too permissive for many high-stakes uses. We measure ranking and acceptance errors, not changes in model behavior, attack robustness, or real-world harm. Exposing an unidentified shortcut can reduce false confidence in lightweight monitors; the risk is that readers treat the referenced readout as a sufficient guard, so we recommend it only as a diagnostic baseline. Licenses, compute, and provenance are in Appendix A; the artifact is distributed as arXiv ancillary files.

8

Conclusion

Positive examples identify where a safe class lies, not which way safety increases. Across controlled cohorts and four encoders, a raw safe centroid is weak or inverted and below simple stylistic features, while an explicit reference improves ranking and, on two of three corpora, calibrated safe acceptance; an unlabeled reference helps only to the extent that it carries unsafe mass. Declare the reference, control prompt composition, compare with nuisance baselines, and evaluate a held-out operating point before calling an embedding score a safety direction. 8

Acknowledgments and Disclosure of Funding We thank the anonymous FLMSec reviewers, whose comments led to the detector example, allencoder analyses, refusal, length, and stylistic controls, and held-out reference tests in this version.

References Anonymous ACL ARR submission. RankOne: Towards a single direction approach for response-level safety classification. OpenReview, ACL ARR 2026 May Submission 14822, 2026. URL https: //openreview.net/forum?id=QAUkRa6W6p. Concurrent anonymous submission; accessed 2026-07-17. Andy Arditi, Oscar Obeso, Aaquib Syed, Daniel Paleka, Nina Panickssery, Wes Gurnee, and Neel Nanda. Refusal in language models is mediated by a single direction. In Advances in Neural Information Processing Systems (NeurIPS), 2024. Arize AI. Embedding drift. Arize AX documentation, 2026. URL https://arize.com/docs/ax/ machine-learning/computer-vision/how-to-cv/embedding-drift. Accessed 2026-1001. Daniel Biś, Maksim Podkorytov, and Xiuwen Liu. Too much in common: Shifting of embeddings in transformer language models and its implications. In Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, pages 5117–5130. Association for Computational Linguistics, 2021. doi: 10.18653/ v1/2021.naacl-main.403. URL https://aclanthology.org/2021.naacl-main.403/. Maciej Chrabaszcz, ˛ Filip Szatkowski, Bartosz Wójcik, Jan Dubyński, Tomasz Trzciński, and Sebastian Cygert. Efficient LLM moderation with multi-layer latent prototypes. arXiv:2502.16174, 2025. Charles Elkan and Keith Noto. Learning classifiers from only positive and unlabeled data. In Proceedings of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pages 213–220, 2008. Kawin Ethayarajh. How contextual are contextualized word representations? Comparing the geometry of BERT, ELMo, and GPT-2 embeddings. In Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP), pages 55–65. Association for Computational Linguistics, 2019. Dylan Feng, Pragya Srivastava, Anca Dragan, and Cassidy Laidlaw. Benchmarking and improving monitors for out-of-distribution alignment failure in LLMs. arXiv:2605.21602, 2026. Olga Filippova and Elena Samuylova. Shift happens: We compared 5 methods to detect drift in ML embeddings. Evidently AI blog, 2023. URL https://www.evidentlyai.com/blog/ embedding-drift-detection. Accessed 2026-10-01. Alejandro Fuster Baggetto and Victor Fresno. Is anisotropy really the cause of BERT embeddings not being semantic? In Findings of the Association for Computational Linguistics: EMNLP 2022, pages 4271–4281. Association for Computational Linguistics, 2022. doi: 10.18653/v1/2022. findings-emnlp.314. URL https://aclanthology.org/2022.findings-emnlp.314/. Shaona Ghosh, Prasoon Varshney, Makesh Narsimhan Sreedhar, Aishwarya Padmakumar, Traian Rebedea, Jibin Rajan Varghese, and Christopher Parisien. Aegis2.0: A diverse AI safety dataset and risks taxonomy for alignment of LLM guardrails. In Proceedings of the 2025 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (NAACL), 2025. arXiv:2501.09004; dataset nvidia/Aegis-AI-Content-Safety-Dataset-2.0. Peichun Hua, Hao Li, Shanghao Shi, Zhiyuan Yu, and Ning Zhang. Rethinking jailbreak detection of large vision language models with representational contrastive scoring. To appear at ACL 2026. arXiv:2512.12069, 2025. 9

