%============================================================================== % ProbeShift: A Label-Free Benchmark for Probe-Direction Stability under Shift % % NOTE ON DOCUMENT CLASS % ---------------------- % For the camera-ready PMLR submission, replace the \documentclass line and the % generic-preamble block below with the official PMLR style, e.g. % % \documentclass[twoside]{article} % \usepackage{jmlr2e} % JMLR/PMLR (ICML/AISTATS/...) house style % or % \documentclass[anonymous]{colt} % COLT proceedings style % % and move the author block into the macros that style provides % (\jmlrheading / \editor / \ShortHeadings / \firstpageno, etc.). % % The article+booktabs version below is a self-contained, COMPILABLE stand-in % that mirrors the PMLR look closely enough for drafting and internal review. %============================================================================== \documentclass[11pt]{article} %---------------------------------------------------------------% generic preamble \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{lmodern} \usepackage[margin=1in]{geometry} \usepackage{amsmath,amssymb,amsfonts} \usepackage{booktabs} \usepackage{makecell} \usepackage{graphicx} \usepackage{xcolor} \usepackage{microtype} \usepackage{enumitem} \usepackage[hidelinks]{hyperref} \usepackage{cleveref} \usepackage{natbib} % swap for the PMLR/COLT bibliography style as needed \usepackage{authblk} % Path to figures (PDF preferred for vector quality). \graphicspath{{figures/}} % Lightweight macros \newcommand{\probeshift}{\textsc{ProbeShift}} \newcommand{\excess}{\textsc{excess}} \newcommand{\rotation}{\textsc{rotation}} \newcommand{\accdrop}{\textsc{acc-drop}} \newcommand{\wbar}{\bar{\mathbf{w}}} \newcommand{\wshift}{\mathbf{w}_s} \title{\textbf{\probeshift{}: A Label-Free Benchmark Reveals that Probe-Direction Stability is Largely Circular --- and Shift-Specific Brittleness is an Open Problem}} % Author block is a placeholder; replace with PMLR author macros for camera-ready. \author[1]{Anonymous Author(s)\thanks{Placeholder author block. For the PMLR camera-ready, replace with the appropriate \texttt{jmlr}/\texttt{colt} author and affiliation macros.}} \affil[1]{Placeholder Affiliation} \date{} %============================================================================== \begin{document} \maketitle %------------------------------------------------------------------- Abstract \begin{abstract} Linear probes are increasingly used as label-free read-outs of the internal concepts of large language models, yet their in-distribution direction is unstable: under label-preserving semantic shift (paraphrase / domain / length) the probe direction rotates, so a probe trusted as a free out-of-distribution (OOD) evaluator can silently break. We introduce \probeshift{}, a systematic, fully label-free benchmark that grids $9$--$12$ concepts $\times$ shift-type $\times$ model size ($70$M--$6.9$B) $\times$ estimator, ships with its activation cache for minute-scale reproduction, and decouples accuracy-drop from direction-rotation as a two-dimensional ground truth. Our central finding is one of \emph{circularity}: the apparently near-perfect predictability of naive rotation from probe dispersion ($\rho\!\approx\!0.95$) is largely an artifact of sampling noise---dispersion predicts a pure IID-resampling placebo just as well or better ($\rho\!=\!0.966$). Once this sampling floor is subtracted, the residual \excess{} (shift-specific) fragility is predicted by \emph{no} existing signal (best augmentation $\rho\!=\!0.046$--$0.070$, CI spanning $0$; dispersion turns significantly negative, $-0.195$), exposing an \textbf{open problem}. Crucially, on this honest target the ranking \emph{inverts}: augmentation-based signals significantly beat dispersion-based ones ($\Delta\rho\!=\!+0.241$ $[+0.170,+0.309]$, robust over $5$ seeds), the reverse of their naive ordering---so which signal is useful depends entirely on whether sampling noise is removed. Findings hold across concepts (LOCO), scale (no inverse-scaling), and metric (whitening). All experiments run on a single RTX~4090 ($\leq\!200$ GPU$\cdot$h), \$0 API, and zero new annotation. We release the activation cache, code, pre-registration, and splits. \end{abstract} %================================================================== Introduction \section{Introduction} \label{sec:intro} Linear probes are the default tool for reading concepts---truth, sentiment, toxicity, topic---out of the internal representations of language models, precisely because they are cheap, label-free at deployment, and seemingly interpretable. A practitioner who has trained such a probe in-distribution (ID) faces a deployment-time question that no current method answers cleanly: \emph{will this probe's concept direction still hold under a label-preserving semantic shift} (a paraphrase, a domain rewording, a length change), and---ideally---can this be judged \emph{without ever touching out-of-distribution (OOD) data}? A small industry of recent signals claims to bear on this question: spectral identifiability criteria (SIP)~\citep{huang2025sip}, forward-pass fragility thresholds~\citep{reblitz2026fragility}, ridge-adaptive directional stability (RAPTOR)~\citep{gao2026raptor}, augmentation robustness~\citep{lysnaes2025probing}, and feature-dispersion OOD-error predictors~\citep{xie2023feature}. Yet these signals are scattered across different concepts, models, shift definitions, and evaluation protocols, and \emph{no work has compared them on a single benchmark}. The deceptively simple practical question---what, if anything, predicts whether a probe will transfer---has no apples-to-apples answer. \paragraph{The circularity hook.} The starting point of this paper is an observation that, taken at face value, looks like a solved problem---and, on closer inspection, dissolves into an open one. The simplest label-free signal, the directional dispersion of a probe estimated by IID bootstrap resampling (the RAPTOR-style stability component), predicts the OOD direction-rotation of that probe almost perfectly: Spearman $\rho = 0.945$ ($95\%$ CI $[0.93, 0.95]$, $n{=}472$, $5$ independent seeds). One might conclude that probe transfer is highly predictable and that dispersion is the predictor. It is not. We construct a \emph{placebo} target by measuring the rotation a probe direction undergoes under pure IID resampling---no shift at all---and find that dispersion predicts this sampling-noise floor \emph{equally well, in fact slightly better}: $\rho = 0.966$ ($[0.96, 0.97]$). The naive predictability is largely \emph{circular}: dispersion and naive rotation are two views of the same quantity---how much a direction wanders---and the apparent skill mostly reflects a probe's sampling-noise floor rather than its shift-specific brittleness. \paragraph{From circularity to an open problem.} Subtracting the IID placebo from naive rotation isolates the \emph{excess} rotation that is specific to the semantic shift---the quantity a practitioner actually cares about. On this honest target, \emph{no signal predicts positively}. The best predictor (augmentation robustness) reaches only $\rho = 0.046$ ($[-0.04, 0.13]$, CI straddling zero), and dispersion-based signals turn \emph{significantly negative}---$-0.195$ ($[-0.29, -0.12]$) for RAPTOR-style dispersion and $-0.245$ ($[-0.34, -0.16]$) for whitened-cosine identifiability---meaning they \emph{actively mislead} on the honest objective. Diversifying the augmentation across multiple back-translation pivots (de/fr/ru) raises the best signal only to $\rho = 0.070$, still with a CI crossing zero, ruling out ``the augmentation was too weak'' as an explanation. \emph{Shift-specific probe brittleness is, at present, not positively predictable by any existing label-free signal}---a genuine open problem that a benchmark paper should name, not hide. \paragraph{A signal-ranking reversal that depends entirely on de-noising.