Related papers: Performance of Hyperbolic Geometry Models on Top-N…
Recent research has shown that alignment between the structure of graph data and the geometry of an embedding space is crucial for learning high-quality representations of the data. The uniform geometry of Euclidean and hyperbolic spaces…
Embedding discrete solvers as differentiable layers has given modern deep learning architectures combinatorial expressivity and discrete reasoning capabilities. The derivative of these solvers is zero or undefined, therefore a meaningful…
Estimating the parameters of a model describing a set of observations using a neural network is in general solved in a supervised way. In cases when we do not have access to the model's true parameters this approach can not be applied.…
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…
Deep learning in hyperbolic space is quickly gaining traction in the fields of machine learning, multimedia, and computer vision. Deep networks commonly operate in Euclidean space, implicitly assuming that data lies on regular grids. Recent…
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…
Autoencoding is a popular method in representation learning. Conventional autoencoders employ symmetric encoding-decoding procedures and a simple Euclidean latent space to detect hidden low-dimensional structures in an unsupervised way.…
It has been shown beneficial for many types of data which present an underlying hierarchical structure to be embedded in hyperbolic spaces. Consequently, many tools of machine learning were extended to such spaces, but only few…
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…
Hyperbolic neural networks have shown great potential for modeling complex data. However, existing hyperbolic networks are not completely hyperbolic, as they encode features in a hyperbolic space yet formalize most of their operations in…
The embedding of complex networks into metric spaces has become a research topic of high interest with a wide variety of proposed methods. Low dimensional hyperbolic spaces offer a natural co-domain for embeddings allowing a roughly uniform…
Hyperbolic neural networks have been popular in the recent past due to their ability to represent hierarchical data sets effectively and efficiently. The challenge in developing these networks lies in the nonlinearity of the embedding space…
Anomaly detection in high-energy physics is essential for identifying new physics beyond the Standard Model. Autoencoders provide a signal-agnostic approach but are limited by the topology of their latent space. This work explores…
Several observations indicate the existence of a latent hyperbolic space behind real networks that makes their structure very intuitive in the sense that the probability for a connection is decreasing with the hyperbolic distance between…
Tilings of the hyperbolic plane are of significant interest among many branches of mathematics, physics and computer science. Yet, their construction remains a non-trivial task. Current approaches primarily use tree-based recursive…
Latent space geometry provides a rigorous and empirically valuable framework for interacting with the latent variables of deep generative models. This approach reinterprets Euclidean latent spaces as Riemannian through a pull-back metric,…
To analyze high-dimensional and complex data in the real world, deep generative models, such as variational autoencoder (VAE) embed data in a low-dimensional space (latent space) and learn a probabilistic model in the latent space. However,…
In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…
Hyperbolic geometry is an effective geometry for embedding hierarchical data structures. Hyperbolic learning has therefore become increasingly prominent in machine learning applications where data is hierarchically organized or governed by…
Artificial neural networks (ANNs) were inspired by the architecture and functions of the human brain and have revolutionised the field of artificial intelligence (AI). Inspired by studies on the latent geometry of the brain, in this…