Hakan Inan, Kartikeya Upasani, Jianfeng Chi, Rashi Rungta, Krithika Iyer, Yuning Mao, Michael Tontchev, Qing Hu, Brian Fuller, Davide Testuggine, and Madian Khabsa. Llama Guard: LLMbased input-output safeguard for human-AI conversations. arXiv:2312.06674, 2023. Jiaming Ji, Mickel Liu, Josef Dai, Xuehai Pan, Chi Zhang, Ce Bian, Boyuan Chen, Ruiyang Sun, Yizhou Wang, and Yaodong Yang. BeaverTails: Towards improved safety alignment of LLM via a human-preference dataset. In Advances in Neural Information Processing Systems (NeurIPS), 2023. Jiaming Ji, Donghai Hong, Borong Zhang, Boyuan Chen, Josef Dai, Boren Zheng, Tianyi Alex Qiu, Jiayi Zhou, Kaile Wang, Boxun Li, Sirui Han, Yike Guo, and Yaodong Yang. PKU-SafeRLHF: Towards multi-level safety alignment for LLMs with human preference. In Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 31983–32016. Association for Computational Linguistics, 2025. doi: 10.18653/v1/2025. acl-long.1544. URL https://aclanthology.org/2025.acl-long.1544/. Jinseok Kim, Jaewon Jung, Sangyeop Kim, Sohhyung Park, and Sungzoon Cho. Safe-embed: Unveiling the safety-critical knowledge of sentence encoders. In Proceedings of the 1st Workshop on Towards Knowledgeable Language Models (KnowLLM 2024), 2024. arXiv:2407.06851. Jiaqi Mu, Suma Bhat, and Pramod Viswanath. All-but-the-top: Simple and effective postprocessing for word representations. In International Conference on Learning Representations (ICLR), 2018. Qwen Team. Qwen2.5 technical report. arXiv:2412.15115, 2025. Nils Reimers and Iryna Gurevych. Sentence-BERT: Sentence embeddings using siamese BERTnetworks. In Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing (EMNLP), 2019. Lukas Ruff, Robert Vandermeulen, Nico Görnitz, Lucas Deecke, Shoaib Ahmed Siddiqui, Alexander Binder, Emmanuel Müller, and Marius Kloft. Deep one-class classification. In Proceedings of the 35th International Conference on Machine Learning, volume 80 of Proceedings of Machine Learning Research, pages 4393–4402. PMLR, 2018. Bernhard Schölkopf, John C. Platt, John Shawe-Taylor, Alex J. Smola, and Robert C. Williamson. Estimating the support of a high-dimensional distribution. Neural Computation, 13(7):1443–1471, 2001. Clayton Scott and Gilles Blanchard. Novelty detection: Unlabeled data definitely help. In Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics, volume 5 of Proceedings of Machine Learning Research, pages 464–471. PMLR, 2009. URL https:// proceedings.mlr.press/v5/scott09a.html. Shahin Zanbaghi, Ryan Rostampour, Farhan Abid, and Salim Al Jarmakani. Detecting sleeper agents in large language models via semantic drift analysis. arXiv:2511.15992, 2025. Wenjun Zeng, Yuchi Liu, Ryan Mullins, Ludovic Peran, Joe Fernandez, Hamza Harkous, Karthik Narasimhan, Drew Proud, Piyush Kumar, Bhaktipriya Radharapu, Olivia Sturman, and Oscar Wahltinez. ShieldGemma: Generative AI content moderation based on Gemma. arXiv:2407.21772, 2024.