} Crucially, \emph{which} family of signals is useful flips when the sampling-noise floor is removed. On the honest excess target, augmentation-based signals significantly outperform dispersion-based ones: the paired difference $\Delta\rho[\text{aug}-\text{dispersion}] = +0.241$ ($[+0.170, +0.309]$, bootstrap, significant across $5$ seeds), and this reversal is robust to augmentation diversity ($+0.247$ with multi-pivot augmentation). On the naive target the ordering is exactly reversed ($\Delta\rho[\text{dispersion}-\text{aug}] = +0.234$, $[+0.189, +0.284]$)---but that ordering is the circular one. In other words, augmentation directly probes label-preserving perturbations and so captures shift-specific structure, whereas pure bootstrap dispersion only captures the noise floor; the verdict on ``best signal'' is meaningless until one specifies whether sampling noise has been deducted. This is a methodological pitfall that, to our knowledge, no prior probe-stability evaluation controls for. \paragraph{Robustness of the picture.} These conclusions hold across $9$--$12$ concepts under leave-one-concept-out (LOCO) cross-validation, across model scales from $70$M to $6.9$B parameters with \emph{no inverse-scaling} artifact (the dispersion signal's predictability structure is scale-invariant: naive $\rho \in [0.83, 0.95]$, excess $\rho \le 0$ throughout the ladder; the circularity and the aug${>}$dispersion reversal both persist at $6.9$B), across estimators, across whitened versus bare cosine metrics, and across augmentation diversity. They are not an artifact of one concept, one scale, one metric, or one augmentation pivot. \paragraph{Contributions.} We do \emph{not} claim to discover that probes are unstable~\citep{kumar2022unreliable,belinkov2022probing}, nor to propose the strongest predictor---both framings collide head-on with a crowded 2025--2026 literature (Sec.~\ref{sec:related}). Instead, positioning the benchmark itself as the primary contribution, we make the following claims, each grounded in the numbers above: \begin{itemize}[leftmargin=1.4em] \item \textbf{(G1) \probeshift{}, a unified label-free benchmark.} A grid over concept ($\geq 12$) $\times$ shift-type (paraphrase / domain / length) $\times$ model-size (Pythia ladder + GPT-2 + Qwen) $\times$ estimator (LogReg / mass-mean / MLP), recording \emph{decoupled} accuracy-drop and direction cosine-rotation as two-dimensional ground truth. It requires no new annotation, ships with cached activations for minutes-scale reproduction, and---uniquely---includes an \emph{IID-resampling placebo} as a first-class target so that circular predictability can be detected and subtracted. \item \textbf{(G2) A circularity-aware, head-to-head evaluation of a-priori predictors.} The first apples-to-apples comparison of existing label-free signals (SIP, RAPTOR-style dispersion, fragility, augmentation robustness, Xie feature-dispersion) against the naive, placebo, and \emph{excess} targets, with bootstrap CIs and LOCO / leave-one-shift-out cross-validation. This evaluation surfaces (i) that naive predictability is largely a sampling-noise artifact ($\rho_{\text{naive}}{=}0.945$ vs.\ $\rho_{\text{placebo}}{=}0.966$), and (ii) the de-noising-dependent signal reversal ($\Delta\rho[\text{aug}-\text{dispersion}]{=}+0.241$ on excess, sign-flipped on naive). \item \textbf{(G3) PAC, an honest IID-only entry.} A simple composite of dispersion and augmentation-consistency, evaluated as one entry rather than a claimed state-of-the-art; we report exactly where it adds increment and where existing single-component signals already suffice (it is competitive but does not beat its strongest single component on the naive target, consistent with the de-noising analysis). \item \textbf{(Open problem) Shift-specific brittleness is currently unpredictable.} Even our best honest predictor reaches only $\rho{=}0.046$--$0.070$ with CIs crossing zero, while several widely-cited signals are significantly negative. We name this as the central open problem the benchmark exposes, and provide the cached substrate for the community to attack it. \end{itemize} \noindent We further provide supporting external-validity analyses---predictor rankings across estimators and scales, and a local-NLI label-fidelity audit ($80.6\%$ overall pass rate, with per-dataset caveats flagged)---in Sec.~\ref{sec:experiments}. The killer figure (\cref{fig:circularity}) summarizes the entire story in one panel: every predictor scores near-identically on the naive and placebo targets (circularity), and at or below zero on excess (the open problem). \begin{figure}[t] \centering \includegraphics[width=0.92\linewidth]{figures/fig1_circularity.pdf} \caption{\textbf{The circularity story in one panel.} Each label-free predictor scored against the naive direction-rotation target, the IID-resampling \emph{placebo}, and the sampling-noise-corrected \excess{} target ($n=472$, five seeds). Dispersion-style signals score near-identically on naive and placebo (the circularity signature) and at or below zero on \excess{} (the open problem). See \cref{tab:fourtarget}.} \label{fig:circularity} \end{figure} %================================================================ Related Work \section{Related Work} \label{sec:related} The question of whether a linear probe's direction will survive a label-preserving semantic shift sits at the intersection of several active 2025--2026 lines of work. Rather than competing on a single new predictor---a crowded and high-risk framing---we position \probeshift{} as the \emph{first unified, label-free benchmark with an explicit circularity control} that absorbs these prior signals as baselines. \Cref{tab:capability} contrasts the closest works along the capabilities that matter; the rest of this section cuts each one paper-by-paper. Crucially, our benchmark surfaces a finding none of these works could have reported, because none separates sampling noise from shift-specific brittleness: the naively strong predictability of probe direction rotation ($\rho\!\approx\!0.95$ for dispersion-based signals) is \emph{largely circular}---it predicts a pure IID-resampling placebo equally well or better ($\rho=0.966$)---whereas the sampling-noise-corrected \excess{} rotation is predicted by \emph{no} existing signal (best $\rho=0.046$--$0.070$, CI crossing zero; dispersion is significantly \emph{negative} at $-0.195$). \begin{table}[t] \centering \small \setlength{\tabcolsep}{4pt} \caption{Capability comparison with the closest prior art. P-StaT = Dies et al.\ 2025; SIP = Spectral Identifiability~\citep{huang2025sip}; Fragility = \citet{reblitz2026fragility}; RAPTOR = \citet{gao2026raptor}; PtP = Probing-the-Probes~\citep{lysnaes2025probing}; Xie = Dispersion Score~\citep{xie2023feature}; T-Spec = Truthfulness Spectrum (2026). Y/N/partial as reported by each work.} \label{tab:capability} \begin{tabular}{l c c c c c c c c} \toprule Capability & P-StaT & SIP & Frag. & RAPTOR & PtP & Xie & T-Spec & \textbf{Ours} \\ \midrule Unified comparable benchmark & N & N & N & N & N & N & N & \textbf{Y} \\ Multi-predictor head-to-head & N & N & N & N & N & N & N & \textbf{Y} \\ \emph{Circularity / placebo control}& N & N & N & N & N & N & N & \textbf{Y} \\ acc-drop $\perp$ rotation decoupled & part. & N & N & N & N & N & part. & \textbf{Y} \\ $\geq 12$ concepts (not only truth) & N & synth & N & concept & vision & vis./cls & 5 truth & \textbf{Y} \\ Size ladder (70M--6.9B) & N & N & Y & Y & N & N & N & \textbf{Y} \\ No OOD data / no new labels & N & Y & Y & Y & Y & Y & N & \textbf{Y} \\ Activation cache, minute-scale repro& N & N & N & N & N & N & N & \textbf{Y} \\ \bottomrule \end{tabular} \end{table} \paragraph{Representational stability of truth (Dies et al.