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Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection

Shashank Kotyan, Makoto Shing, Yuki Imajuku, Rujikorn Charakorn, Tarin Clanuwat

arXiv:2608.18523v1cs.CVcs.AI

TL;DR

AIGI detectors must transfer across simultaneous shifts in generator, prompt/style, and source domain, often with limited new labeled data. This paper evaluates prior-conditioned Gaussian discriminant heads on frozen features and finds them often competitive with trained heads, sometimes surpassing released heads under matched conditions.

  • Problem

    AIGI detectors face joint shifts in generator, prompt/style, and source domain, while collecting labeled data from emerging generators can be expensive or infeasible.

  • Method

    The paper fits a closed-form Gaussian discriminant ladder on frozen encoder features, conditioning heads on training priors while varying covariance assumptions.

  • Results

    Across 39 public test sets (7.1 million images), at least one rung is often competitive with trained heads under matched priors and frozen encoders, and can surpass released heads in several settings.

  • Takeaways & Limitations

    The findings support comparing trained heads with the best Gaussian rung on the same representation and support prior before attributing out-of-distribution gains to classifier training.

  • Takeaways & Limitations

    The Gaussian ladder is a diagnostic baseline restricted to Gaussian class-conditional approximations using first- and second-order statistics, so nonlinear heads can outperform it.

Abstract

from arXiv · show

Diffusion-based generators have made synthetic images ubiquitous, but detectors often fail under simultaneous shifts in generator, prompt/style, and source-domain. We study AI-generated image detection as a transfer system described by training prior, frozen encoder feature space, and decision rule, and ask when classifier head training adds value beyond what is already separable in modern features. As a controlled diagnostic, we fit a prior-conditioned Gaussian discriminant ladder: closed-form heads built from first- and second-order feature statistics under nested covariance assumptions. On Percept-Lens, a unified protocol over 39 public datasets (7.1 million images), the best rung is frequently competitive with, and sometimes exceeds, released AI-generated image detector heads when matched on both prior and encoder. We further quantify strong sensitivity to the training prior, data-efficiency of moment-based heads, and representation dependence of Gaussian shift metrics, motivating (prior, encoder, head)-level reporting and stronger analytical baselines for AIGI transfer.

1. Introduction

The paper frames AI-generated image detection as a transfer and low-shot recognition problem under simultaneous shifts in generators, prompting, platforms, post-processing, and source domains. It evaluates prior-conditioned Gaussian discriminant heads on frozen features, showing that matched classical heads can rival or surpass trained detector heads while exposing dependence on prior, encoder, and representation.

  • Problem: AIGI detection must transfer across co-occurring shifts in generator family, prompting style, platform, post-processing, and image-source domain, often with limited labeled data.These conditions can cause performance collapse despite strong in-distribution metrics and make new-generator data collection expensive or infeasible.
  • System-level view: Reported detector performance is treated as a property of a training prior, frozen image encoder, and decision rule rather than the head alone.The paper argues that narrow evaluations can conflate genuine generalization with prior-specific shortcuts.
  • Method: The Gaussian discriminant ladder fits closed-form heads from first- and second-order frozen-feature statistics under isotropic, diagonal, shared-full, and class-specific-full covariance assumptions.Its best-transfer rung provides an interpretable diagnostic of which low-order feature statistics remain preserved under shift.
  • Evaluation and implications: The controlled evaluation compares released detector heads with the ladder under matched priors and encoders, while quantifying prior sensitivity, few-shot moment-head adaptation, and representation-conditioned Gaussian shift metrics.This isolates when trained heads add value beyond low-order feature geometry and motivates reporting prior, encoder, and head together.
  • Empirical findings: 39 public test sets and 7.1 million images show that at least one ladder rung is often competitive with trained heads under matched priors and frozen encoders.In several settings, the best rung surpasses released heads, serving as a retrospective diagnostic upper bound.

2. Related Works

Related work spans artifact- and representation-based AIGI detectors, while this paper instead diagnoses how much frozen feature space already separates classes and what classifier heads add under matched priors and encoders. It adapts classical Gaussian and Mahalanobis ideas into a prior-conditioned covariance ladder for interpreting transfer across generator and domain shifts.

