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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...
arXiv:2606. 01443v1 Announce Type: cross Abstract: A central difficulty in training Joint-Embedding Predictive Architectures (JEPAs) is preventing representation collapse.
The paper investigates the use of the squared norm of a whitened foundation‑model embedding as a training‑free likelihood surrogate. It shows that the apparent Gaussianity of whitened coordinates stems from the projection central limit theorem, not from a true joint Gaussian distribution, and that the norm is systematically over‑dispersed compared to a Gaussian reference. The authors explain that whitening reverses the encoder’s spectral hierarchy, concentrating norm contributions in near‑degenerate directions dominated by noise, and propose interpreting the squared norm as a Mahalanobis measure of semantic atypicality rather than a log‑likelihood.
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...
The paper introduces the spherical Cauchy distribution as a new hyperspherical posterior for variational autoencoders, avoiding the complications of the von Mises–Fisher and Power Spherical alternatives. By using stereographic projection and a Möbius transformation, the authors obtain exact posterior samples and a closed‑form KL divergence that terminates in a finite polynomial for even dimensions and admits certified truncation for odd dimensions. Empirical results show that the spherical Cauchy yields faster inference and lower reconstruction loss on MNIST and improved negative log‑likelihood on smallNORB compared to existing methods.
The paper introduces the Geometric Observability Index (GOI), a per-feature sensitivity metric for SE(3) pose estimation that quantifies the pose perturbation induced by a single measurement via the Gauss‑Newton curvature restricted to the observable subspace. GOI is shown to equal the norm of the M‑estimator influence function, to coincide with the Fisher information operator, and its smallest observable eigenvalue determines both worst‑case measurement amplification and a finite‑sample stability radius. Experiments on synthetic data and real RGB‑D/KITTI sequences validate that GOI accurately predicts leave‑one‑out pose shifts and explains the robustness of residual gating while highlighting the pitfalls of raw‑influence gating in weakly observable geometries.