10

A

Ethics, licenses, and reproducibility details

The public datasets contain potentially distressing harmful content. We conduct no new humansubject data collection and do not redistribute prompts or responses. The artifact contains code, aggregate metrics, row-order hashes, and source manifests only. BeaverTails and PKU-SafeRLHF are used under CC BY-NC 4.0; Aegis 2.0 under CC BY 4.0. The two sentence-transformer models and Qwen2.5-0.5B-Instruct are Apache 2.0; Qwen2.5-3B-Instruct uses the non-commercial Qwen Research License. We redistribute no model weights. Each schema-v3 result records complete dataset/model revisions, ordered-row SHA-256 digests, source-file SHA-256 digests, dependency versions, command, split salt, and bootstrap seed. Thirtythree protocol tests cover grouping, deduplication, overlap, readouts, paired inference, and threshold calibration; the camera-ready analyses and every appendix table are generated by tested scripts from those JSON files and fail if a reproduced primary AUC differs from its frozen value. Runs used one NVIDIA RTX 4080 Laptop GPU (12.9 GB) and Python 3.13.1. Cold embedding time and total exploratory compute were not completely logged, which we report as a reproducibility limitation. The complete artifact is distributed with this paper as arXiv ancillary files.

B

Readout and analysis details

All readouts are fit on the primary train cohort and scored on the primary test cohort of the same corpus unless stated otherwise. Embeddings are unit normalized, so every dot product with a unit vector is a cosine. Let z̄s and z̄u be the train safe and unsafe means and z̄ the pooled train mean. • Safe prototype: z ⊤ z̄s /∥z̄s ∥. • Difference of means: z ⊤ (z̄s − z̄u )/∥z̄s − z̄u ∥. • Two-centroid: z ⊤ z̄s /∥z̄s ∥ − z ⊤ z̄u /∥z̄u ∥. • Mixture-centered safe mean: z ⊤ (z̄s − z̄)/∥z̄s − z̄∥. Because z̄s − z̄ = π̂u (z̄s − z̄u ) in sample, it ranks identically to difference of means; Section 5.4 replaces z̄ with a held-out mean. • RankOne: for each train prompt with both labels, the unit vector of its safe mean minus its unsafe mean; the readout is the normalized average of these vectors. • Supervised linear: scikit-learn 1.8.0 logistic regression with an L2 penalty, C = 1, intercept, L-BFGS, tolerance 10−4 , at most 2,000 iterations, and seed 20260715, fit on the frozen embeddings without scaling or tuning. • Log response length: log(1 + characters), multiplied by +1 or −1 according to which class has the larger train mean. • Refusal-template indicator: 1 if the first 120 characters of the response match an explicit refusal template (“I cannot/can’t/won’t/will not/am unable/am not able/must decline/refuse”, “Sorry, (but) I”, “I’m sorry, but”, or “As an AI”), else 0, sign-oriented like length. The exact pattern is stored in the artifact. • Stylistic features: logistic regression as above, after standardization, on log(1 + characters), log(1 + words), log(1 + lines), mean word length, type–token ratio, punctuation, digit, and uppercase fractions, the fraction of list-formatted lines, question-mark and exclamation counts, and the refusal indicator. Operating-point thresholds accept a response as safe iff its score is at least the next representable value above the validation unsafe score at rank ⌊target × nunsafe ⌋ in descending order, which guarantees a validation false-safe rate no greater than the target. The held-out references (Section 5.4) use the validation split, which is prompt-disjoint from train and test. The population reference uses every validation response without labels. The cohort pool is the validation primary cohort. The 5%, 10%, and 25% pools subsample the population, keeping all safe rows when possible and subsampling unsafe rows (or the reverse when unsafe rows are scarce). The labeled reference draws k unsafe validation responses, where k equals the 5% pool’s unsafe count. All draws use seed 20260715.

11

C

Per-cell results and statistics

Corpus

Encoder

Prototype

Two-centroid

Diff. means

Mixture-centered

RankOne

Linear

Log length

BeaverTails BeaverTails BeaverTails BeaverTails

MiniLM mpnet Qwen-0.5B Qwen-3B

.533 [.502,.559] .509 [.482,.536] .545 [.514,.572] .529 [.497,.556]

.591 .594 .617 .622

.588 [.559,.616] .590 [.566,.615] .617 [.590,.643] .622 [.596,.648]

.588 .590 .617 .622

.614 .624 .631 .636

.632 .639 .690 .695

.529 .529 .529 .529

PKU-SafeRLHF PKU-SafeRLHF PKU-SafeRLHF PKU-SafeRLHF

MiniLM mpnet Qwen-0.5B Qwen-3B

.491 [.481,.502] .457 [.447,.467] .501 [.488,.514] .481 [.468,.494]