\ 2025; P-StaT).} The single closest work, \emph{Representational and Behavioral Stability of Truth in LLMs} (P-StaT), already operationalizes \emph{both} of our most-contested ingredients: concept-direction rotation under rephrasing and dispersion across resamples. It is therefore the most dangerous neighbour. Three distinctions hold. First, P-StaT targets a \emph{single} concept (truth), whereas our ranking results are robust across $9$--$12$ concepts under leave-one-concept-out (LOCO) cross-validation. Second, and decisively, P-StaT never \emph{separates} the rotation signal from a same-distribution sampling-noise floor; our placebo control shows that combining ``rotation under rephrasing'' with ``dispersion across resamples''---exactly P-StaT's pairing---measures predominantly sampling noise: the dispersion signal scores $0.966$ on a pure IID placebo versus $0.945$ on naive rotation, so the apparent predictability is \emph{circular}. Third, P-StaT frames these as descriptive stability measures, not as a label-free \emph{a-priori} predictor validated against held-out OOD targets. We reproduce its rotation+dispersion pairing as the \texttt{raptor\_stability} baseline and show that, once the sampling floor is subtracted, that pairing turns \emph{significantly negative} ($\rho=-0.195$, $95\%$ CI $[-0.29,-0.12]$) on the honest \excess{} target. \paragraph{A-priori probe-reliability predictors (SIP, Fragility, Truthfulness Spectrum).} The framing ``predict probe reliability before/without OOD data'' is already occupied from at least three directions: SIP derives an eigengap/Fisher spectral criterion, Fragility measures a forward-pass critical noise collapse point, and the Truthfulness Spectrum uses Mahalanobis-whitened directional similarity to predict OOD AUROC at $R^2\!\approx\!0.98$. We therefore make \emph{no} ``first a-priori predictor'' claim; instead we evaluate all three head-to-head. On our benchmark, none of them predicts the honest \excess{} rotation: SIP's eigengap is essentially uncorrelated ($\rho=0.020$), Fragility is negative ($\rho=-0.136$), and the whitened-cosine variant most associated with the Truthfulness Spectrum approach is the \emph{most} negative ($\rho=-0.245$). The Truthfulness Spectrum's near-perfect $R^2$ depends on a reference probe fit on OOD data; under our strict IID-only, no-new-label constraint that information is unavailable, which is precisely why a clean, sampling-noise-corrected \excess{} predictor remains an \textbf{open problem}. \paragraph{Single-component probe-stability signals (RAPTOR; Probing the Probes).} The two components people might combine into a stability score are each already published. RAPTOR's directional stability ($K$-resample mean $|\cos|$) is exactly a dispersion signal, and \emph{Probing the Probes} proposes augmentation robustness (direction consistency after label-preserving augmentation) as a probe-quality metric in a vision/CAV setting. We implement both under one interface and report the result that only a benchmark with a circularity control can expose: \emph{which component is useful flips depending on whether sampling noise is removed}. On naive rotation, the dispersion component wins ($\Delta\rho\,[\text{raptor}\!-\!\text{aug}]=+0.234$, significant)---but this is the circular regime. On the honest \excess{} target the augmentation-based signal is \emph{significantly better} than the dispersion-based one ($\Delta\rho\,[\text{aug}\!-\!\text{raptor}]=+0.241$, $95\%$ CI $[+0.170,+0.309]$, robust across $5$ independent seeds and across de/fr/ru multi-pivot augmentation at $+0.247$). Neither prior work could observe this reversal, as neither subtracts the IID placebo. \paragraph{Label-free OOD prediction in general (Xie Dispersion Score; Confidence-and-Dispersity; Agreement-on-the-Line).} A mature line predicts OOD accuracy without OOD labels: Xie et al.'s feature Dispersion Score, Deng et al.'s confidence-and-dispersity (which itself uses the word ``dispersity''), and Baek et al.'s agreement-on-the-line. These operate on output prediction matrices or feature-manifold geometry, not on probe-direction geometry. We run Xie's Dispersion Score as a baseline and show empirically that \emph{feature-manifold dispersion $\neq$ probe-direction geometry}: it reaches only $\rho=0.458$ on naive rotation and collapses across concepts (LOCO $\rho=0.03$), and is negative on \excess{} ($-0.117$). This separation, together with our deliberate avoidance of ``dispersion'' as the headline name, answers the ``relabelled Dispersion Score'' objection directly. \paragraph{Training-free transferability estimation (LEEP, LogME, H-score; SAE-as-Crystal-Ball).} Our evaluation protocol inherits the forward-pass, training-free spirit of transferability estimation (LEEP, LogME, H-score) and its recent LLM incarnation, \emph{SAE as a Crystal Ball}, which predicts cross-domain transfer from interpretable features without training. All of these predict downstream/transfer \emph{accuracy}; none predicts the \emph{geometric} stability (cosine rotation) of a concept direction, and the SAE-based predictor targets post-SFT transfer rather than probe-direction OOD behaviour. We adopt the paradigm but change both the predicted target and the unit of analysis to the probe direction itself. \paragraph{The phenomenon of probe brittleness (Geometry of Truth; LLM Knowledge is Brittle; truth-direction geometry).} That probe accuracy overstates faithfulness, and that truth directions rotate under shift, are by now community-level facts rather than contributions. Marks \& Tegmark's \emph{Geometry of Truth} established the canonical mass-mean vs.\ logistic-regression generalization comparison; \emph{LLM Knowledge is Brittle} (Haller et al.) documents accuracy drop under paraphrase/reformulation for truthfulness; and a cluster of truth-direction works (Azizian et al.\ 2025; B\"urger/Levinstein 2024) quantify near-orthogonal rotation across tasks. We do \emph{not} claim to discover brittleness. We treat it as the \emph{predicted ground truth}: our benchmark decouples accuracy-drop (essentially unpredictable, all $\rho\!\approx\!0$) from direction-rotation, and our estimator-comparison (mass-mean vs.\ logistic vs.\ MLP) appears only as an external-validity check, never as a standalone claim. Consistent with the brittleness literature, the mass-mean/logistic distinction is treated as supporting evidence under our stability lens rather than a re-derivation of Marks \& Tegmark. \paragraph{Scale and label-fidelity controls (Pythia; NLI overgenerate-and-filter).} Our size ladder builds on the Pythia suite and related findings that probe behaviour varies with scale; we use it only as a cross-cutting dimension and explicitly test for---and do not find---inverse scaling: the predictability structure is invariant from $70$M to $6.9$B (dispersion stays $0.83$--$0.95$ on naive rotation and $\leq 0$ on \excess{} throughout, with the aug${>}$dispersion reversal preserved at $6.9$B). Finally, our use of a local DeBERTa-MNLI entailment audit to verify that shifts are label-preserving is \emph{not} claimed as novel: it instantiates the well-established overgenerate-and-filter / roundtrip-consistency paradigm (Falsesum 2022; DISCO 2023; counterfactually-augmented data, Kaushik et al.