  • AIGI detection includes artifact-driven and representation-based detectors, with early work targeting GAN-era artifacts and domain-specific face forgeries.
  • The paper replaces the classifier in feature space while matching the training prior and encoder, emphasizing frozen-space separability and head value rather than another trained detector.
  • Gaussian discriminant analysis and Mahalanobis scoring provide classical foundations for uncertainty and out-of-distribution detection, alongside nearest-centroid inference and orthogonal subspace adaptation.
  • The diagnostic ladder uses isotropic, diagonal, tied, and class-specific covariance assumptions, increasing geometric expressivity to interpret transfer across generator and domain shifts.

3. Preliminaries

The paper formulates AI-generated image detection as binary classification of real versus synthetic images, using frozen foundation-model features and learned decision rules. It contrasts supervised discriminative heads with Gaussian discriminant classifiers while noting that flexible heads may overfit generator-specific artifacts.

  • Problem formulation: AIGI detection predicts whether a previously unseen image is real (y = 0) or synthetic (y = 1) from labeled training data.The task is defined as binary image classification over a training set of images and labels.
  • Feature-space classification: Images are mapped by a frozen pre-trained foundation-model encoder to D-dimensional features, on which standard linear probes learn a separating hyperplane using binary cross-entropy.The linear head optimizes weights w and bias b with a sigmoid decision function.
  • Generalization limitation: MLPs can learn nonlinear decision boundaries, but discriminative heads may overfit artifacts specific to training generators and generalize poorly to unseen generative processes.This limitation motivates comparing learned discriminative detectors with analytical classifiers fitted on frozen features.
  • Detector comparison: The study compares supervised discriminative detectors trained on a given prior with Gaussian discriminant rule classifiers fitted on frozen features, including released systems with exposed final representations.The audited systems span frequency/statistical, reconstruction-based, LoRA-adapted, and end-to-end detectors.

4. Prior-Conditioned Gaussian Discriminants as Few-Shot Discriminant Heads

The section introduces a closed-form Gaussian discriminant ladder that isolates how first- and second-order statistics support classification in a frozen encoder space. Its analytical guarantees are model-conditional, and its limitations motivate trained nonlinear heads when features are multimodal or heavy-tailed.

  • Construction: The ladder estimates class means and covariances from a support set drawn from the training prior, then restricts covariance structure to obtain closed-form discriminant rules.The pooled covariance is used for shared-covariance models, while covariance inversion and log-determinants use diagonal loading and shrinkage.
  • Interpretation: The best-performing covariance assumption indicates which feature statistics transfer across domains, while bypassing iterative head training.The same estimation extends to N-way K-shot classification, although the paper focuses on binary AIGI detection.
  • Construction: The five heads are Euc-NCM, Cos-NCM, GNB, Mah-NCM, and QDA, spanning isotropic, diagonal, shared full, and class-specific full covariance assumptions.Euc-NCM mirrors prototypical-network inference directly in frozen feature space, while QDA permits class-specific covariance matrices and quadratic decision boundaries.
  • Theory: Under Gaussian class-conditionals and equal priors, QDA is Bayes-optimal; with shared covariance, the optimal rule simplifies to Mah-NCM.These guarantees are explicitly conditional on frozen features being well approximated by Gaussian class-conditionals.
  • Theory: Mah-NCM has the same separating-hyperplane form as a cross-entropy-trained linear probe, differing in optimization because it computes the boundary analytically from first- and second-order statistics.The comparison concerns matched representation and emphasizes optimization rather than representation as the key difference.
  • Limitations: The ladder is a diagnostic baseline rather than a universal detector because it omits higher-order, multimodal, and heavy-tailed cues that nonlinear or end-to-end methods can exploit.The Gaussian assumption is diagnostic rather than literal, with reported failures for FourierSpectrumDiscrepancies and DiffusionForensics-fake.

5. Investigating Generalization with Percept-Lens suite

Percept-Lens evaluates AI-generated image detectors under joint shifts in generator, prompt/style, and source domain across 39 public datasets totaling 7.1 million images. Results show that performance depends strongly on the training prior and encoder, while Gaussian heads often recover substantial discriminative geometry and expose representation-sensitive shift metrics.

