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: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.
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: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: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:2607. 01895v1 Announce Type: new Abstract: We study ridge-regularized log-density-ratio estimation in the Gaussian location model with a common covariance matrix.
arXiv:2312. 15341v1 Announce Type: cross Abstract: We provide an overview of recent progress in statistical inverse problems with random experimental design, covering both linear and nonlinear inverse problems.
arXiv:2609. 03129v1 Announce Type: cross Abstract: Several classical machine-learning methods, such as KRRs and SVRs, are both computationally and analytically tractable since their estimators either admit closed-form expressions or are obtained by minimizing convex training objectives; neither feature is generally available for deep neural networks.
arXiv:2505. 07124v3 Announce Type: replace Abstract: We study inverse problems where an unknown potential is observed only through samples from the measure it induces by a convex variational principle.
The paper investigates diffusion models trained in a lazy high‑dimensional regime, extending benign overfitting theory to generative settings. By analyzing denoising score matching in a vector‑valued RKHS with an inner‑product kernel, the authors derive exact risk trajectories under gradient flow when the number of samples scales proportionally with dimensionality. These trajectories reveal three distinct phases—spectral generalization, noise‑dominated interpolation, and empirical Bayes memorization—whose interplay shapes the distribution of generated samples.
arXiv:2502. 11665v3 Announce Type: replace-cross Abstract: The classical kernel ridge regression problem aims to find the best fit for the output $Y$ as a function of the input data $X\in \mathbb{R}^d$, with a fixed choice of regularization term imposed by a given choice of a reproducing kernel Hilbert space, such as a Sobolev space.
arXiv:2410. 02628v5 Announce Type: replace Abstract: Learning conditional distributions $\pi^*(\cdot|x)$ is a central problem in machine learning, which is typically approached via supervised methods with paired data $(x,y) \sim \pi^*$.