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Although self-/un-supervised methods have led to rapid progress in visual representation learning, these methods generally treat objects and scenes using the same lens. In this paper, we focus on learning representations for objects and…

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…

Hyperbolic representation learning has been widely used to extract implicit hierarchies within data, and recently it has found its way to the open-world classification task of Generalized Category Discovery (GCD). However, prior hyperbolic…

Many learning problems involve symmetries, and while invariance can be built into neural architectures, it can also emerge implicitly when training on group-structured data. We study this phenomenon in classical Hopfield networks and show…

With the recent advance of geometric deep learning, neural networks have been extensively used for data in non-Euclidean domains. In particular, hyperbolic neural networks have proved successful in processing hierarchical information of…

Learning embeddings from large-scale networks is an open challenge. Despite the overwhelming number of existing methods, is is unclear how to exploit network structure in a way that generalizes easily to unseen nodes, edges or graphs. In…

Network-structured data becomes ubiquitous in daily life and is growing at a rapid pace. It presents great challenges to feature engineering due to the high non-linearity and sparsity of the data. The local and global structure of the…

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging,…

Hyperbolic spaces provide a natural geometry for representing hierarchical and tree-structured data due to their exponential volume growth. To leverage these benefits, neural networks require intrinsic and efficient components that operate…

Given data, finding a faithful low-dimensional hyperbolic embedding of the data is a key method by which we can extract hierarchical information or learn representative geometric features of the data. In this paper, we explore a new method…

Various topological techniques and tools have been applied to neural networks in terms of network complexity, explainability, and performance. One fundamental assumption of this line of research is the existence of a global (Euclidean)…

The Laplace operator encodes the behavior of physical systems at vastly different scales, describing heat flow, fluids, as well as electric, gravitational, and quantum fields. A key input for the Laplace equation is the curvature of space.…

Electroencephalography (EEG)-based brain-computer interfaces facilitate direct communication with a computer, enabling promising applications in human-computer interactions. However, their utility is currently limited because EEG decoding…

Recently, graph neural networks have been widely used for network embedding because of their prominent performance in pairwise relationship learning. In the real world, a more natural and common situation is the coexistence of pairwise…

Adversarial examples in neural networks have been extensively studied in Euclidean geometry, but recent advances in \textit{hyperbolic networks} call for a reevaluation of attack strategies in non-Euclidean geometries. Existing methods such…

Network embedding techniques aim at representing structural properties of graphs in geometric space. Those representations are considered useful in downstream tasks such as link prediction and clustering. However, the number of graph…

Recent research on network embedding in hyperbolic space have proven successful in several applications. However, nodes in real world networks tend to interact through several distinct channels. Simple aggregation or ignorance of this…

Embedding real-world networks presents challenges because it is not clear how to identify their latent geometries. Embedding some disassortative networks, such as scale-free networks, to the Euclidean space has been shown to incur…

The exponential volume growth of hyperbolic geometry can embed the hierarchical relationships between states in reinforcement learning (RL) with far less distortion than Euclidean space. However, hyperbolic deep RL faces severe optimization…

Generative network models play an important role in algorithm development, scaling studies, network analysis, and realistic system benchmarks for graph data sets. A complex network model gaining considerable popularity builds random…