Related papers: Geometry-Aware Backdoor Attacks: Leveraging Curvat…

Deep neural networks have been shown to be vulnerable to backdoor attacks, which could be easily introduced to the training set prior to model training. Recent work has focused on investigating backdoor attacks on natural images or toy…

Backdoor attacks compromise the integrity and reliability of machine learning models by embedding a hidden trigger during the training process, which can later be activated to cause unintended misbehavior. We propose a novel backdoor…

Hyperbolic geometry has recently found applications in social networks, machine learning and computational biology. With the increasing popularity, questions about the best representations of hyperbolic spaces arise, as each representation…

Hierarchical data is common in many domains like life sciences and e-commerce, and its embeddings often play a critical role. While hyperbolic embeddings offer a theoretically grounded approach to representing hierarchies in low-dimensional…

We develop the foundations of the theory of quasi-visual approximations of bounded metric spaces. Roughly speaking, these are sequences of covers of a given space for which the diameters of the sets in the covers shrink to zero and for…

Mechanochemical patterns arising in the actomyosin cortex drive many cellular processes. Here we consider a hydrodynamic model for the actomyosin cortex of cells and study the sensitivity of the emergent patterns to both physical parameters…

Learning low-dimensional numerical representations from symbolic data, e.g., embedding the nodes of a graph into a geometric space, is an important concept in machine learning. While embedding into Euclidean space is common, recent…

Machine learning is vulnerable to adversarial manipulation. Previous literature has demonstrated that at the training stage attackers can manipulate data and data sampling procedures to control model behaviour. A common attack goal is to…

Recent papers in the graph machine learning literature have introduced a number of approaches for hyperbolic representation learning. The asserted benefits are improved performance on a variety of graph tasks, node classification and link…

Current backdoor defenses assume that neutralizing a known trigger removes the backdoor. We show this trigger-centric view is incomplete: \emph{alternative triggers}, patterns perceptually distinct from training triggers, reliably activate…

A rich class of network models associate each node with a low-dimensional latent coordinate that controls the propensity for connections to form. Models of this type are well established in the network analysis literature, where it is…

We extend the recently developed discrete geometric singular perturbation theory to the non-normally hyperbolic regime. Our primary tool is the Takens embedding theorem, which provides a means of approximating the dynamics of particular…

Real-world graphs naturally exhibit hierarchical or cyclical structures that are unfit for the typical Euclidean space. While there exist graph neural networks that leverage hyperbolic or spherical spaces to learn representations that embed…

This survey reviews hyperbolic graph embedding models, and evaluate them on anomaly detection, highlighting their advantages over Euclidean methods in capturing complex structures. Evaluating models like \textit{HGCAE},…

Attention mechanisms are developing into a viable alternative to convolutional layers as elementary building block of NNs. Their main advantage is that they are not restricted to capture local dependencies in the input, but can draw…

Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…

We introduce hyperbolic attention networks to endow neural networks with enough capacity to match the complexity of data with hierarchical and power-law structure. A few recent approaches have successfully demonstrated the benefits of…

Recently, it has been revealed that a variety of novel phenomena emerge in hyperbolic spaces, while non-Hermitian physics has significantly enriched the landscape of condensed matter physics. Building on these developments, we construct a…

Hyperbolic deep learning has become a growing research direction in computer vision due to the unique properties afforded by the alternate embedding space. The negative curvature and exponentially growing distance metric provide a natural…

We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…