.670 .699 .716 .738

.668 [.656,.683] .690 [.678,.703] .716 [.703,.729] .738 [.726,.751]

.668 .690 .716 .738

.667 .691 .718 .743

.733 .775 .819 .843

.595 .595 .595 .595

Aegis jury Aegis jury Aegis jury Aegis jury

MiniLM mpnet Qwen-0.5B Qwen-3B

.358 [.317,.395] .389 [.353,.427] .381 [.339,.422] .405 [.362,.448]

.739 .764 .746 .756

.772 [.739,.803] .793 [.764,.821] .754 [.720,.789] .761 [.726,.794]

.772 .793 .754 .761

N/A† N/A† N/A† N/A†

.818 .856 .843 .857

.554 .554 .554 .554

Table 4: Primary controlled response-only ROC-AUC for every audited readout. Brackets are 95% prompt-cluster bootstrap intervals (500 draws, conditional on the train fit). The in-sample mixturecentered safe mean equals difference of means in every cell, as Eq. 4 predicts. † Aegis RankOne has only six mixed-label fit groups and is not interpreted.

Corpus

Encoder

Prototype AUC

z

p

Holm

TOST

∆+

cos(µs , µu )

BeaverTails BeaverTails BeaverTails BeaverTails

MiniLM mpnet Qwen-0.5B Qwen-3B

.533 [.502,.559] .509 [.482,.536] .545 [.514,.572] .529 [.497,.556]

+2.29 +0.65 +3.04 +1.93

2.2e-02 5.1e-01 2.4e-03 5.4e-02

no no yes no

no yes no no

+0.0044 −0.0042 +0.0028 +0.0016

0.947 0.951 0.999 0.999

PKU-SafeRLHF PKU-SafeRLHF PKU-SafeRLHF PKU-SafeRLHF

MiniLM mpnet Qwen-0.5B Qwen-3B

.491 [.481,.502] .457 [.447,.467] .501 [.488,.514] .481 [.468,.494]

−1.79 −8.32 +0.21 −2.90

7.4e-02 < 10−15 8.4e-01 3.7e-03

no yes no yes

yes no yes yes

−0.0053 −0.0154 +0.0034 +0.0008

0.967 0.964 0.998 0.999

Aegis jury Aegis jury Aegis jury Aegis jury

MiniLM mpnet Qwen-0.5B Qwen-3B

.358 [.317,.395] .389 [.353,.427] .381 [.339,.422] .405 [.362,.448]

−7.13 −5.88 −5.60 −4.31

1.0e-12 4.2e-09 2.1e-08 1.6e-05

yes yes yes yes

no no no no

−0.0346 −0.0227 −0.0126 −0.0062

0.837 0.825 0.997 0.998

Table 5: Prototype-versus-chance tests and class-mean geometry. z and two-sided p use a normal approximation from the bootstrap interval half-width. Holm: Holm–Bonferroni rejection at familywise α = 0.05 over the 12 cells. TOST: conservative equivalence to chance within ±0.05 (95% interval contained in [0.45, 0.55]). ∆+ is the measured expected score gap of Eq. 2 on the test cohort.

12

D

Operating points for all encoders

Corpus

Encoder

Target

Prototype test FSR

Prototype safe accept.

Diff. means test FSR

Diff. means safe accept.

BeaverTails

MiniLM

BeaverTails

mpnet

BeaverTails

Qwen-0.5B

BeaverTails

Qwen-3B

5% 10% 5% 10% 5% 10% 5% 10%

.050 [.021,.074] .091 [.057,.130] .038 [.012,.071] .090 [.043,.140] .044 [.025,.075] .109 [.078,.150] .070 [.045,.112] .127 [.100,.162]

.082 [.038,.109] .124 [.084,.171] .037 [.014,.073] .092 [.042,.153] .060 [.034,.100] .143 [.096,.183] .068 [.047,.098] .115 [.090,.151]

.045 [.025,.085] .104 [.068,.159] .053 [.026,.082] .102 [.061,.148] .034 [.021,.058] .072 [.045,.106] .037 [.020,.065] .082 [.053,.127]