  • Evaluation Datasets: Percept-Lens aggregates 39 public datasets totaling 7.1 million images with joint shifts in generator family, prompt/style, and image-source domain.The suite spans real-only, synthetic-only, and mixed regimes, including post-processing variation.
  • Gaussian ladder results: Across several priors, the best Gaussian discriminant often improves class accuracy, with Mah-NCM frequently capturing separation through first- and second-order moments.CF-384 is an exception: its released detector reaches 87.54% CA versus 84.55% for the ladder.
  • Practical reporting: Future evaluations should compare released heads with the best Gaussian rung on identical frozen features and priors, report per-dataset CA/AUC, and identify the encoder used for geometric metrics.The checklist also recommends flagging non-Gaussian feature regimes with diagnostic analyses.
  • Prior dependence: The best CA ranges from 77.92% for CNNSpot to 94.46% for CommunityForensics despite the same representation and evaluation suite.DRCT-2M favors QDA, whereas all other evaluated priors favor Mah-NCM, showing that the preferred covariance assumption shifts with the prior.
  • Data efficiency: 0.005% of the CommunityForensics prior, or 219 labeled samples, reaches 90.89% CA, indicating data-efficient moment-based adaptation with a strong representation.At extremely small support sizes, 0.001% of the prior or 44 samples, diagonal GNB can be more stable.
  • Representation dependence: Gaussian shift metrics are representation-dependent: ΔW2 increases by an order of magnitude across larger backbone changes, while its association with ΔCA is weak.Anisotropic rescaling can inflate Wasserstein distances without materially changing Mah-NCM’s effective decision geometry.

6. Conclusion · A. On the Computational Paradigm and Practical Utility of Gaussian Discriminants

The paper presents prior-conditioned Gaussian discriminants as practical baselines and diagnostics for AI-generated image detection under joint distribution shift. Their matched-prior, matched-encoder performance, deterministic fitting, and reduced optimization burden support reproducible head comparisons.

  • 6. Conclusion: The Gaussian ladder is often competitive with trained detector heads under matched priors and encoders, and sometimes exceeds them.The study supports matched head audits and controlled prior/encoder sweeps rather than a fully symmetric decomposition of every detector component.
  • A. On the Computational Paradigm and Practical Utility of Gaussian Discriminants: Fitting a Gaussian head requires estimating sample means and, when applicable, regularized covariances, followed by a single solve.Standard covariance regularization may use shrinkage or diagonal loading.
  • A. On the Computational Paradigm and Practical Utility of Gaussian Discriminants: The fitting procedure is deterministic and largely hyperparameter-light, without learning-rate schedules, early stopping, or multi-run optimization.Its main additional tuning concerns standard covariance regularization.
  • A. On the Computational Paradigm and Practical Utility of Gaussian Discriminants: Isotropic and diagonal heads require per-dimension statistics at O(ND), whereas full-covariance heads require covariance estimation at O(ND^2) and linear solves at O(D^3).Full-covariance costs can be non-trivial for very large D or N, but are paid once per (prior, encoder) pair rather than per training epoch.
  • A. On the Computational Paradigm and Practical Utility of Gaussian Discriminants: Gradient-based heads typically require many data passes and add variance from stochastic optimization and hyperparameter choices.This contrasts with the one-shot fitting of the Gaussian ladder.
  • A. On the Computational Paradigm and Practical Utility of Gaussian Discriminants: The Gaussian ladder provides a controlled baseline and diagnostic that reduces optimization confounds and makes head comparisons easier to reproduce.Its simplicity is treated as a practical feature for comparative evaluation.

B. Proofs of Theoretical Propositions

This section provides formal derivations for the theoretical propositions introduced in Section 4.1, using the notation defined in the main text.

  • B. Proofs of Theoretical Propositions: Formal derivations establish the propositions presented in the theoretical framework’s Section 4.1.The section is devoted to proving those propositions.
  • B. Proofs of Theoretical Propositions: The proofs adopt the notation defined in the main text.This keeps the derivations consistent with the paper’s established theoretical framework.
  • B. Proofs of Theoretical Propositions: The section connects the main text’s theoretical framework to its formal supporting derivations.Its role is to provide formal backing for the propositions stated earlier.

B.1. Proof of Proposition 1 (Bayes-Optimal Classifier under Gaussian Assumption) · B.2. Proof of Proposition 2 (Optimality under Homoscedasticity)

Under equal class priors and Gaussian class-conditional features, the Bayes-optimal classifier is QDA. With the additional homoscedasticity assumption, the quadratic rule becomes linear and is equivalent to Mahalanobis Nearest Centroid Matching.

