Related papers: GSVD for Geometry-Grounded Dataset Comparison: An …
This paper provides an advanced mathematical theory of the Generalized Singular Value Decomposition (GSVD) and its applications. We explore the geometry of the GSVD which provides a long sought for ellipse picture which includes a…
The generalized singular value decomposition (GSVD, a.k.a. "SVD triplet", "duality diagram" approach) provides a unified strategy and basis to perform nearly all of the most common multivariate analyses (e.g., principal components,…
It is well known that vision classification models suffer from poor calibration in the face of data distribution shifts. In this paper, we take a geometric approach to this problem. We propose Geometric Sensitivity Decomposition (GSD) which…
The generalized singular value decomposition (GSVD) is a valuable tool that has many applications in computational science. However, computing the GSVD for large-scale problems is challenging. Motivated by applications in hyper-differential…
Correspondence analysis, multiple correspondence analysis and their discriminant counterparts (i.e., discriminant simple correspondence analysis and discriminant multiple correspondence analysis) are methods of choice for analyzing…
Single-view depth estimation (SVDE) plays a crucial role in scene understanding for AR applications, 3D modeling, and robotics, providing the geometry of a scene based on a single image. Recent works have shown that a successful solution…
The higher-order generalized singular value decomposition (HO-GSVD) is a matrix factorization technique that extends the GSVD to $N \ge 2$ data matrices, and can be used to identify shared subspaces in multiple large-scale datasets with…
Building on the abstract Generalized Singular Value Decomposition (GSVD) theory of Brown et al. [2025], we prove that most modern neural architectures admit a generalized SVD representation in which they are left-invertible before a final…
Generalized zero-shot learning (GZSL) aims to classify samples under the assumption that some classes are not observable during training. To bridge the gap between the seen and unseen classes, most GZSL methods attempt to associate the…
For the computation of the generalized singular value decomposition (GSVD) of a large matrix pair $(A,B)$ of full column rank, the GSVD is commonly formulated as two mathematically equivalent generalized eigenvalue problems, so that a…
Low-rank approximation of images via singular value decomposition is well-received in the era of big data. However, singular value decomposition (SVD) is only for order-two data, i.e., matrices. It is necessary to flatten a higher order…
Feed-forward surround-view autonomous driving scene reconstruction offers fast, generalizable inference ability, which faces the core challenge of ensuring generalization while elevating novel view quality. Due to the surround-view with…
Generalised zero-shot learning (GZSL) methods aim to classify previously seen and unseen visual classes by leveraging the semantic information of those classes. In the context of GZSL, semantic information is non-visual data such as a text…
The generalized singular value decomposition (GSVD) of a matrix pair $\{A, L\}$ with $A\in\mathbb{R}^{m\times n}$ and $L\in\mathbb{R}^{p\times n}$ generalizes the singular value decomposition (SVD) of a single matrix. In this paper, we…
Generalised zero-shot learning (GZSL) is a classification problem where the learning stage relies on a set of seen visual classes and the inference stage aims to identify both the seen visual classes and a new set of unseen visual classes.…
Generalized Zero-Shot Learning (GZSL) aims to recognize both seen and unseen classes by training only the seen classes, in which the instances of unseen classes tend to be biased towards the seen class. In this paper, we propose a…
Graph Similarity Computation (GSC) is a fundamental graph related task where Graph Edit Distance (GED) serves as a prevalent metric. GED is determined by an optimal alignment between a pair of graphs that partitions each into aligned…
Monocular 3D shape recovery is fundamental to geometric understanding, yet achieving robust generalization across arbitrary viewpoints and unseen object categories remains a significant challenge. In this paper, we present a generalizable…
Learning dense correspondences across deformable 3D shapes remains a long-standing challenge due to structural variability, non-isometric deformation, and inconsistent topology. Existing methods typically trade off generalization, geometric…
3D Gaussian Splatting (3DGS) enables efficient rendering, yet accurate surface reconstruction remains challenging due to unreliable geometric supervision. Existing approaches predominantly rely on depth-based reprojection to infer…