Related papers: Provably Accurate and Scalable Linear Classifiers …

Matrix Factorization (MF) is a common method for generating recommendations, where the proximity of entities like users or items in the embedded space indicates their similarity to one another. Though almost all applications implicitly use…

Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…

Most previous heterogeneous graph embedding models represent elements in a heterogeneous graph as vector representations in a low-dimensional Euclidean space. However, because heterogeneous graphs inherently possess complex structures, such…

This paper presents a novel online learning method that aims at finding a separator hyperplane between data points labelled as either positive or negative. Since weights and biases of artificial neurons can directly be related to…

Data across modalities such as images, text, and graphs often contains hierarchical and relational structures, which are challenging to model within Euclidean geometry. Hyperbolic geometry provides a natural framework for representing such…

In machine learning, data is usually represented in a (flat) Euclidean space where distances between points are along straight lines. Researchers have recently considered more exotic (non-Euclidean) Riemannian manifolds such as hyperbolic…

Multi-step reasoning is a fundamental challenge in artificial intelligence, with applications ranging from mathematical problem-solving to decision-making in dynamic environments. Reinforcement Learning (RL) has shown promise in enabling…

Many algorithms require discriminative boundaries, such as separating hyperplanes or hyperballs, or are specifically designed to work on spherical data. By applying inversive geometry, we show that the two discriminative boundaries can be…

Scene graph representations enable structured visual understanding by modeling objects and their relationships, and have been widely used for multiview and 3D scene reasoning. Existing methods such as MSG learn scene graph embeddings in…

Hyperbolic neural networks (HNNs) have been proved effective in modeling complex data structures. However, previous works mainly focused on the Poincar\'e ball model and the hyperboloid model as coordinate representations of the hyperbolic…

Data representation in non-Euclidean spaces has proven effective for capturing hierarchical and complex relationships in real-world datasets. Hyperbolic spaces, in particular, provide efficient embeddings for hierarchical structures. This…

Single Positive Multi-Label Learning (SPMLL) addresses the challenging scenario where each training sample is annotated with only one positive label despite potentially belonging to multiple categories, making it difficult to capture…

Hyperbox-based classification has been seen as a promising technique in which decisions on the data are represented as a series of orthogonal, multidimensional boxes (i.e., hyperboxes) that are often interpretable and human-readable.…

Hierarchical data pervades diverse machine learning applications, including natural language processing, computer vision, and social network analysis. Hyperbolic space, characterized by its negative curvature, has demonstrated strong…

We prove existence and uniqueness of strong (pointwise) solutions to a linear nonlocal strongly coupled hyperbolic system of equations posed on all of Euclidean space. The system of equations comes from a linearization of a nonlocal model…

We introduce a simple autoencoder based on hyperbolic geometry for solving standard collaborative filtering problem. In contrast to many modern deep learning techniques, we build our solution using only a single hidden layer. Remarkably,…

Transformer model architectures have become an indispensable staple in deep learning lately for their effectiveness across a range of tasks. Recently, a surge of "X-former" models have been proposed which improve upon the original…

Machine unlearning methods have become increasingly important for selective concept removal in large pre-trained models. While recent work has explored unlearning in Euclidean contrastive vision-language models, the effectiveness of concept…

Generalized Category Discovery (GCD) is an intriguing open-world problem that has garnered increasing attention. Given a dataset that includes both labelled and unlabelled images, GCD aims to categorize all images in the unlabelled subset,…

Learning in hyperbolic spaces has attracted increasing attention due to its superior ability to model hierarchical structures of data. Most existing hyperbolic learning methods use fixed distance measures for all data, assuming a uniform…