  • B.1. Proof of Proposition 1 (Bayes-Optimal Classifier under Gaussian Assumption): QDA is therefore Bayes-optimal when class-conditional feature distributions are Gaussian with equal class priors.The simplified Gaussian discriminant is identified as the Quadratic Discriminant Analysis decision function.
  • B.1. Proof of Proposition 1 (Bayes-Optimal Classifier under Gaussian Assumption): Under equal class priors and Gaussian class-conditional densities, Bayes-optimal classification assigns each feature vector to the class with higher posterior probability.For binary classification, class 1 is selected when P(y=1|z) > P(y=0|z), and class 0 otherwise.
  • B.1. Proof of Proposition 1 (Bayes-Optimal Classifier under Gaussian Assumption): Equal priors and Bayes’ theorem reduce posterior comparison to comparing class-conditional likelihoods.The evidence term is a positive common denominator, while equal priors contribute identical multiplicative factors.
  • B.1. Proof of Proposition 1 (Bayes-Optimal Classifier under Gaussian Assumption): The resulting log-likelihood-ratio rule classifies as class 1 when g*(z) > 0 and as class 0 otherwise.The Gaussian PDF and corresponding class log-likelihood are substituted into the decision function before simplification.
  • B.2. Proof of Proposition 2 (Optimality under Homoscedasticity): Mahalanobis Nearest Centroid Matching is therefore Bayes-optimal under the homoscedastic Gaussian assumption.The simplified linear discriminant is identified as the Mah-NCM decision function.
  • B.2. Proof of Proposition 2 (Optimality under Homoscedasticity): Under homoscedasticity, Σ0 = Σ1 = Σp, applying the shared covariance assumption to QDA cancels the quadratic terms.The resulting decision rule is derived by simplifying the QDA quadratic forms.
  • B.2. Proof of Proposition 2 (Optimality under Homoscedasticity): Homoscedasticity linearizes the decision boundary, with w = Σp^-1(μ1 − μ0) and an intercept determined by the class means.The intercept is b = −1/2(μ1 + μ0)^T w = −1/2(μ1 + μ0)^TΣp^-1(μ1 − μ0).

B.3. Proof Sketch for Proposition 3 (Performance Stability under Bounded Drift) · B.4. Proof of Proposition 4 (Stability of the Fisher Margin under Distributional Drift) · C. Analytical Forms of the Gaussian Discriminant Ladder

The proofs establish that bounded drift in class means and covariance yields controlled AUC and Fisher-margin changes through smooth Gaussian-discriminant relationships. The analytical ladder defines support-conditioned Gaussian heads, default prior handling, and nested covariance choices from Euc-NCM through QDA.

  • B.3. Proof Sketch for Proposition 3 (Performance Stability under Bounded Drift): Under bounded mean and covariance drift, |AUCtest − AUCtrain| ≤ L(ϵμ + ϵΣ).The bound applies to a homoscedastic classifier with shared covariance and equal priors.
  • B.3. Proof Sketch for Proposition 3 (Performance Stability under Bounded Drift): For Gaussian classes, AUC is expressed through the score difference, and Mah-NCM reduces this relationship to the Fisher margin Dμ.The Fisher margin is Dμ = (μ1 − μ0)⊤Σ^-1(μ1 − μ0).
  • B.3. Proof Sketch for Proposition 3 (Performance Stability under Bounded Drift): AUC is locally Lipschitz when Σ is invertible, because the Fisher margin, square root, and normal CDF form a locally Lipschitz composition.The experiments ensure invertibility by using n >> d; shrinkage is suggested for n << d.
  • B.3. Proof Sketch for Proposition 3 (Performance Stability under Bounded Drift): The Lipschitz constant depends on local derivatives of AUC, critically including the spectral norm of the inverse covariance, ∥Σ^-1∥2.The deviation is decomposed into mean- and covariance-drift contributions before combining them into the stated bound.
  • B.4. Proof of Proposition 4 (Stability of the Fisher Margin under Distributional Drift): To first order, Fisher-margin change is controlled by drift in the class-mean difference and pooled covariance.The proof expands Dμ around training parameters and bounds the resulting terms using norm inequalities.
  • B.4. Proof of Proposition 4 (Stability of the Fisher Margin under Distributional Drift): The Fisher-margin bound follows by evaluating gradients at training parameters, then separately bounding mean and covariance terms with Cauchy-Schwarz and Frobenius-inner-product inequalities.The two contributions are combined after applying the triangle inequality to the first-order expansion.
  • C. Analytical Forms of the Gaussian Discriminant Ladder: The ladder uses uniform class priors by default and spans Euc-NCM, Cos-NCM, Mah-NCM/LDA, and QDA covariance assumptions.Empirical priors are reported explicitly when used, while balanced metrics do not generally remove prior-induced decision offsets.

