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We introduce a simple autoencoder based on hyperbolic geometry for solving standard collaborative filtering problem. In contrast to many modern deep learning techniques, we build our solution using only a single hidden layer. Remarkably,…

Decision trees and models that use them as primitives are workhorses of machine learning in Euclidean spaces. Recent work has further extended these models to the Lorentz model of hyperbolic space by replacing axis-parallel hyperplanes with…

The distance metric plays an important role in nearest neighbor (NN) classification. Usually the Euclidean distance metric is assumed or a Mahalanobis distance metric is optimized to improve the NN performance. In this paper, we study the…

Hyperbolic space is quickly gaining traction as a promising geometry for hierarchical and robust representation learning. A core open challenge is the development of a mathematical formulation of hyperbolic neural networks that is both…

Transformer based models, especially large language models (LLMs) dominate the field of NLP with their mass adoption in tasks such as text generation, summarization and fake news detection. These models offer ease of deployment and…

Classifying large scale networks into several categories and distinguishing them according to their fine structures is of great importance with several applications in real life. However, most studies of complex networks focus on properties…

Heterogeneous graphs have attracted a lot of research interests recently due to the success for representing complex real-world systems. However, existing methods have two pain points in embedding them into low-dimensional spaces: the…

Convolutional neural networks (CNNs), in a few decades, have outperformed the existing state of the art methods in classification context. However, in the way they were formalised, CNNs are bound to operate on euclidean spaces. Indeed,…

Graph Neural Networks (GNNs) have gained popularity in various learning tasks, with successful applications in fields like molecular biology, transportation systems, and electrical grids. These fields naturally use graph data, benefiting…

Forecasting chaotic dynamics beyond a few Lyapunov times is difficult because infinitesimal errors grow exponentially. Existing Echo State Networks (ESNs) mitigate this growth but employ reservoirs whose Euclidean geometry is mismatched to…

Hypergraph neural networks (HNNs) using neural networks to encode hypergraphs provide a promising way to model higher-order relations in data and further solve relevant prediction tasks built upon such higher-order relations. However,…

Building on existing work with Hyperblocks, which classify data using minimum and maximum bounds for each attribute, we focus on enhancing interpretability, decreasing training time, and reducing model complexity without sacrificing…

Hypergraph Convolutional Neural Networks (HGCNNs) have demonstrated their potential in modeling high-order relations preserved in graph-structured data. However, most existing convolution filters are localized and determined by the…

We study the representation capacity of deep hyperbolic neural networks (HNNs) with a ReLU activation function. We establish the first proof that HNNs can $\varepsilon$-isometrically embed any finite weighted tree into a hyperbolic space of…

Recently, there has been an interest in embedding networks in hyperbolic space, since hyperbolic space has been shown to work well in capturing graph/network structure as it can naturally reflect some properties of complex networks.…

Convolutional Neural Networks (CNNs) have achieved remarkable success across a wide range of machine learning tasks by leveraging hierarchical feature learning through deep architectures. However, the large number of layers and millions of…

We present a large scale hyperbolic recommender system. We discuss why hyperbolic geometry is a more suitable underlying geometry for many recommendation systems and cover the fundamental milestones and insights that we have gained from its…

Representation learning over temporal networks has drawn considerable attention in recent years. Efforts are mainly focused on modeling structural dependencies and temporal evolving regularities in Euclidean space which, however,…

Existing deep convolutional neural networks (CNNs) have shown their great success on image classification. CNNs mainly consist of convolutional and pooling layers, both of which are performed on local image areas without considering the…

Hypergraphs serve as an effective model for depicting complex connections in various real-world scenarios, from social to biological networks. The development of Hypergraph Neural Networks (HGNNs) has emerged as a valuable method to manage…