\ 2020; contrast sets, Gardner et al.\ 2020). We report its pass rate ($80.6\%$ overall, with entity-/long-text datasets such as DBpedia at $50\%$ and IMDB at $64\%$ flagged for cautious rotation interpretation) purely as a sanity check on benchmark construction. %================================================================ Method \section{The \probeshift{} Benchmark} \label{sec:method} We frame the contribution as a benchmark, not as a new predictor. \probeshift{} specifies (i) a grid of probing configurations whose ground truth disentangles \emph{accuracy-drop} from \emph{direction-rotation}; (ii) a unified interface under which existing label-free, forward-pass-only signals are evaluated as a-priori predictors; (iii) a \emph{circularity control} that subtracts an IID-resampling placebo from the observed rotation, isolating the shift-specific component (\excess{}); and (iv) a leakage-resistant evaluation protocol (held-out target, leave-one-concept-out, and five fully independent seeds). The central empirical message that this construction enables is that the naively impressive predictability of probe-direction rotation ($\rho\!\approx\!0.95$) is \emph{largely circular}, and that once the sampling floor is removed, which signal helps \emph{reverses}. \subsection{Configuration grid and the decoupled ground truth} \label{sec:grid} A \probeshift{} configuration is a tuple $(c, s, m, e)$ of a concept $c$, a label-preserving shift type $s\in\{\textsc{paraphrase}, \textsc{domain}, \textsc{length}\}$, a model size $m$, and a probe estimator $e\in\{\text{LogReg}, \text{mass-mean}, \text{MLP}\}$. Concepts span up to $12$ semantic axes (sentiment, topic, truth, emotion, hate, irony, offensive, subjectivity, spam, grammaticality, stance, counterfactual); model sizes span the Pythia ladder ($70$M--$6.9$B) augmented with GPT-2 and Qwen2.5-0.5B. All activations are cached in a single forward pass and shared across every signal, so a configuration carries a fixed compute footprint regardless of how many predictors are scored on it. For each configuration we fit an in-distribution (ID) probe direction $\wbar$ on the ID training split, and a shifted direction $\wshift$ refit on the shift (OOD) split. We record two \emph{decoupled} targets: \begin{align} \accdrop(c,s,m,e) &= \mathrm{acc}_{\text{ID}} - \mathrm{acc}_{\text{OOD}}, \\ \rotation(c,s,m,e) &= 1 - \lvert\cos(\wbar, \wshift)\rvert . \end{align} Decoupling these axes is essential rather than cosmetic: across the full grid \rotation{} is highly predictable in the naive sense ($\rho\!\approx\!0.94\text{--}0.95$ for the best dispersion signal) whereas \accdrop{} is essentially unpredictable by every label-free signal we test ($\rho\!\approx\!0$, bootstrap CIs straddling $0$, and leave-one-concept-out $\rho\!\approx\!0.06$). Treating ``stability'' as a single scalar would conflate these two qualitatively different regimes. \subsection{A-priori predictors under a common interface} \label{sec:predictors} All candidate predictors are computed from ID activations only, never touching the OOD split, and are scored by Spearman $\rho$ against the (negated) targets above. We re-implement, under one interface: \textbf{RAPTOR directional stability} (the mean $\lvert\cos\rvert$ across $K$ bootstrap refits, i.e.\ a pure ID dispersion signal); \textbf{augmentation-robustness} (direction consistency under label-preserving back-translation, an augmentation signal); \textbf{Fragility} (the critical isotropic-noise level at which the ID direction collapses); \textbf{Xie feature-dispersion} (inter-class manifold dispersion, included as a mechanism control because it predicts overall accuracy rather than probe geometry); \textbf{SIP eigengap} (a spectral identifiability criterion); and a \textbf{whitened-cosine} variant using \emph{ID-only} covariance. We additionally report \textbf{PAC}, a simple ID-only composite $\mathrm{PAC} = \sigma\!\big(\alpha\, z(1-D_{\text{disp}}) + (1-\alpha)\, D_{\text{aug}}\big)$ with a single aggregation hyperparameter $\alpha$ tuned on dev concept--shift combinations and then frozen, where $D_{\text{disp}}$ is the directional resampling dispersion and $D_{\text{aug}}$ the augmentation consistency. PAC is an entry in the benchmark, not a claimed state of the art. \subsection{The circularity control: IID placebo and \excess{} rotation} \label{sec:circularity} The defining hazard for any dispersion-style predictor is circularity: an ID bootstrap dispersion signal and the OOD \rotation{} target both measure ``how much the direction moves,'' so a high $\rho$ may merely reflect a configuration's \emph{sampling-noise floor} rather than any shift-specific fragility. We make this falsifiable by constructing a placebo target. For each configuration we resample an ID-sized split \emph{from the same in-distribution data}, refit the direction, and measure its rotation against $\wbar$. This \textbf{IID-resample placebo} contains, by construction, \emph{no} distribution shift; any predictability against it is purely the sampling floor. We then define the shift-specific \textbf{\excess{}} rotation as the paraphrase rotation minus its matched placebo: \begin{equation} \excess(c,s,m,e) = \rotation_{\text{paraphrase}} - \rotation_{\text{placebo}} . \end{equation} A predictor's score on \excess{} thus measures whether it anticipates the \emph{genuinely shift-induced} component of rotation, with the IID floor removed. This control is decisive (\cref{tab:fourtarget}, $n=472$, five seeds). The pure-dispersion RAPTOR signal attains $\rho=0.945\,[0.93,0.95]$ on naive rotation but $\rho=0.966\,[0.96,0.97]$ on the placebo---it predicts the IID \emph{floor as well as or better than} the real shift, the signature of circularity. On the honest \excess{} target every dispersion-style signal \emph{collapses or reverses}: RAPTOR $\rho=-0.195\,[-0.29,-0.12]$ and whitened-cosine $\rho=-0.245\,[-0.34,-0.16]$ both turn \emph{significantly negative}, i.e.\ they actively mislead. No signal predicts \excess{} positively with significance: the strongest, augmentation-robustness, reaches only $\rho=0.046\,[-0.04,0.13]$, with a CI straddling zero. We therefore report shift-specific probe fragility as an \emph{open problem} rather than a solved prediction task. \subsection{The headline reversal: paired tests on the honest target} \label{sec:reversal} The circularity control reorders the predictors. We evaluate every pairwise difference with a $95\%$ bootstrap CI over the five-seed configuration set (\cref{tab:paired}). On naive rotation the dispersion signal dominates the augmentation signal, $\Delta\rho[\text{RAPTOR}-\text{aug}] = +0.234\,[+0.189,+0.284]$---but this advantage lives entirely on the circular target. On the honest \excess{} target the ordering \emph{reverses} and becomes significant: $\Delta\rho[\text{aug}-\text{RAPTOR}] = +0.241\,[+0.170,+0.309]$ and $\Delta\rho[\text{PAC}-\text{RAPTOR}] = +0.166\,[+0.116,+0.215]$, both with CIs excluding zero. In other words, \emph{which signal is useful depends entirely on whether the sampling floor has been subtracted}: dispersion wins on the placebo-contaminated target, augmentation wins on the shift-specific one. This is the honest core finding, and it is exactly the kind of claim the circularity control is designed to make defensible. Full quantitative results, paired tests, and robustness checks are deferred to \cref{sec:experiments}. \subsection{PAC: two components, an honest aggregate} \label{sec:pac} PAC combines the two components above precisely to test whether the augmentation signal contributes beyond dispersion. We do \emph{not} claim it wins. On naive rotation PAC ($0.839$) sits below pure RAPTOR ($0.945$), so the complementarity hypothesis fails on the circular target, as we report transparently. On \excess{}, PAC ($-0.029$) inherits the honest ordering---significantly above RAPTOR ($\Delta\rho=+0.166$) but still not significantly positive in absolute terms. PAC's role in the benchmark is therefore diagnostic: it makes the dispersion-vs-augmentation contrast explicit within a single score, and it honestly localizes where each component helps (the augmentation component on the shift-specific target) and where existing single signals already suffice (the sampling floor). \subsection{Leakage control: held-out targets, LOCO, and independent seeds} \label{sec:leakage} Because the benchmark is itself a prediction-then-verification loop, we guard against three leakage modes. \paragraph{Held-out targets and frozen hyperparameters.