.084 [.056,.130] .163 [.112,.229] .092 [.061,.134] .165 [.112,.221] .067 [.044,.109] .147 [.093,.196] .095 [.062,.137] .171 [.126,.236]

PKU-SafeRLHF

MiniLM

PKU-SafeRLHF

mpnet

PKU-SafeRLHF

Qwen-0.5B

PKU-SafeRLHF

Qwen-3B

5% 10% 5% 10% 5% 10% 5% 10%

.064 [.047,.078] .119 [.090,.147] .065 [.047,.081] .115 [.087,.135] .051 [.035,.070] .103 [.082,.124] .050 [.034,.064] .097 [.078,.117]

.061 [.043,.077] .117 [.089,.139] .039 [.028,.057] .081 [.061,.097] .048 [.035,.069] .104 [.084,.124] .050 [.032,.064] .084 [.068,.101]

.052 [.039,.066] .090 [.072,.115] .050 [.033,.071] .098 [.079,.128] .041 [.029,.057] .087 [.067,.105] .046 [.029,.061] .099 [.071,.120]

.170 [.133,.198] .250 [.222,.299] .153 [.113,.191] .246 [.215,.291] .230 [.186,.268] .361 [.315,.397] .263 [.222,.303] .394 [.350,.431]

Aegis jury

MiniLM

Aegis jury

mpnet

Aegis jury

Qwen-0.5B

Aegis jury

Qwen-3B

5% 10% 5% 10% 5% 10% 5% 10%

.042 [.019,.066] .081 [.055,.108] .037 [.021,.065] .072 [.051,.102] .060 [.037,.089] .107 [.077,.138] .054 [.029,.074] .086 [.059,.119]

.019 [.004,.037] .034 [.012,.063] .004 [.000,.029] .049 [.020,.076] .038 [.011,.065] .075 [.043,.113] .045 [.018,.073] .075 [.044,.110]

.053 [.029,.085] .117 [.081,.150] .066 [.041,.095] .126 [.092,.161] .044 [.027,.076] .089 [.063,.127] .053 [.029,.078] .089 [.064,.126]

.245 [.160,.318] .358 [.288,.476] .291 [.205,.401] .468 [.386,.548] .189 [.133,.292] .351 [.278,.431] .208 [.147,.325] .370 [.301,.454]

Table 6: Validation-calibrated operating points for all four encoders. Brackets are 95% intervals from 10,000 validation/test prompt-cluster draws that recalibrate the threshold in each draw, conditional on a fixed train fit.

E

Input-mode ablation for all encoders

ROC-AUC (95% prompt-cluster CI)

Input-mode ablation on prompt-matched safety cohorts BeaverTails mixed-label prompts

SafeRLHF native pairs Safe prototype Two-centroid

0.70 0.65 0.60 0.55 0.50 0.45

t Promp

only

e

spons

t + re Promp

n Respo

ly

se on

nly

to Promp

t+ Promp

n respo

se

se on

n Respo

ly

Figure 3: MiniLM input-mode ablation on prompt-matched cohorts (“SafeRLHF” is PKU-SafeRLHF). Prompt-only scores are at chance or near chance after matching, despite strong prompt-only signal on the full corpus populations. Error bars are conditional 95% prompt-cluster intervals. All four encoders are reported in Table 7.

13

Corpus

Encoder

Prompt only, full

Prompt only, controlled

Prompt+response (proto / 2c)

Response (proto / 2c)

BeaverTails BeaverTails BeaverTails BeaverTails

MiniLM mpnet Qwen-0.5B Qwen-3B

.713 .731 .679 .692

.522 [.495,.547] .531 [.503,.558] .543 [.515,.566] .548 [.521,.572]

.515 / .558 .546 / .579 .545 / .598 .523 / .610

.533 / .591 .509 / .594 .545 / .617 .529 / .622

PKU-SafeRLHF PKU-SafeRLHF PKU-SafeRLHF PKU-SafeRLHF

MiniLM mpnet Qwen-0.5B Qwen-3B

.780 .831 .741 .768

.500 [.500,.500] .500 [.500,.500] .500 [.500,.500] .500 [.500,.500]

