相关论文: Garland's Technique for Posets and High Dimensiona…
The intuition that local flatness of the loss landscape is correlated with better generalization for deep neural networks (DNNs) has been explored for decades, spawning many different flatness measures. Recently, this link with…
The validity of estimation and smoothing parameter selection for the wide class of generalized additive models for location, scale and shape (GAMLSS) relies on the correct specification of a likelihood function. Deviations from such…
We develop a generalized gradient expansion of the inhomogeneous dynamical mean-field theory method for determining properties of ultracold atoms in a trap. This approach goes beyond the well-known local density approximation and at higher…
We address the problem of generalizability for multi-view 3D human pose estimation. The standard approach is to first detect 2D keypoints in images and then apply triangulation from multiple views. Even though the existing methods achieve…
Thanks to earlier work of Koiran, it is known that the truth of the Generalized Riemann Hypothesis (GRH) implies that the dimension of algebraic sets over the complex numbers can be determined within the polynomial-hierarchy. The truth of…
Exemplar-based models have achieved great success on localizing the parts of semi-rigid objects. However, their efficacy on highly articulated objects such as humans is yet to be explored. Inspired by hierarchical object representation and…
Generalizable 3D Gaussian Splatting reconstruction showcases advanced Image-to-3D content creation but requires substantial computational resources and large datasets, posing challenges to training models from scratch. Current methods…
We present a customized 3D mesh Transformer model for the pose transfer task. As the 3D pose transfer essentially is a deformation procedure dependent on the given meshes, the intuition of this work is to perceive the geometric…
We show that recent results on randomized dimension reduction schemes that exploit structural properties of data can be applied in the context of persistent homology. In the spirit of compressed sensing, the dimension reduction is…
Finding constrained saddle points on Riemannian manifolds is significant for analyzing energy landscapes arising in physics and chemistry. Existing works have been limited to special manifolds that admit global regular level-set…
Multidimensional scaling (MDS) is the act of embedding proximity information about a set of $n$ objects in $d$-dimensional Euclidean space. As originally conceived by the psychometric community, MDS was concerned with embedding a fixed set…
In recent years, the proximal gradient method and its variants have been generalized to Riemannian manifolds for solving optimization problems with an additively separable structure, i.e., $f + h$, where $f$ is continuously differentiable,…
We establish a symmetrization procedure in a context of general orthogonal expansions associated with a second order differential operator $L$, a `Laplacian'. Combined with a unified conjugacy scheme furnished in our earlier article it…
Generalized feed-forward Gaussian models have achieved significant progress in sparse-view 3D reconstruction by leveraging prior knowledge from large multi-view datasets. However, these models often struggle to represent high-frequency…
We study, in d-dimensions, the random walker with geometrically shrinking step sizes at each hop. We emphasize the integrated quantities such as expectation values, cumulants and moments rather than a direct study of the probability…
We introduce a new class of autoequivalences that act on the derived categories of certain vector bundles over Grassmannians. These autoequivalences arise from Grassmannian flops: they generalize Seidel-Thomas spherical twists, which can be…
The geometry of unit $N$-dimensional $\ell_{p}$ balls has been intensively investigated in the past decades. A particular topic of interest has been the study of the asymptotics of their projections. Apart from their intrinsic interest,…
It has been known for some time that generalised geometry provides a particularly elegant rewriting of the action and symmetries of 10-dimensional supergravity theories, up to the lowest nontrivial order in fermions. By exhibiting the full…
We reframe linear dimensionality reduction as a problem of Bayesian inference on matrix manifolds. This natural paradigm extends the Bayesian framework to dimensionality reduction tasks in higher dimensions with simpler models at greater…
Axially symmetric processes on spheres, for which the second-order dependency structure may substantially vary with shifts in latitude, are a prominent alternative to model the spatial uncertainty of natural variables located over large…