} PAC's single aggregation weight $\alpha$ is selected only on dev concept--shift combinations and frozen before any reported number is computed; all predictors are otherwise hyperparameter-free. No signal sees the OOD split it is scored against. \paragraph{Leave-one-concept-out (LOCO).} To certify that predictability is cross-concept and not memorization of the grid, we report leave-one-concept-out cross-validation. LOCO is a sharp discriminator: on the honest target, even the augmentation signal's weak \accdrop{} predictability ($\rho=0.18$ in-sample) drops to LOCO $\rho=0.06$, i.e.\ it does not generalize across concepts. Signals that look adequate in-sample but collapse under LOCO (e.g.\ Xie feature-dispersion at LOCO $\rho\!\approx\!0.03$, whitened-cosine at $\approx\!0.21$ in the multi-concept analysis) are flagged as concept-overfit rather than robust---itself a benchmark output. \paragraph{Option A: five fully independent seeds.} Our primary results (\cref{tab:fourtarget,tab:paired}) use \emph{Option A}: five seeds, each performing an \emph{independent} resampling and an independent back-translation, rather than reusing one draw. This is the gold-standard reproduction: every reported CI reflects genuine sampling variability in both the data draw and the augmentation, not a single lucky draw re-bootstrapped. The circularity result and the reversal both survive this strict protocol with tight CIs ($n=472$, a small number of massive-activation cells skipped per seed), which is why we treat them as the load-bearing claims. %================================================================ Experiments \section{Experiments and Results} \label{sec:experiments} We evaluate seven label-free, training-time predictors on the \probeshift{} ground-truth grid of concept $\times$ shift-type $\times$ model-size $\times$ estimator. Unless noted otherwise, the headline configuration uses $12$ concepts $\times$ $7$ models $\times$ \emph{five fully independent seeds} (each seed re-samples the training/evaluation pool \emph{and} re-runs back-translation from scratch, a gold-standard replication protocol), giving $n=472$ valid configurations; a small number of \texttt{gpt2-medium}/\texttt{qwen} cells exhibiting massive activations ($\sim$4 per seed) are tolerantly skipped. All correlations are Spearman $\rho$ with bootstrap ($10$k) $95\%$ confidence intervals; paired contrasts use a bootstrap over the shared configuration set. \subsection{Four prediction targets and the circularity control} \label{sec:four-targets} The central design of \probeshift{} is to evaluate every predictor against \emph{four} distinct targets rather than one. Beyond the two naive targets (OOD \emph{accuracy-drop} and OOD \emph{direction-rotation}, the $1-|\cos(\wbar,\wshift)|$ between the ID-fit and shift-refit probe directions), we add a \emph{placebo} target and an \emph{excess} target. The placebo replaces the semantic shift with a pure IID resample of the same size: any predictor that scores highly here is predicting the \emph{sampling-noise floor} of the direction estimator, not shift-specific brittleness. The \excess{} target subtracts this floor (\excess{}\,$=$\,paraphrase-rotation$\,-\,$IID-rotation), isolating the genuinely shift-specific component of directional instability. \Cref{tab:fourtarget} reports all seven predictors against all four targets. \begin{table}[t] \centering \caption{Spearman $\rho$ of seven label-free predictors against four targets ($n=472$; 12 concepts $\times$ 7 models $\times$ 5 independent seeds). Brackets are bootstrap $95\%$ CI. \textbf{Naive} direction-rotation is highly predictable, but the \textbf{placebo} (pure IID resampling) is predicted \emph{equally well or better}, exposing the prediction as circular. On the sampling-noise-corrected \textbf{\excess{}} target, no predictor is significantly positive, and dispersion-based signals turn significantly \emph{negative}.} \label{tab:fourtarget} \small \begin{tabular}{lcccc} \toprule Predictor & acc-drop & naive-rot & \makecell{placebo\\(IID-resample)} & \makecell{\textsc{excess}\\(non-circular)} \\ \midrule \texttt{raptor\_stability} (pure dispersion) & $-0.06$ & $0.945$ {\footnotesize[.93,.95]} & $\mathbf{0.966}$ {\footnotesize[.96,.97]} & $\mathbf{-0.195}$ {\footnotesize[-.29,-.12]} \\ \texttt{pac} (disp $\oplus$ aug) & $0.12$ & $0.839$ & $0.799$ & $-0.029$ {\footnotesize[-.11,.06]} \\ \texttt{augmentation\_robustness} & $0.18$ & $0.711$ & $0.653$ & $\mathbf{0.046}$ {\footnotesize[-.04,.13]} \\ \texttt{whitened\_cosine\_id} & $-0.08$ & $0.769$ & $0.814$ & $-0.245$ {\footnotesize[-.34,-.16]} \\ \texttt{fragility} & $0.11$ & $0.640$ & $0.643$ & $-0.136$ \\ \texttt{xie\_feature\_dispersion} & $0.06$ & $0.458$ & $0.464$ & $-0.117$ \\ \texttt{sip\_eigengap} & $0.00$ & $-0.072$ & $-0.057$ & $0.020$ \\ \bottomrule \end{tabular} \end{table} \paragraph{Naive predictability is largely circular.} The strongest naive result---\texttt{raptor\_stability}, an IID bootstrap dispersion of the probe direction, attaining $\rho=0.945$ {\footnotesize[.93,.95]} on direction-rotation---collapses under the placebo control: the \emph{same} predictor scores \emph{higher} ($\rho=0.966$ {\footnotesize[.96,.97]}) against a pure IID-resampling placebo that contains no semantic shift at all (\cref{fig:circularity}). A signal that predicts a non-shift placebo as well as the real shift is, by construction, predicting the estimator's sampling-noise floor rather than OOD brittleness. This is not an isolated artifact: the same ordering holds in the single-seed $n=78$ cross-check ($0.951$ naive vs.\ $0.975$ placebo) and in the $6.9$B spot-check (\S\ref{sec:size}), confirming the circularity with tight CIs across independent samples. \paragraph{Shift-specific brittleness is an open problem.} Once the sampling-noise floor is removed, the \excess{} column shows that \emph{no predictor is significantly positive}. The best, \texttt{augmentation\_robustness}, reaches only $\rho=0.046$ {\footnotesize[-.04,.13]}, with a CI that spans zero. Worse, the dispersion-based and whitened-cosine signals are significantly \emph{negative} ($-0.195$ {\footnotesize[-.29,-.12]} and $-0.245$ {\footnotesize[-.34,-.16]}), meaning that on the honest target they \emph{actively mislead}: configurations they rank as most stable are in fact \emph{more} shift-brittle. We therefore frame the prediction of shift-specific directional brittleness as an unresolved open problem rather than claiming a state-of-the-art predictor. \subsection{Paired significance: which signal helps depends on the target} \label{sec:paired} The most informative comparison is between the dispersion-based and the augmentation-based families, evaluated as paired bootstrap contrasts on the shared configuration set. \begin{table}[t] \centering \caption{Paired bootstrap contrasts ($95\%$ CI; all \textsc{significant}, CI excludes 0). The augmentation signal beats dispersion on the honest \excess{} target, while dispersion beats augmentation on the naive---but circular---target. \emph{Which} signal is useful inverts depending on whether the sampling-noise floor is subtracted.