相关论文: Learning Infinitesimal Generators of Continuous Sy…

We propose a neural network-based approach that computes a stable and generalizing metric (LSiM) to compare data from a variety of numerical simulation sources. We focus on scalar time-dependent 2D data that commonly arises from motion and…

Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…

Structure learning algorithms that learn the graph of a Bayesian network from observational data often do so by assuming the data correctly reflect the true distribution of the variables. However, this assumption does not hold in the…

Raven's Progressive Matrices are one of the widely used tests in evaluating the human test taker's fluid intelligence. Analogously, this paper introduces geometric generalization based zero-shot learning tests to measure the rapid learning…

Despite progress in the rapidly developing field of geometric deep learning, performing statistical analysis on geometric data--where each observation is a shape such as a curve, graph, or surface--remains challenging due to the…

Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…

Symmetry is an important aesthetic criteria in graph drawing and network visualisation. Symmetric graph drawings aim to faithfully represent automorphisms of graphs as geometric symmetries in a drawing. In this paper, we design and…

Many supervised learning tasks have intrinsic symmetries, such as translational and rotational symmetry in image classifications. These symmetries can be exploited to enhance performance. We formulate the symmetry constraints into a concise…

Symmetry is ubiquitous throughout nature and can often give great insights into the formation, structure and stability of objects studied by mathematicians, physicists, chemists and biologists. However, perfect symmetry occurs rarely so…

The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric integer programs are studied from a group theoretical viewpoint. We investigate the structure of integer solutions of integer programs and show…

We survey the role of symmetry in diffeomorphic registration of landmarks, curves, surfaces, images and higher-order data. The infinite dimensional problem of finding correspondences between objects can for a range of concrete data types be…

In many physical systems, inputs related by intrinsic system symmetries are mapped to the same output. When inverting such systems, i.e., solving the associated inverse problems, there is no unique solution. This causes fundamental…

We describe a generalization of the group testing problem termed symmetric group testing. Unlike in classical binary group testing, the roles played by the input symbols zero and one are "symmetric" while the outputs are drawn from a…

Quantifying the uncertainty of predictions is a core problem in modern statistics. Methods for predictive inference have been developed under a variety of assumptions, often -- for instance, in standard conformal prediction -- relying on…

Deep generative models are universal tools for learning data distributions on high dimensional data spaces via a mapping to lower dimensional latent spaces. We provide a study of latent space geometries and extend and build upon previous…

Recently there has been increasing interest in developing and deploying deep graph learning algorithms for many tasks, such as fraud detection and recommender systems. Albeit, there is a limited number of publicly available graph-structured…

A particularly interesting instance of supervised learning with kernels is when each training example is associated with two objects, as in pairwise classification (Brunner et al., 2012), and in supervised learning of preference relations…

This paper is concerned with the development, analysis and numerical realization of a novel variational model for the regularization of inverse problems in imaging. The proposed model is inspired by the architecture of generative…

Graph learning algorithms have attained state-of-the-art performance on many graph analysis tasks such as node classification, link prediction, and clustering. It has, however, become hard to track the field's burgeoning progress. One…

Generative modeling of symmetric densities has a range of applications in AI for science, from drug discovery to physics simulations. The existing generative modeling paradigm for invariant densities combines an invariant prior with an…