.490 / .615 .499 / .630 .506 / .680 .458 / .705

.491 / .670 .457 / .699 .501 / .716 .481 / .738

Aegis jury Aegis jury Aegis jury Aegis jury

MiniLM mpnet Qwen-0.5B Qwen-3B

.669 .670 .662 .642

.639 [.599,.677] .649 [.611,.686] .643 [.601,.681] .621 [.580,.660]

.337 / .689 .431 / .690 .422 / .736 .426 / .769

.358 / .739 .389 / .764 .381 / .746 .405 / .756

Table 7: Input-mode ablation for all encoders, two-centroid (2c) readout unless marked. “Full” is the prompt-disjoint full population; “controlled” is the primary cohort (mixed-label prompts, native pairs, or the Aegis jury source control, which is not prompt-matched). Brackets are 95% prompt-cluster intervals.

F

Cross-corpus transfer for all encoders Fit → evaluate

Encoder

Prototype

Diff. means

BeaverTails → PKU-SafeRLHF

MiniLM mpnet Qwen-0.5B Qwen-3B

.524 [.512,.536] .478 [.469,.490] .502 [.489,.515] .481 [.467,.495]

.648 [.635,.661] .657 [.646,.670] .690 [.679,.702] .698 [.687,.709]

BeaverTails → Aegis jury

MiniLM mpnet Qwen-0.5B Qwen-3B

.275 [.240,.313] .253 [.221,.285] .365 [.324,.405] .384 [.344,.423]

.628 [.590,.663] .682 [.645,.714] .577 [.534,.623] .559 [.518,.605]

PKU-SafeRLHF → BeaverTails

MiniLM mpnet Qwen-0.5B Qwen-3B

.516 [.486,.543] .501 [.469,.528] .544 [.513,.573] .523 [.491,.550]

.608 [.577,.637] .613 [.587,.639] .631 [.605,.654] .641 [.617,.665]

PKU-SafeRLHF → Aegis jury

MiniLM mpnet Qwen-0.5B Qwen-3B

.306 [.273,.344] .291 [.259,.323] .375 [.334,.414] .375 [.336,.413]

.585 [.546,.622] .662 [.626,.699] .551 [.507,.598] .548 [.504,.594]

Aegis jury → BeaverTails

MiniLM mpnet Qwen-0.5B Qwen-3B

.514 [.488,.538] .500 [.471,.529] .540 [.511,.568] .529 [.498,.558]

.532 [.508,.558] .560 [.535,.587] .549 [.520,.577] .553 [.526,.580]

Aegis jury → PKU-SafeRLHF

MiniLM mpnet Qwen-0.5B Qwen-3B

.471 [.460,.484] .448 [.437,.459] .492 [.479,.506] .471 [.457,.485]

.544 [.535,.554] .579 [.570,.589] .572 [.561,.584] .579 [.568,.593]

Table 8: Cross-corpus transfer between primary controlled cohorts after exact prompt decontamination, for all four encoders. Brackets are 95% prompt-cluster intervals on the evaluation cohort.

14

G

Refusal-template sensitivity

Corpus

Encoder

Refusal % (S / U)

Indicator AUC

Rows kept

Prototype, no refusals

Diff. means, no refusals

BeaverTails BeaverTails BeaverTails BeaverTails

MiniLM mpnet Qwen-0.5B Qwen-3B

5.1 / 0.6 5.1 / 0.6 5.1 / 0.6 5.1 / 0.6

.523 .523 .523 .523

1,814/1,868 1,814/1,868 1,814/1,868 1,814/1,868

.523 [.497,.551] .501 [.472,.530] .543 [.515,.573] .534 [.502,.564]

.578 [.548,.605] .582 [.556,.608] .603 [.574,.632] .608 [.580,.636]

PKU-SafeRLHF PKU-SafeRLHF PKU-SafeRLHF PKU-SafeRLHF

MiniLM mpnet Qwen-0.5B Qwen-3B

3.2 / 0.5 3.2 / 0.5 3.2 / 0.5 3.2 / 0.5

.513 .513 .513 .513

3,421/3,486 3,421/3,486 3,421/3,486 3,421/3,486

.491 [.481,.501] .457 [.448,.468] .505 [.493,.518] .488 [.474,.502]