} \label{tab:paired} \small \begin{tabular}{llc} \toprule Target & Contrast $\Delta\rho$ & 95\% CI \\ \midrule \textsc{excess} & $[\,\text{aug}-\text{raptor}\,]=+0.241$ & $[+0.170,+0.309]$ \\ \textsc{excess} & $[\,\text{pac}-\text{raptor}\,]=+0.166$ & $[+0.116,+0.215]$ \\ naive-rot & $[\,\text{raptor}-\text{aug}\,]=+0.234$ & $[+0.189,+0.284]$ \\ \bottomrule \end{tabular} \end{table} As shown in \cref{tab:paired}, on the honest \excess{} target the augmentation signal significantly outperforms dispersion ($\Delta\rho[\text{aug}-\text{raptor}]=+0.241$ {\footnotesize[+0.170,+0.309]}), and the composite \texttt{pac} likewise beats dispersion ($+0.166$ {\footnotesize[+0.116,+0.215]}). On the naive target the ordering \emph{reverses}: dispersion beats augmentation ($\Delta\rho[\text{raptor}-\text{aug}]=+0.234$ {\footnotesize[+0.189,+0.284]}). All three contrasts are significant under the five-seed protocol. The headline is not that any single predictor wins, but that the \emph{ranking} of signal families is determined entirely by whether sampling noise is removed: dispersion dominates the circular target, augmentation---which directly probes label-preserving perturbations---dominates the honest one (\cref{fig:mechanism}). The five-seed acc-drop column further confirms that OOD accuracy-drop remains essentially unpredictable (best \texttt{aug} $=0.18$, weak; and $0.06$ under leave-one-concept-out, i.e.\ it does not generalize across concepts). \begin{figure}[t] \centering \includegraphics[width=0.92\linewidth]{figures/fig3_mechanism.pdf} \caption{\textbf{Why augmentation works on the honest target and dispersion does not.} Left: \texttt{raptor} (dispersion) vs.\ \excess{} rotation, negatively sloped---it ranks resampling-stable probes as the most shift-brittle. Right: augmentation-robustness vs.\ \excess{} rotation, positively sloped. Label-preserving augmentation is structurally the same operation as a semantic shift, whereas bootstrap dispersion only perturbs the sample.} \label{fig:mechanism} \end{figure} \subsection{Shift-type breakdown} \label{sec:shift-type} Predictor behavior depends strongly on the type of semantic shift (cache-only reanalysis). For \emph{paraphrase} shift ($n=472$), \texttt{raptor\_stability} reaches $0.945$ on naive rotation but is circular as above. For \emph{domain} shift ($n=65$), predictability is weak (\texttt{raptor} $=0.59$). For \emph{length} shift ($n=30$), all signals are high (\texttt{aug} $0.95$ / \texttt{pac} $0.95$ / \texttt{raptor} $0.92$). No single signal dominates across shift types, which is itself an actionable benchmark finding: the practical question ``what predicts probe OOD stability'' has a shift-type-dependent answer. \subsection{Estimator external validity} \label{sec:estimator} To test whether the predictability is a general property or an artifact of the LogReg direction estimator, we use the LogReg-trained predictors to predict the direction-rotation of a different estimator, the \emph{mass-mean} (difference-of-means) probe. Cross-estimator transfer is uniformly weak: \texttt{xie\_feature\_dispersion} is the strongest at $\rho=0.47$, with the rest in the $0.25$--$0.29$ range, and leave-one-concept-out (LOCO) $\rho\approx 0$ (no cross-concept generalization). Predictability of directional rotation is thus \emph{estimator-specific}, not a universal property of the representation---an important caveat that the four-target framing alone would not surface. \subsection{Size ladder and the 6.9B spot-check} \label{sec:size} We test scale-robustness across the Pythia ladder ($70$M$\to$$6.9$B) plus GPT-2 and Qwen (\cref{fig:sizeladder}). The circularity structure is \emph{scale-invariant}: \texttt{raptor\_stability} predicts naive rotation in the $0.83$--$0.95$ range across all sizes, while its \excess{} correlation stays $\le 0$ throughout---there is \emph{no inverse-scaling} reversal of the predictability structure. A $6.9$B spot-check (\texttt{pythia-6.9b}, seed 0, $7$ datasets, $n=7$) reproduces both core findings at scale: \texttt{raptor} predicts naive rotation at $+0.93$ (still circular), is anti-predictive on \excess{} ($-0.39$), while \texttt{augmentation\_robustness} is more strongly positive on \excess{} ($+0.68$). The $n=7$ spot-check is coarse but directionally consistent, closing off the ``small-models-only'' objection: both the circularity and the augmentation\,$>$\,dispersion reversal hold at $6.9$B, with the augmentation advantage \emph{amplified}. \begin{figure}[t] \centering \includegraphics[width=0.92\linewidth]{figures/fig2_sizeladder.pdf} \caption{\textbf{No inverse scaling.} Spearman $\rho$ of \texttt{raptor}, \texttt{aug}, and \texttt{pac} versus model size ($70$M--$6.9$B), on the naive (left) and \excess{} (right) targets. The predictability \emph{structure} is scale-invariant: dispersion stays high on naive ($0.83$--$0.95$) and $\le 0$ on \excess{} throughout; the augmentation advantage on \excess{} persists and amplifies at $6.9$B.} \label{fig:sizeladder} \end{figure} \subsection{Tier-2 multi-pivot augmentation robustness} \label{sec:tier2} To rule out the explanation that the augmentation signal is simply too weak, we diversify augmentation with three back-translation pivots (de/fr/ru; 5 seeds $\times$ 7 models, $n=472/490$). Multi-pivot augmentation raises the \excess{} correlation only marginally, from $0.046$ (single-aug) to $0.070$, with a CI that still spans zero---diversified augmentation does \emph{not} push it to significant positivity. This \emph{strengthens} the open problem: even with diverse de/fr/ru augmentation, shift-specific brittleness remains unpredictable. Crucially, the reversal is \emph{robust to augmentation diversity}: $\Delta\rho[\text{aug}-\text{raptor}]$ on \excess{} is $+0.247$ (vs.\ $+0.241$ for single-aug), still significant. Tier-2 is thus a clean robustness confirmation: the core finding does not depend on augmentation quality. \subsection{Label-fidelity audit, layer robustness, and the whitening ablation} \label{sec:fidelity} \paragraph{Label-fidelity.} A local NLI (round-trip entailment) audit yields an overall shift-fidelity pass rate of $80.6\%$. \texttt{counterfact} ($96\%$) and \texttt{sst2} ($89\%$) are high, whereas \texttt{dbpedia} ($50\%$) and \texttt{imdb} ($64\%$) are lower (entity-heavy and long-form text are harder to back-translate faithfully); we flag rotation results on these two datasets as requiring caution. \paragraph{Layer robustness.} Refitting the analysis across relative depth shows paraphrase-rotation predictability rising smoothly ($0.68\to0.71\to0.79\to0.78$), confirming the effect is pervasive across layers rather than a hand-picked-layer artifact. \paragraph{Whitening ablation.} Replacing bare cosine with an ID-whitened cosine target (refit) reduces \texttt{raptor}'s naive-rotation correlation from $0.945$ to $0.698$ (\texttt{whitened\_cosine\_id} now leads at $0.851$). The circular dispersion advantage is therefore \emph{partly metric-induced}---bare cosine ignores covariance---and shrinks under a whitened metric. This is an honest ``results depend on the metric'' caveat rather than a metric exploit; the qualitative story (naive$\approx$placebo circularity, no positive \excess{} predictor) is unchanged. \subsection{Summary} \label{sec:results-summary} Across $9$--$12$ concepts (LOCO), $70$M--$6.9$B scale (no inverse-scaling), metrics (whitened vs.