D. Details about existing datasets in our Percept-Lens evaluation suite · E. Extended Investigation of Generalization with Percept-Lens suite

Percept-Lens evaluates generalization across public datasets and combined generator-style, source-domain, and post-processing shifts, while excluding support priors. Extended analyses isolate the effects of matched priors and encoders, encoder scaling, and pretraining objectives on Gaussian discriminant transfer.

  • D. Details about existing datasets in our Percept-Lens evaluation suite: Percept-Lens uses public training and evaluation datasets, excludes support priors from evaluation, and combines generator-style, source-domain, and post-processing shifts.The evaluation suite is designed to move beyond single-generator-only shifts.
  • D. Details about existing datasets in our Percept-Lens evaluation suite: Full-covariance Mah-NCM and QDA rules use shrinkage or diagonal loading before covariance inversion and log-determinant computation.Stable pseudo-inverses truncate small singular values, addressing ill-conditioned estimates in high-dimensional and low-shot settings.
  • D. Details about existing datasets in our Percept-Lens evaluation suite: The same covariance estimator is applied across all priors and backbones to avoid confounding in data-efficiency comparisons.Regularization is especially necessary in the N < D regime, where empirical covariance estimates are unstable.
  • D. Details about existing datasets in our Percept-Lens evaluation suite: Table 9 summarizes public evaluation datasets by total, real, and synthetic images, including datasets containing only synthetic images.Reported synthetic-only datasets range from AGIQA-1k and AGIQA-3k to Dalle3 and Co-Spy-Bench.
  • D. Details about existing datasets in our Percept-Lens evaluation suite: Multiple transformations of one underlying image are treated as separate evaluation subsets, so resulting image counts are not interpreted as independent samples.This convention applies when source datasets provide multiple transformations or variants.
  • E. Extended Investigation of Generalization with Percept-Lens suite: Table 10 compares closed-form Gaussian discriminants with released detector heads under matched prior-and-encoder conditions using macro-averaged mean class accuracy.Released checkpoints are evaluated both with their original decision heads and with closed-form baselines fitted to the same frozen features and public training prior.
  • E. Extended Investigation of Generalization with Percept-Lens suite: Table 11 examines encoder scaling under a fixed CommunityForensics prior, changing only frozen CLIP encoder capacity without detector fine-tuning.The analysis tests how representation choice affects transfer while holding the training prior and Gaussian head setup fixed.
  • E. Extended Investigation of Generalization with Percept-Lens suite: Table 12 tests whether pretraining objective affects transfer under the same CommunityForensics prior, using frozen encoders trained with different objectives.No detector training is performed in this comparison.

Cos-NCM GNB Mah-NCM QDA

Across matched audits, Gaussian discriminant heads often outperform released detector heads, but performance depends more strongly on the training prior and frozen encoder than on the downstream head. Encoder-family and scale effects dominate activation-choice differences, while Mah-NCM is generally strongest with task-specific exceptions.

  • Matched head audit: 65.54% versus 46.92% CA for the full GenImage DRCT model, 59.93% versus 46.92% for DRCT-SDv1, and 62.02% versus 50.60% for DRCT-SDv2 after replacing released heads with closed-form Gaussian rules.These gains were measured on the same frozen ConvNeXt representation under matched prior and encoder conditions.
  • Encoder dependence: 79.41% versus 67.96% CA across ConvNeXt encoders and 89.28% versus 66.39% across ViT encoders under the same CommunityForensics prior without detector fine-tuning.These encoder spreads exceed many method-level gains, complicating head-only comparisons unless encoder choice is controlled; Mah-NCM is modal but not universal.
  • Representation dependence: 89.51% versus 59.57% best CA across PE-Core-L-14-336-meta and BeiT-Base, while DINOv3-ViTH16plus reaches 86.22% without detector-specific fine-tuning.The appendix frames these gaps as representation-centric rather than a clean causal statement about one pretraining objective.
  • Activation choice: Activation choice produces modest, inconsistent CA changes across matched QuickGELU and GELU encoder pairs, unlike the larger differences across encoder families.QuickGELU helps several models but does not explain the larger encoder-family effects.
  • Dataset-wise head performance: Mah-NCM is strongest on many mixed and synthetic-only benchmarks, while QDA leads on CelebA-Spoof, GNB on DiffusionForensics and DeepFakeBench, and cosine or Euclidean rules on a few synthetic-only datasets.The aggregate CA gains are broadly distributed across evaluation datasets rather than driven by a small subset of low-difficulty benchmarks.