.664 [.650,.678] .686 [.672,.698] .703 [.691,.714] .724 [.712,.736]

Aegis jury Aegis jury Aegis jury Aegis jury

MiniLM mpnet Qwen-0.5B Qwen-3B

0.8 / 2.0 0.8 / 2.0 0.8 / 2.0 0.8 / 2.0

.506 .506 .506 .506

932/948 932/948 932/948 932/948

.357 [.317,.397] .389 [.350,.428] .382 [.339,.424] .407 [.364,.447]

.774 [.742,.810] .796 [.765,.828] .756 [.721,.789] .763 [.727,.800]

Table 9: Refusal-template sensitivity. A response is a refusal if its first 120 characters match an explicit refusal template (Appendix B). Refusal-opening responses are removed from both fit and test before refitting.

H

Held-out unlabeled reference

Corpus

Encoder

Prototype

Diff. means

Population

Cohort pool

25%

10%

5%

Labeled k

BeaverTails BeaverTails BeaverTails BeaverTails

MiniLM mpnet Qwen-0.5B Qwen-3B

.533 .509 .545 .529

.588 .590 .617 .622

.581 .582 .600 .609

.590 .583 .605 .613

.561 .553 .573 .570

.520 .498 .543 .534

.505 .481 .530 .523

.571 .577 .597 .612

PKU-SafeRLHF PKU-SafeRLHF PKU-SafeRLHF PKU-SafeRLHF

MiniLM mpnet Qwen-0.5B Qwen-3B

.491 .457 .501 .481

.668 .690 .716 .738

.623 .640 .666 .668

.643 .671 .703 .728

.556 .543 .598 .597

.516 .495 .549 .546

.506 .483 .533 .530

.625 .636 .685 .693

Aegis jury Aegis jury Aegis jury Aegis jury

MiniLM mpnet Qwen-0.5B Qwen-3B

.358 .389 .381 .405

.772 .793 .754 .761

.701 .710 .563 .643

.756 .782 .737 .736

.677 .687 .540 .624

.583 .591 .474 .558

.557 .563 .460 .543

.753 .791 .728 .720

Table 10: Held-out references (ROC-AUC on the primary test cohort). The safe mean is fit on labeled-safe train responses and centered by the mean of a prompt-disjoint validation sample: the full validation population (no labels used); the validation primary cohort (label-selected for BeaverTails and PKU-SafeRLHF); the population subsampled to 25%, 10%, or 5% unsafe (labels used only to set composition); or k labeled unsafe validation responses, with k equal to the 5% pool’s unsafe count (Table 11).

Corpus

Encoder

Population rows

π̂u

k

cos, population

cos, 5%

cos, labeled k

Shift

BeaverTails BeaverTails BeaverTails BeaverTails

MiniLM mpnet Qwen-0.5B Qwen-3B

4,603 4,603 4,603 4,603

.568 .568 .568 .568

105 105 105 105

.888 .873 .938 .929

.139 .085 .266 .288

.783 .788 .907 .895

.855 .848 .636 .685

PKU-SafeRLHF PKU-SafeRLHF PKU-SafeRLHF PKU-SafeRLHF

MiniLM mpnet Qwen-0.5B Qwen-3B

24,341 24,341 24,341 24,341

.505 .505 .505 .505

634 634 634 634

.824 .782 .793 .776

.120 −.063 .226 .193

.816 .823 .775 .782

1.385 1.403 .977 .946

Aegis jury Aegis jury Aegis jury Aegis jury

MiniLM mpnet Qwen-0.5B Qwen-3B

2,143 2,143 2,143 2,143

.293 .293 .293 .293

80 80 80 80

.471 .495 .164 .250

.118 .132 −.180 −.021

.772 .816 .886 .888

.835 .821 1.052 1.310

Table 11: Reference pools and geometry. “cos” is the cosine between a reference direction and the difference-of-means direction. Shift is ∥z̄strain − z̄sval ∥/∥z̄strain − z̄utrain ∥: the difference between the safe means of the primary train cohort and the full validation population, in class-gap units. It reflects sampling and composition differences and does not depend on the reference’s unsafe share.

15

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