Related papers: Topology-Driven Generative Completion of Lacunae i…

We generate new mathematical tools with which to quantify the macroscopic topological structure of large directed networks. This is achieved via a statistical mechanical analysis of constrained maximum entropy ensembles of directed random…

In topology optimization using deep learning, load and boundary conditions represented as vectors or sparse matrices often miss the opportunity to encode a rich view of the design problem, leading to less than ideal generalization results.…

Matrix completion is a classical problem in data science wherein one attempts to reconstruct a low-rank matrix while only observing some subset of the entries. Previous authors have phrased this problem as a nuclear norm minimization…

Learning the structure of a network from time series data, in particular cyclostationary data, is of significant interest in many disciplines such as power grids, biology and finance. In this article, an algorithm is presented for…

Automated Machine Learning encompasses a set of meta-algorithms intended to design and apply machine learning techniques (e.g., model selection, hyperparameter tuning, model assessment, etc.). TPOT, a software for optimizing machine…

We introduce a theory-driven mechanism for learning a neural network model that performs generative topology design in one shot given a problem setting, circumventing the conventional iterative process that computational design tasks…

The task of point cloud completion aims to predict the missing part for an incomplete 3D shape. A widely used strategy is to generate a complete point cloud from the incomplete one. However, the unordered nature of point clouds will degrade…

Topological correctness plays a critical role in many image segmentation tasks, yet most networks are trained using pixel-wise loss functions, such as Dice, neglecting topological accuracy. Existing topology-aware methods often lack robust…

We present a new unified graph-based representation of medical data, combining genetic information and medical records of patients with medical knowledge via a unique knowledge graph. This approach allows us to infer meaningful information…

We consider the problem of matrix completion on an $n \times m$ matrix. We introduce the problem of Interpretable Matrix Completion that aims to provide meaningful insights for the low-rank matrix using side information. We show that the…

We study online robust matrix completion on graphs. At each iteration a vector with some entries missing is revealed and our goal is to reconstruct it by identifying the underlying low-dimensional subspace from which the vectors are drawn.…

In this paper, we propose a sensitivity-free and multi-objective structural design methodology called data-driven topology design. It is schemed to obtain high-performance material distributions from initially given material distributions…

In real world clinical environments, training and applying deep learning models on multi-modal medical imaging data often struggles with partially incomplete data. Standard approaches either discard missing samples, require imputation or…

Query optimization has been studied using machine learning, reinforcement learning, and, more recently, graph-based convolutional networks. Ontology, as a structured, information-rich knowledge representation, can provide context,…

Machine learning models for repeated measurements are limited. Using topological data analysis (TDA), we present a classifier for repeated measurements which samples from the data space and builds a network graph based on the data topology.…

We propose the design of novel categorical generative AI architectures (GAIAs) using topos theory, a type of category that is ``set-like": a topos has all (co)limits, is Cartesian closed, and has a subobject classifier. Previous theoretical…

We propose a model-based, automated, bottom-up approach for design, which is applicable to various physical domains, but in this work we focus on the electrical domain. This bottom-up approach is based on a meta-topology in which each link…

Commonly, learning-based topological navigation approaches produce a local policy while preserving some loose connectivity of the space through a topological map. Nevertheless, spurious or missing edges in the topological graph often lead…

Semantic map models (SMMs) construct a network-like conceptual space from cross-linguistic instances or forms, based on the connectivity hypothesis. This approach has been widely used to represent similarity and entailment relationships in…

Topological data analysis provides a collection of tools to encapsulate and summarize the shape of data. Currently it is mainly restricted to \emph{mapper algorithm} and \emph{persistent homology}. In this paper we introduce new…