Related papers: Learning Topological Invariance
Real world data often lie on low-dimensional Riemannian manifolds embedded in high-dimensional spaces. This motivates learning degenerate normalizing flows that map between the ambient space and a low-dimensional latent space. However, if…
Invariance has recently proven to be a powerful inductive bias in machine learning models. One such class of predictive or generative models are tensor networks. We introduce a new numerical algorithm to construct a basis of tensors that…
We examine the structure and dimensionality of the Jones polynomial using manifold learning techniques. Our data set consists of more than 10 million knots up to 17 crossings and two other special families up to 2001 crossings. We introduce…
Matching images and sentences demands a fine understanding of both modalities. In this paper, we propose a new system to discriminatively embed the image and text to a shared visual-textual space. In this field, most existing works apply…
Graph matching refers to finding node correspondence between graphs, such that the corresponding node and edge's affinity can be maximized. In addition with its NP-completeness nature, another important challenge is effective modeling of…
Graph neural networks use relational information as an inductive bias to enhance prediction performance. Not rarely, task-relevant relations are unknown and graph structure learning approaches have been proposed to learn them from data.…
Image-language matching tasks have recently attracted a lot of attention in the computer vision field. These tasks include image-sentence matching, i.e., given an image query, retrieving relevant sentences and vice versa, and region-phrase…
Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potential for machine learning applications and offer a unifying view of common tensor decomposition models…
The majority of model-based learned image reconstruction methods in medical imaging have been limited to uniform domains, such as pixelated images. If the underlying model is solved on nonuniform meshes, arising from a finite element method…
Virtual knots are defined diagrammatically as a collection of figures, called virtual knot diagrams, that are considered equivalent up to finite sequences of extended Reidemeister moves. By contrast, knots in $\mathbb{R}^3$ can be defined…
Most equivariant neural networks rely on a single global symmetry, limiting their use in domains where symmetries are instead local. We introduce Torsor CNNs, a framework for learning on graphs with local symmetries encoded as edge…
Knowledge graph (KG) alignment - the task of recognizing entities referring to the same thing in different KGs - is recognized as one of the most important operations in the field of KG construction and completion. However, existing…
Despite significant advances in the field of deep learning in ap-plications to various areas, an explanation of the learning pro-cess of neural network models remains an important open ques-tion. The purpose of this paper is a comprehensive…
The invariant theory of Killing tensors (ITKT) is extended by introducing the new concepts of covariants and joint invariants of (product) vector spaces of Killing tensors defined in pseudo-Riemannian spaces of constant curvature. The…
Assumptions about invariances or symmetries in data can significantly increase the predictive power of statistical models. Many commonly used models in machine learning are constraint to respect certain symmetries in the data, such as…
Complex networks represented as node adjacency matrices constrains the application of machine learning and parallel algorithms. To address this limitation, network embedding (i.e., graph representation) has been intensively studied to learn…
In this article we shall give an account of certain developments in knot theory which followed upon the discovery of the Jones polynomial in 1984. The focus of our account will be recent glimmerings of understanding of the topological…
Representation learning of textual networks poses a significant challenge as it involves capturing amalgamated information from two modalities: (i) underlying network structure, and (ii) node textual attributes. For this, most existing…
Graph matching aims to establish correspondences between vertices of graphs such that both the node and edge attributes agree. Various learning-based methods were recently proposed for finding correspondences between image key points based…
Artificial neural networks and machine learning have now reached a new era after several decades of improvement where applications are to explode in many fields of science, industry, and technology. Here, we use artificial neural networks…