arXiv Statistics ML
The Geometry of Anisotropic Dilation for Optimal Regularization
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arXiv Machine Learning
Jul 9
Statistical inverse learning and $\ell^1$-regularization
arXiv:2607. 07468v1 Announce Type: cross Abstract: We study the recovery of sparse functions from finite, noisy, and indirect observations in the framework of statistical inverse learning.
arXiv Machine Learning
Jun 17
Expanding SPHERE-JEPA: A Family of Statistical Regularizers for the Hypersphere
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 AI
Aug 25
Radial Compensation: The Inverse Base-Distribution Problem for Chart-Based Generative Models on Riemannian Manifolds
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 Machine Learning
Jun 30
A Distributionally Robust Framework for Learned Reconstructions in Inverse Problems
arXiv:2606. 30230v1 Announce Type: cross Abstract: Learned reconstruction operators for inverse problems are typically trained under a fixed noise model, and generalize poorly when the distribution during testing differs from the one assumed during training.
arXiv AI
Sep 10
Newton Matching for Generative Modeling: A Unified Framework for Fine-Tuning and Sampling
arXiv:2609.05727v1 Announce Type: cross Abstract: We develop Newton Matching, a unified framework for fine-tuning and sampling in generative modeling. The target is $\pi\propto\mu e^{\tau r}$, where...
arXiv Machine Learning
Jul 3
Regularized Variational and Spectral Log-Density-Ratio Estimation in the Gaussian Location Model
arXiv:2607. 01895v1 Announce Type: new Abstract: We study ridge-regularized log-density-ratio estimation in the Gaussian location model with a common covariance matrix.