The paper investigates how kernel-based metrics like KID and KAD perform as two‑sample tests on real embeddings of symbolic music, audio, and images. By applying mean shifts, isotropic contractions, and rotations to one sample, the authors find that the default kernels often fail to detect rotations at 780 samples per side, while they reliably detect mean shifts. Adjusting kernel bandwidths or using alternative kernels (e.g., narrower Gaussian, Laplace) restores sensitivity, and the authors recommend reporting the sample budget and detectable changes for any reported kernel distance.
arXiv:2608.24881v1 Announce Type: cross Abstract: Generative models are commonly ranked by Fr\'echet Inception Distance (FID) and Kernel Inception Distance (KID), yet FID's first-two-moment summary c...
arXiv:2608. 01268v1 Announce Type: cross Abstract: Detecting that a stream of high-dimensional embeddings has changed is usually framed as a choice of statistic.
arXiv:2610.05518v1 Announce Type: cross Abstract: The Fr\'echet distance is a de facto standard for evaluating generative models across domains, appearing as FID for images and FVD for videos. It sum...
DANCo (Dimensionality from Angle and Norm Concentration) jointly calibrates nearest-neighbor distance and angular statistics and consistently reaches state-of-the-art accuracy on clean intrinsic-dimen...
arXiv:2507. 12843v3 Announce Type: replace Abstract: Are two distributions close to each other with statistical significance?
arXiv:2609.37114v1 Announce Type: new Abstract: DANCo (Dimensionality from Angle and Norm Concentration) jointly calibrates nearest-neighbor distance and angular statistics and consistently reaches s...
The paper introduces Shared Gaussianization (SG), a characteristic‑function test that evaluates Gaussianity of the average of two normalized views scaled by an independent χ_d radius. SG detects both misalignment and non‑uniformity in contrastive learning, vanishing exactly at aligned, uniform minimizers of population InfoNCE, and provides a sharp, dimension‑free bound on InfoNCE excess. The study also explores how SG behaves under different kernels, alignment weights, batch sizes, and latent‑variable models, revealing optimization gaps and the impact of nuisance channels.
arXiv:2610.08277v1 Announce Type: cross Abstract: Deciding whether two samples come from the same distribution is a classical problem in statistics, and generative transport offers a new way to appro...
arXiv:2610.08533v1 Announce Type: cross Abstract: Geometric alignment scores based on Gram determinants provide a compact way to model higher-order consistency among modalities, yet how such scores r...
arXiv:2609.10224v1 Announce Type: new Abstract: Vision-language models such as CLIP embed images and text in a shared space, where modality-specific distributions often remain separated. Existing acc...
The paper introduces a unified framework for measuring divergences between conditional distributions using kernel embeddings, termed conditional maximum mean discrepancy (CMMD). It defines a family of CMMD metrics—CMMD_0, CMMD_1, and CMMD_2—each based on different RKHS embeddings, and generalizes them to a level‑s CMMD with clear assumptions and operator‑based smoothing connections. Additionally, the authors present a novel doubly robust estimator for CMMD and demonstrate through experiments that the metric captures complex conditional dependencies for statistical testing.
arXiv:2607. 24235v1 Announce Type: cross Abstract: Over the past 20 years, kernel discrepancies have been leveraged as a highly powerful tool for quantifying the disagreement of distributions, with numerous successful applications in two-sample, goodness-of-fit, and independence testing, among others.