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.
arXiv:2506. 21278v3 Announce Type: replace-cross Abstract: We propose spherical Cauchy (spCauchy) latent variables for variational autoencoders on hyperspherical latent spaces.
arXiv:2606. 17603v1 Announce Type: new Abstract: In Self-Supervised Learning (SSL), preventing representation collapse by explicitly enforcing a uniform distribution on the unit hypersphere has proven to be effective.
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...
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:2607. 05531v1 Announce Type: new Abstract: Variational Autoencoders (VAEs) frequently suffer from posterior collapse, a failure mode in which the approximate posterior converges to the prior, rendering the latent code uninformative.
arXiv:2511. 01064v3 Announce Type: replace-cross Abstract: Variational inference (VI) approximates a target density $p$ by the best match $q$ in a family of tractable distributions.
The paper addresses a flaw in latent‑variable generative models on Riemannian manifolds such as spheres and hyperbolic spaces, where the usual practice of sampling a Gaussian in a tangent space and mapping it onto the manifold inadvertently imposes a fixed chi‑distribution on distances from a base point. The authors formulate and solve the inverse problem: given a desired distance distribution, they derive the exact tangent‑space density that yields it, prove its uniqueness for isotropic, chart‑independent likelihoods, and provide a lower bound on the cost of ignoring this issue in variational autoencoders. Experiments with exact normalization audits show that the compensated prior is chart‑invariant, stable across scales, and leads to significant improvements in curvature recovery and protein‑orientation likelihoods. whyItMatters":"By correcting the implicit distance distribution, the method enables more accurate and stable generative modeling on curved spaces, directly improving performance on tasks such as protein orientation."
arXiv:2605. 05629v3 Announce Type: replace-cross Abstract: We study the problem of learning generative models for discrete sequences in a continuous embedding space.
arXiv:2606. 01443v1 Announce Type: cross Abstract: A central difficulty in training Joint-Embedding Predictive Architectures (JEPAs) is preventing representation collapse.
arXiv:2608. 02668v1 Announce Type: cross Abstract: Residual connections are the de facto mechanism for training deep neural networks stably.
arXiv:2608. 15215v1 Announce Type: cross Abstract: Token-level knowledge distillation (KD) matches two conditional distributions per position, yet the standard objectives compare them pointwise: a Kullback-Leibler gradient is blind to which wrong token receives probability mass.
arXiv:2608.22334v1 Announce Type: new Abstract: Near a smooth data manifold, one tangent space summarizes local geometry. At a branch point, the corresponding first-order object is instead a measure...