相关论文: The Numerical Stability of Hyperbolic Representati…

Hyperbolic geometry have shown significant potential in modeling complex structured data, particularly those with underlying tree-like and hierarchical structures. Despite the impressive performance of various hyperbolic neural networks…

Learning good image representations that are beneficial to downstream tasks is a challenging task in computer vision. As such, a wide variety of self-supervised learning approaches have been proposed. Among them, contrastive learning has…

Hyperbolic space naturally encodes hierarchical structures such as phylogenies (binary trees), where inward-bending geodesics reflect paths through least common ancestors, and the exponential growth of neighborhoods mirrors the…

Metric learning plays a critical role in training image retrieval and classification. It is also a key algorithm in representation learning, e.g., for feature learning and its alignment in metric space. Hyperbolic embedding has been…

Most mathematical distortions used in ML are fundamentally integral in nature: $f$-divergences, Bregman divergences, (regularized) optimal transport distances, integral probability metrics, geodesic distances, etc. In this paper, we unveil…

In large-scale recommender systems, the user-item networks are generally scale-free or expand exponentially. The latent features (also known as embeddings) used to describe the user and item are determined by how well the embedding space…

We investigate lower asymptotic bounds of number variances for invariant locally square-integrable random measures on Euclidean and real hyperbolic spaces. In the Euclidean case we show that there are subsequences of radii for which the…

Most real-world datasets consist of a natural hierarchy between classes or an inherent label structure that is either already available or can be constructed cheaply. However, most existing representation learning methods ignore this…

The problem of identifying geometric structure in heterogeneous, high-dimensional data is a cornerstone of representation learning. While there exists a large body of literature on the embeddability of canonical graphs, such as lattices or…

Recent research in Vision-Language Models (VLMs) has significantly advanced our capabilities in cross-modal reasoning. However, existing methods suffer from performance degradation with domain changes or require substantial computational…

Learning hyperbolic embeddings for knowledge graph (KG) has gained increasing attention due to its superiority in capturing hierarchies. However, some important operations in hyperbolic space still lack good definitions, making existing…

Signed network embedding methods aim to learn vector representations of nodes in signed networks. However, existing algorithms only managed to embed networks into low-dimensional Euclidean spaces whereas many intrinsic features of signed…

This paper investigates the notion of learning user and item representations in non-Euclidean space. Specifically, we study the connection between metric learning in hyperbolic space and collaborative filtering by exploring Mobius…

Backward compatible representation learning enables updated models to integrate seamlessly with existing ones, avoiding to reprocess stored data. Despite recent advances, existing compatibility approaches in Euclidean space neglect the…

Geometric representation learning has recently shown great promise in several machine learning settings, ranging from relational learning to language processing and generative models. In this work, we consider the problem of performing…

Recently, hyperbolic space has risen as a promising alternative for semi-supervised graph representation learning. Many efforts have been made to design hyperbolic versions of neural network operations. However, the inspiring geometric…

We propose a method for representing malignant lymphoma pathology images, from high-resolution cell nuclei to low-resolution tissue images, within a single hyperbolic space using self-supervised learning. To capture morphological changes…

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with…

Selective state-space models excel at long-sequence modeling, but their capacity for language representation -- in complex hierarchical reasoning -- remains underexplored. Most large language models rely on \textit{flat} Euclidean…

Embedding geometry plays a fundamental role in retrieval quality, yet dense retrievers for retrieval-augmented generation (RAG) remain largely confined to Euclidean space. However, natural language exhibits hierarchical structure from broad…