Related papers: A Hyperbolic Perspective on Hierarchical Structure…

This paper extends the possibility to examine the underlying curvature of data through the lens of topology by using the Betti curves, tools of Persistent Homology, as key topological descriptors, building on the clique topology approach.…

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…

Graph-based collaborative filtering is capable of capturing the essential and abundant collaborative signals from the high-order interactions, and thus received increasingly research interests. Conventionally, the embeddings of users and…

In the field of machine learning, hyperbolic space demonstrates superior representation capabilities for hierarchical data compared to conventional Euclidean space. This work focuses on the Coarse-To-Fine Few-Shot Class-Incremental Learning…

Hierarchical reinforcement learning deals with the problem of breaking down large tasks into meaningful sub-tasks. Autonomous discovery of these sub-tasks has remained a challenging problem. We propose a novel method of learning sub-tasks…

We introduce HYPERPOSE, a novel 3D human pose estimation framework that performs spatio-temporal reasoning entirely within the Lorentz model of hyperbolic space $\mathbb{H}^d$ to natively preserve the hierarchical tree topology of the human…

Euclidean embeddings of data are fundamentally limited in their ability to capture latent semantic structures, which need not conform to Euclidean spatial assumptions. Here we consider an alternative, which embeds data as discrete…

Unsupervised representation learning techniques, such as learning word embeddings, have had a significant impact on the field of natural language processing. Similar representation learning techniques have not yet become commonplace in the…

Embedded topic models are able to learn interpretable topics even with large and heavy-tailed vocabularies. However, they generally hold the Euclidean embedding space assumption, leading to a basic limitation in capturing hierarchical…

Hyperbolic representations are effective in modeling knowledge graph data which is prevalently used to facilitate multi-hop reasoning. However, a rigorous and detailed comparison of the two spaces for this task is lacking. In this paper,…

This work presents a reformulation of the recently proposed Wasserstein autoencoder framework on a non-Euclidean manifold, the Poincar\'e ball model of the hyperbolic space. By assuming the latent space to be hyperbolic, we can use its…

Incomplete Multi-View Clustering (IMVC) faces the challenge of learning discriminative representations from fragmentary observations while maintaining robustness against missing views. However, prevalent Euclidean-based methods suffer from…

Zero-Shot Learning (ZSL) has received extensive attention and successes in recent years especially in areas of fine-grained object recognition, retrieval, and image captioning. Key to ZSL is to transfer knowledge from the seen to the unseen…

Visual and semantic concepts are often structured in a hierarchical manner. For instance, textual concept `cat' entails all images of cats. A recent study, MERU, successfully adapts multimodal learning techniques from Euclidean space to…

Learning generalized face anti-spoofing (FAS) models against presentation attacks is essential for the security of face recognition systems. Previous FAS methods usually encourage models to extract discriminative features, of which the…

Most state-of-the-art deep geometric learning single-view reconstruction approaches rely on encoder-decoder architectures that output either shape parametrizations or implicit representations. However, these representations rarely preserve…

Many complex systems involve interactions between more than two agents. Hypergraphs capture these higher-order interactions through hyperedges that may link more than two nodes. We consider the problem of embedding a hypergraph into…

The ability to decompose complex natural scenes into meaningful object-centric abstractions lies at the core of human perception and reasoning. In the recent culmination of unsupervised object-centric learning, the Slot-Attention module has…

We are concerned with the discovery of hierarchical relationships from large-scale unstructured similarity scores. For this purpose, we study different models of hyperbolic space and find that learning embeddings in the Lorentz model is…

Object-centric learning aims to represent visual data with a set of object entities (a.k.a. slots), providing structured representations that enable systematic generalization. Leveraging advanced architectures like Transformers, recent…