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 investigates how training data limits the geometry of an optimizer through the covectors that a specified information channel can observe. It establishes that, under affine‑invariant Riemannian geometry, a full‑column‑rank positive‑definite compression can be uniquely completed via a split‑Hadamard metric submetry, yielding exact variational reduction from the full geometry to the visible target. The resulting framework provides explicit formulas for pullback metrics, Gram matrices, and prior‑data shrinkage, and characterizes the gauge‑invariant rank stratification of the positive‑definite cone as the channel varies.
The paper investigates how the choice of geometry in online mirror descent affects performance, particularly when loss gradients are sparse. It introduces randomized block‑norm mirror maps that interpolate between Euclidean and entropic geometries, achieving polynomial‑in‑dimension regret improvements over standard methods for various convex sets. The authors also demonstrate that naive alternation between mirror maps can lead to linear regret and propose a Hedge‑based meta‑algorithm that competes with the best mirror map in a finite portfolio, achieving near‑optimal regret for random block geometries.
arXiv:2606. 15442v1 Announce Type: cross Abstract: We design a new unconstrained coordinate system where a $p\times p$ symmetric positive definite (SPD) matrix $\Theta$ is represented by a reverse telescoping map $\Theta(x)=\rm{RT}(x)$, with $x=(v,d,r)\in\mathbb{R}\times\mathbb{R}^{(p-1)}\times\mathbb{R}^{p(p-1)/2}$, representing respectively the log volume or log determinant; and the shape, as encoded by log relative diagonal scales and partial covariances among the nodes.
arXiv:2607. 08987v1 Announce Type: new Abstract: Spectral embedding methods are widely used for dimensionality reduction and clustering of high-dimensional datasets with intrinsic low-dimensional structures.
arXiv:2502. 00753v4 Announce Type: replace-cross Abstract: Smoothness is crucial for attaining fast rates in first-order optimization.
arXiv:2604. 21407v2 Announce Type: replace Abstract: When approximating an intractable density via variational inference (VI) the variational family is typically chosen as a simple parametric family that very likely does not contain the target.
arXiv:2607. 23182v1 Announce Type: cross Abstract: We prove the identifiability of deep generative models (DGMs) with piecewise-affine (PWA) decoders and Gaussian mixture model (GMM) priors, in a purely unsupervised setting.
arXiv:2507. 15431v4 Announce Type: replace Abstract: We offer a theoretical mathematical background through Lagrangian optimization on the unit hyperspherical manifold and its tangential structure.
arXiv:2510. 07758v3 Announce Type: replace Abstract: Sharpness (of the loss minima) is widely believed to be a good indicator of generalization of neural networks.
arXiv:2608. 11749v1 Announce Type: cross Abstract: Multi-objective optimization (MOO) has demonstrated significant success in multi-task learning by mitigating task conflicts through gradient manipulation.
arXiv:2606. 01216v1 Announce Type: new Abstract: The elementwise Hadamard product of two low-rank matrices provides a parameter-efficient model for data with multiplicative structure, but its modeling is challenging due to the presence of additional symmetries under coupled row/column scalings between the two factors.