相关论文: Resolving the Geometric Locus Dilemma for Support …

When three-dimensional bodies contain thin features, non-trivial topology, or scan-derived surfaces, volumetric meshing can become the dominant bottleneck in simulation workflows. We replace this step with a learned geometric…

The manifold hypothesis presumes that high-dimensional data lies on or near a low-dimensional manifold. While the utility of encoding geometric structure has been demonstrated empirically, rigorous analysis of its impact on the learnability…

In this paper, we address two challenging problems in unsupervised subspace learning: 1) how to automatically identify the feature dimension of the learned subspace (i.e., automatic subspace learning), and 2) how to learn the underlying…

We design strategies in nonlinear geometric analysis to temper the effects of adversarial learning for sufficiently smooth data of numerical method-type dynamics in encoder-decoder methods, variational and deterministic, through the use of…

The success of deep neural networks in image classification and learning can be partly attributed to the features they extract from images. It is often speculated about the properties of a low-dimensional manifold that models extract and…

We develop a mathematical framework to address a broad class of metric and preference learning problems within a Hilbert space. We obtain a novel representer theorem for the simultaneous task of metric and preference learning. Our key…

We study the problem of discrete geometric packing. Here, given weighted regions (say in the plane) and points (with capacities), one has to pick a maximum weight subset of the regions such that no point is covered more than its capacity.…

It is common in machine learning and statistics to use symmetries derived from expert knowledge to simplify problems or improve performance, using methods like data augmentation or penalties. In this paper we consider the unsupervised and…

Deep learning is the mainstream technique for many machine learning tasks, including image recognition, machine translation, speech recognition, and so on. It has outperformed conventional methods in various fields and achieved great…

Agnostic learning of Boolean halfspaces is a fundamental problem in computational learning theory, but it is known to be computationally hard even for weak learning. Recent work [CKKMK24] proposed smoothed analysis as a way to bypass such…

This paper generalizes the notion of geometric curves such as hyperbolas and ellipses to more general vector spaces with an associated inner product. This is done by generalizing the definition in terms of loci and foci of said curves in…

We consider the classification problem and focus on nonlinear methods for classification on manifolds. For multivariate datasets lying on an embedded nonlinear Riemannian manifold within the higher-dimensional ambient space, we aim to…

A good classification method should yield more accurate results than simple heuristics. But there are classification problems, especially high-dimensional ones like the ones based on image/video data, for which simple heuristics can work…

We prove an existence result for the Backus interior problem in the Euclidean ball. The problem consists in determining a harmonic function in the ball from the knowledge of the modulus of its gradient on the boundary. The problem is…

The underspecification of most machine learning pipelines means that we cannot rely solely on validation performance to assess the robustness of deep learning systems to naturally occurring distribution shifts. Instead, making sure that a…

We propose new estimates for the frontier of a set of points. They are defined as kernel estimates covering all the points and whose associated support is of smallest surface. The estimates are written as linear combinatio- ns of kernel…

Machine learning problems have an intrinsic geometric structure as central objects including a neural network's weight space and the loss function associated with a particular task can be viewed as encoding the intrinsic geometry of a given…

Statistical learning theory provides the foundation to applied machine learning, and its various successful applications in computer vision, natural language processing and other scientific domains. The theory, however, does not take into…

Proper learning refers to the setting in which learners must emit predictors in the underlying hypothesis class $H$, and often leads to learners with simple algorithmic forms (e.g. empirical risk minimization (ERM), structural risk…

This technical report outlines the top-ranking solution for RoboSense 2025: Track 3, achieving state-of-the-art performance on 3D object detection under various sensor placements. Our submission utilizes GBlobs, a local point cloud feature…