Related papers: Pseudo-Riemannian Embedding Models for Multi-Relat…

Riemannian neural networks, which extend deep learning techniques to Riemannian spaces, have gained significant attention in machine learning. To better classify the manifold-valued features, researchers have started extending Euclidean…

Symmetric Positive Definite (SPD) matrix learning methods have become popular in many image and video processing tasks, thanks to their ability to learn appropriate statistical representations while respecting Riemannian geometry of…

An isometric embedding of a graph into a metric space is an embedding of the vertices such that the smallest number of edges connecting any two vertices equals to the distance in the metric space between the images. In this paper, we study…

Recent interest in graph embedding methods has focused on learning a single representation for each node in the graph. But can nodes really be best described by a single vector representation? In this work, we propose a method for learning…

Multi-domain graph pre-training integrates knowledge from diverse domains to enhance performance in the target domains, which is crucial for building graph foundation models. Despite initial success, existing solutions often fall short of…

Representing a manifold of very high-dimensional data with generative models has been shown to be computationally efficient in practice. However, this requires that the data manifold admits a global parameterization. In order to represent…

Multiplex networks are collections of networks with identical nodes but distinct layers of edges. They are genuine representations for a large variety of real systems whose elements interact in multiple fashions or flavors. However,…

We propose Embedding Propagation (EP), an unsupervised learning framework for graph-structured data. EP learns vector representations of graphs by passing two types of messages between neighboring nodes. Forward messages consist of label…

In machine learning, data is usually represented in a (flat) Euclidean space where distances between points are along straight lines. Researchers have recently considered more exotic (non-Euclidean) Riemannian manifolds such as hyperbolic…

We show that every analytic semi-Riemannian manifold can be isometrically embeddded into an Einstein maifold in co-dimension one.

I show that all FRW models (four dimensional pseudo-Riemannian manifolds with maximally symmetric space) can be embedded in a flat Minkowski manifold with 5 dimensions. The pseudo Riemannian metric of space-time is induced by the flat…

Recent works on representation learning for Knowledge Graphs have moved beyond the problem of link prediction, to answering queries of an arbitrary structure. Existing methods are based on ad-hoc mechanisms that require training with a…

Graph transformers typically embed every node in a single Euclidean space, blurring heterogeneous topologies. We prepend a lightweight Riemannian mixture-of-experts layer that routes each node to various kinds of manifold, mixture of…

We recall the notion of (vertical) translating solitons in a product of a semi-Riemannian manifold $(M,g)$ and the real line. Mainly, we restrict our attention to those which are the graph of a smooth function. When dealing with…

Knowledge graph embedding has recently become a popular way to model relations and infer missing links. In this paper, we present a group theoretical perspective of knowledge graph embedding, connecting previous methods with different group…

The theory of flat Pseudo-Riemannian manifolds and flat affine manifolds is closely connected to the topic of prehomogeneous affine representations of Lie groups. In this article, we exhibit several aspects of this correspondence. At the…

This work studies the representational mapping across multimodal data such that given a piece of the raw data in one modality the corresponding semantic description in terms of the raw data in another modality is immediately obtained. Such…

This paper presents primarily two Euclidean embeddings of the quotient space generated by matrices that are identified modulo arbitrary row permutations. The original application is in deep learning on graphs where the learning task is…

Learning representations on Grassmann manifolds is popular in quite a few visual recognition tasks. In order to enable deep learning on Grassmann manifolds, this paper proposes a deep network architecture by generalizing the Euclidean…

Following our approach to metric Lie algebras developed in math.DG/0312243 we propose a way of understanding pseudo-Riemannian symmetric spaces which are not semi-simple. We introduce cohomology sets (called quadratic cohomology) associated…