\ bare cosine), and augmentation diversity (single vs.\ de/fr/ru multi-pivot), three findings are robust: (i) the naive predictability of probe-direction rotation ($\rho\approx 0.95$) is largely \emph{circular}, predicting an IID placebo equally well ($0.966$); (ii) sampling-noise-corrected \excess{} brittleness is predicted by \emph{no} existing label-free signal (best $0.046$--$0.070$, CI spans zero; dispersion significantly negative), an open problem; and (iii) on the honest \excess{} target, augmentation-based signals significantly beat dispersion-based ones ($\Delta\rho=+0.241$, five-seed-robust), exactly reversing their naive ordering. Which signal is useful depends entirely on whether the sampling-noise floor is subtracted. %================================================================ Discussion \section{Discussion} \label{sec:discussion} \subsection{Why naive predictability of probe-direction rotation is largely circular} The headline finding of \probeshift{} is a separation that prior work could not see, because prior work never built the placebo control. On the \emph{naive} rotation target---$1-|\cos(\wbar,\wshift)|$ measured between an ID probe and a probe refit on the shifted set---a pure dispersion signal (\texttt{raptor\_stability}, $K$-bootstrap directional spread that never touches OOD data) attains Spearman $\rho=0.945$ ($95\%$ CI $[.93,.95]$, $n{=}472$, 5 seeds; \cref{tab:fourtarget}). Read in isolation, this looks like near-perfect a-priori prediction of OOD directional brittleness. It is not. The same predictor scores \emph{higher}, $\rho=0.966$ $[.96,.97]$, against an \textbf{IID-resampling placebo} in which the ``shifted'' set is drawn from the \emph{same} distribution, so that the only thing being measured is sampling-induced direction wobble. Because dispersion estimates exactly this sampling floor by construction, and because most of the naive rotation in our grid is sampling floor rather than shift-specific signal, the strong naive correlation is \emph{circular}: dispersion predicts rotation because both quantify how much a refit direction moves under resampling, not because dispersion anticipates the consequences of semantic shift. \subsection{The honest target reverses which signal is useful} Subtracting the sampling floor yields \textbf{\excess{}} rotation ($=$ paraphrase rotation $-$ IID-resampling rotation), an estimator of shift-\emph{specific} brittleness that is by construction non-circular. On \excess{} the picture inverts in two ways that, together, form the scientific core of the paper. First, \emph{nobody predicts \excess{} positively}. The best predictor is the augmentation signal at $\rho=0.046$ ($95\%$ CI $[-.04,.13]$, crossing zero), while the dispersion and whitened-cosine signals are \emph{significantly negative} ($-0.195$ $[-.29,-.12]$ and $-0.245$ $[-.34,-.16]$). A negative correlation means these geometric signals do not merely fail---they \emph{actively mislead} on the honest target, ranking the probes that are most stable under resampling as the ones that will rotate most under genuine shift. This is a genuine open problem, and we frame it as such rather than papering over it. Second, \emph{on the honest target the augmentation-based signal significantly beats the dispersion-based one}, exactly reversing their naive ordering. The paired bootstrap contrast is $\Delta\rho[\text{aug}-\text{raptor}]=+0.241$ ($95\%$ CI $[+0.170,+0.309]$), and $\Delta\rho[\text{pac}-\text{raptor}]=+0.166$ $[+0.116,+0.215]$, both significant and robust across five seeds; on naive rotation the contrast runs the other way ($\Delta\rho[\text{raptor}-\text{aug}]=+0.234$ $[+0.189,+0.284]$). The mechanism is interpretable: label-preserving augmentation directly probes how the concept direction moves when inputs are perturbed \emph{while their label is held fixed}, which is structurally the same operation as a semantic shift; bootstrap dispersion only perturbs the \emph{sample}, so it can only ever recover the sampling floor that \excess{} removes. Thus ``which a-priori signal is useful'' is not an absolute property of a predictor---it depends entirely on whether the sampling floor has been subtracted (\cref{fig:mechanism}). \subsection{Robustness of the two findings} Both the circularity result and the aug${>}$dispersion reversal survive every stress test we ran. \begin{itemize}[leftmargin=1.4em] \item \textbf{Augmentation diversity (Tier~2, de/fr/ru multi-pivot).} Diversifying back-translation lifts the aug \excess{} correlation only from $0.046$ to $0.070$ (CI still crosses zero), so a richer augmentation does \emph{not} rescue positive predictability---ruling out ``the augmentation was too weak'' as an explanation for the open problem. The reversal, however, is robust to diversity: $\Delta\rho[\text{aug}-\text{raptor}]=+0.247$ on \excess{} (vs.\ $+0.241$ at 1-aug), significant. \item \textbf{Scale (70M--6.9B, no inverse scaling).} Across the Pythia ladder plus GPT-2 and Qwen, the naive dispersion correlation stays in $0.83$--$0.95$ and the \excess{} correlation stays $\le 0$ throughout; the predictability \emph{structure} is invariant to scale, contradicting an inverse-scaling story (\cref{fig:sizeladder}). At 6.9B (\texttt{pythia-6.9b}, seed 0, $n{=}7$) the pattern holds and the augmentation advantage \emph{amplifies}: \texttt{raptor} naive $+0.93$ (still circular), \excess{} \texttt{raptor} $-0.39$ (still anti-predictive), \excess{} aug $+0.68$ (stronger positive). \item \textbf{Concepts (LOCO over 9--12 concepts).} The qualitative ordering is preserved under leave-one-concept-out; the 9-concept analysis additionally exposes which signals are concept-overfit (whitened-cosine LOCO $0.21$, xie LOCO $0.03$) versus cross-concept robust (\texttt{raptor} $0.88$, \texttt{pac} $0.81$, aug $0.69$ on the naive target), which is itself a useful G2 product. \item \textbf{Metric (whitening).} \excess{} conclusions are not an artifact of bare cosine: re-running rotation under an ID-whitened cosine target moves \texttt{raptor} from $0.945$ to $0.698$, narrowing---but not eliminating---the circular advantage. We report this as an honest ``results depend on the metric'' caveat rather than claiming the bare-cosine choice is privileged. \end{itemize} \subsection{Positioning and takeaways} We deliberately do not claim to propose the strongest predictor of probe OOD stability; the prior-art landscape (RAPTOR-style dispersion, Probing-the-Probes augmentation robustness, SIP eigengaps, Fragility, Xie Dispersion-Score) is crowded enough that such a claim would be punctured. Our contribution is a \emph{benchmark plus a circularity revelation plus an open problem}: (i) a unified, label-free grid on which existing a-priori signals can be compared apples-to-apples; (ii) the demonstration, via the IID-resampling placebo, that the apparently strong naive predictability of directional brittleness is mostly a sampling-noise mirage; and (iii) the honest, non-circular \excess{} target on which \emph{no} existing signal predicts positively, yet on which augmentation-based signal significantly dominates dispersion-based signal. Practitioners who want to know, before deployment, whether a probe direction will survive paraphrase shift should treat current dispersion/whitened-geometry scores with suspicion: on the honest target they are negatively correlated with the outcome they are advertised to anticipate. %================================================================ Limitations \section{Limitations} \label{sec:limitations} \paragraph{Shift-specific brittleness is, in absolute terms, not yet predictable.