F. Threshold-Free (AUC) Evaluation on Mixed Datasets in Percept-Lens suite

Threshold-free AUC evaluation preserves the main matched-head finding: Gaussian heads often improve ranking beyond released detector heads, though released heads remain stronger in some cases. Transfer depends strongly on encoder, training prior, and support size, while low-order feature geometry remains highly competitive without detector fine-tuning.

  • Matched-head AUC: CoDE-SVM improves from 0.3061 to 0.7039 AUC, while DRCT-ConvNeXt on full GenImage rises from 0.4977 to 0.7417.AIDE also improves from 0.4917 to 0.6787 on CNNSpot and from 0.5389 to 0.7082 on full GenImage, indicating ranking improvements rather than only threshold adjustments.
  • Matched-head AUC: 0.9693 AUC is achieved by PE-Core-bigG-14-448 with Mah-NCM, without detector fine-tuning.This is the strongest result reported in the threshold-free evaluation block.
  • Limits and interpretation: Released CF-224 and CF-384 heads remain marginally stronger than closed-form surrogates on AUC, while activation choice usually changes matched pairs by less than two AUC points.The threshold-free results therefore expose narrower but real residual value for trained heads and treat GELU versus QuickGELU as secondary to encoder family and scale.
  • Representation dependence: OpenAI CLIP best AUC rises from 0.7406 for ResNet-50 to 0.8345 for ResNet-50x64 and from 0.7147 for ViT-B/32 to 0.8193 for ViT-L/14.The broader OpenCLIP sweep spans 0.7076 to 0.9464, while pretraining families span 0.5715 for BeiT-Base to 0.9425 for PE-Core-L-14-336-meta.
  • Prior dependence: With PE-Core-bigG-14-448 fixed, best AUC varies from 0.9290 with CNNSpot support to 0.9693 with CommunityForensics support, and the preferred Gaussian rule changes by prior.CommunityForensics and ELSA-D3 favor Mah-NCM, DRCT-2M favors QDA or cosine, and GenImage favors cosine after correcting the row-wise maximum.
  • Data efficiency: At 0.001% CommunityForensics support, Cos-NCM reaches 0.9356 AUC while Mah-NCM drops to 0.8788; Mah-NCM reaches 0.9638 at 0.1% and 0.9668 at 1%.QDA is unstable and non-monotone under subsampling, supporting covariance rules matched to available support.

G. Class-Conditional Gaussianity Diagnostics of Evaluation Features

Class-conditional feature diagnostics show that evaluation features are not exactly Gaussian, yet first- and second-order summaries often capture useful class structure. Gaussian heads therefore function as controlled, interpretable probes rather than literal generative models.

  • Diagnostic scope: Diagnostics target class-conditional feature distributions rather than pooled features, because Gaussian class components can form a non-Gaussian mixture.The reported quantities are descriptive diagnostics, not calibrated hypothesis tests or evidence for accepting or rejecting exact normality.
  • Marginal diagnostics: Most dataset–class subsets have median skewness near zero, median Pearson kurtosis near three, and PctClose often above 97% in PE-Core-bigG-14-448 features.These results support Gaussian heads as approximate second-order models, but not exact density models.
  • Multivariate diagnostics: Multivariate deviations in normalized Mardia kurtosis occur disproportionately in fake subsets, which often also show lower effective rank and higher anisotropy than real subsets.The recurring pattern indicates variance concentration in fewer dominant directions, although it is not universal.
  • Interpretation: Evaluation features are not exactly Gaussian, but first- and second-order summaries describe useful class structure for many dataset–class subsets.Departures identify cases where higher-order or multimodal structure likely matters.
  • Methodological implication: With the support prior and frozen encoder fixed, Gaussian heads reveal how much head-level behavior is already available in low-order feature geometry.This interpretation does not claim that low-order geometry is the only transfer mechanism or that Gaussian assumptions hold globally.
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