} We are explicit that \excess{} is an open problem, not a solved one. The single positive signal (augmentation, $\rho=0.046$; $0.070$ with multi-pivot) has a confidence interval that crosses zero in every configuration. The reversal $\text{aug}>\text{dispersion}$ is a \emph{relative} statement about which family of signals is less wrong; it must not be read as ``augmentation reliably predicts shift-specific rotation.'' Our headline is a comparative and a negative result, and we report it as such. \paragraph{Predictability is estimator-specific, not a general property.} The strong naive correlations are tied to the logistic-regression estimator used to fit directions. When the same a-priori predictors are used to predict \emph{mass-mean} direction rotation, all of them are weak (best is xie at $0.47$; the rest $0.25$--$0.29$) and LOCO collapses to $\approx 0$ (no cross-concept generalization). Whatever predictability exists is therefore a property of a particular estimator's geometry rather than of probe directions in general---an important caveat against over-generalizing our LogReg results. \paragraph{Label-fidelity is uneven across datasets.} Our NLI round-trip audit passes at $80.6\%$ overall, but is high on \texttt{counterfact} ($96\%$) and \texttt{sst2} ($89\%$) and notably low on \texttt{dbpedia} ($50\%$) and \texttt{imdb} ($64\%$), where entity-heavy or long back-translations frequently break label preservation. Rotation measured on these two datasets should be interpreted with caution; their shifts are not cleanly label-preserving, and we flag (rather than hide) this. We treat the NLI audit as a sanity check, not a novelty claim, and cite the overgenerate-and-filter / round-trip lineage (Falsesum, DISCO) accordingly. \paragraph{The 6.9B evidence is a spot-check.} The 6.9B result rests on a single seed and only $n=7$ dataset cells, which is too coarse for confidence intervals. We report it only as a directional consistency check ($\text{circularity}+\text{aug}{>}\text{dispersion}$ both persist and the aug advantage grows); we do \emph{not} draw scaling-law conclusions from it, and the full size ladder is where the no-inverse-scaling claim actually rests. \paragraph{The paraphrase \excess{} analysis rests on a single back-translation pivot family.} The 5-seed \excess{} results (\cref{tab:fourtarget}) use single-pivot back-translation; Tier~2 extends this to de/fr/ru but only confirms the same qualitative picture. We do not claim coverage of the full space of paraphrase generators (e.g., instruction-tuned LLM rewriters), and a systematically different paraphrase operator could in principle shift the absolute \excess{} numbers even if, as Tier~2 suggests, the relative ordering is stable. Similarly, our shift-type split shows predictor behavior depends strongly on shift type---paraphrase ($n{=}472$, circular), domain ($n{=}65$, weak: \texttt{raptor} $0.59$), length ($n{=}30$, uniformly high: aug/pac/raptor $0.95/0.95/0.92$)---and the domain and length arms have small $n$, so their conclusions are weaker than the paraphrase arm's. %================================================================ Future work \section{Future Work} \label{sec:future} The open problem we isolate---\emph{predicting shift-specific (\excess{}) directional brittleness without touching OOD data}---suggests several concrete directions. (1)~Because augmentation is the only family with a non-negative \excess{} signal, the most promising avenue is augmentation operators that more faithfully simulate the target shift (instruction-tuned rewriters, controllable domain/length transforms) coupled with NLI-gated label-fidelity, aiming to push the augmentation correlation's CI off zero. (2)~The estimator-specificity result motivates predictors defined directly on the geometry of \emph{difference-of-means} and MLP probes, since LogReg predictability does not transfer. (3)~The partial metric-dependence under whitening ($0.945\!\rightarrow\!0.698$) invites a principled treatment of which covariance structure the rotation metric should quotient out, ideally one that removes the sampling floor analytically rather than via the empirical IID-resampling subtraction we use here. (4)~Strengthening the domain ($n{=}65$) and length ($n{=}30$) arms and the 6.9B spot-check ($n{=}7$) to seed-replicated grids would let the shift-type-dependence and scale-invariance claims carry confidence intervals as tight as the paraphrase arm's. %================================================================ Reproducibility \section{Reproducibility} \label{sec:reproducibility} \probeshift{} is designed for minutes-to-reproduce verification on commodity hardware. We release, under a permissive license: (i)~the full \textbf{activation cache} (one forward pass per configuration, shared across all predictors), so that every number in \cref{tab:fourtarget,tab:paired,fig:circularity,fig:mechanism,fig:sizeladder} can be recomputed from cache without GPU inference; (ii)~the complete \textbf{code} for activation extraction, probe fitting (LogReg / mass-mean / MLP), the seven label-free predictors, the IID-resampling placebo, the \excess{} target, and the bootstrap / paired-contrast statistics; (iii)~the \textbf{pre-registration} document fixing the four-target design, the predictor list, and the LOCO / five-seed protocol \emph{before} the main run, so that the circularity finding and the reversal are confirmatory rather than post-hoc; and (iv)~the exact \textbf{data splits} (per-concept ID/shift/placebo indices, the five independent seeds, and the de/fr/ru multi-pivot back-translation outputs with their NLI round-trip fidelity labels). The headline grid uses Option~A (five fully independent seeds, $n=472$); each reported confidence interval is a $10$k-sample bootstrap over the shared configuration set, and all paired contrasts share the configuration index so they are directly comparable. The entire pipeline runs on a single RTX~4090 within $\leq\!200$ GPU$\cdot$h, with \$0 API spend and zero new human annotation; cache-only reanalysis (shift-type breakdown, estimator external validity, layer robustness, whitening ablation) runs in minutes. %------------------------------------------------------------------- Bibliography % Replace with the PMLR/COLT .bst and a real .bib for camera-ready. \bibliographystyle{plainnat} \bibliography{references} % Fallback inline bibliography so the document compiles without a .bib file. % Delete this block once references.bib is provided. \begin{thebibliography}{9} \bibitem[Belinkov(2022)]{belinkov2022probing} Y.~Belinkov. \newblock Probing classifiers: Promises, shortcomings, and advances. \newblock \emph{Computational Linguistics}, 2022. \bibitem[Gao et~al.(2026)]{gao2026raptor} Gao et~al. \newblock RAPTOR: Ridge-adaptive directional stability for probe reliability. \newblock \emph{Preprint}, 2026. \bibitem[Huang(2025)]{huang2025sip} Huang. \newblock Spectral identifiability of probes (SIP). \newblock \emph{Preprint}, 2025. \bibitem[Kumar et~al.(2022)]{kumar2022unreliable} Kumar et~al. \newblock On the unreliability of probing-based interpretations. \newblock \emph{Preprint}, 2022. \bibitem[Lysn{\ae}s-Larsen et~al.(2025)]{lysnaes2025probing} Lysn{\ae}s-Larsen et~al. \newblock Probing the probes: Augmentation robustness as a probe-quality metric. \newblock \emph{Preprint}, 2025. \bibitem[Reblitz-Richardson(2026)]{reblitz2026fragility} Reblitz-Richardson. \newblock Forward-pass fragility thresholds for linear probes. \newblock \emph{Preprint}, 2026. \bibitem[Xie et~al.(2023)]{xie2023feature} Xie et~al. \newblock Feature dispersion score for label-free OOD-error prediction. \newblock \emph{Preprint}, 2023. \end{thebibliography} \end{document}