Related papers: Narrowing the Gap between Combinatorial and Hyperb…

This work addresses the inverse identification of apparent elastic properties of random heterogeneous materials using machine learning based on artificial neural networks. The proposed neural network-based identification method requires the…

Regression has attracted immense interest lately due to its effectiveness in tasks like predicting values. And Regression is of widespread use in multiple fields such as Economics, Finance, Business, Biology and so on. While considerable…

We show that the community structure of a network can be used as a coarse version of its embedding in a hidden space with hyperbolic geometry. The finding emerges from a systematic analysis of several real-world and synthetic networks. We…

We consider a variant of regression problem, where the correspondence between input and output data is not available. Such shuffled data is commonly observed in many real world problems. Taking flow cytometry as an example, the measuring…

In the past decade, topological data analysis (TDA) has emerged as a powerful approach in data science. The main technique in TDA is persistent homology, which tracks topological invariants over the filtration of point cloud data using…

Classical network embeddings create a low dimensional representation of the learned relationships between features across nodes. Such embeddings are important for tasks such as link prediction and node classification. In the current paper,…

Human proximity networks are temporal networks representing the close-range proximity among humans in a physical space. They have been extensively studied in the past 15 years as they are critical for understanding the spreading of diseases…

Deep learning has been shown to achieve impressive results in several tasks where a large amount of training data is available. However, deep learning solely focuses on the accuracy of the predictions, neglecting the reasoning process…

This paper introduces a new approach to finding knots and links with hidden symmetries using "hidden extensions", a class of hidden symmetries defined here. We exhibit a family of tangle complements in the ball whose boundaries have…

This paper studies rotational virtual knot theory and its relationship with quantum link invariants. Every quantum link invariant for classical knots and links extends to an invariant of rotational virtual knots and links. The paper sets up…

Representing entities and relations in an embedding space is a well-studied approach for machine learning on relational data. Existing approaches, however, primarily focus on improving accuracy and overlook other aspects such as robustness…

Given a sequence of sets, where each set contains an arbitrary number of elements, the problem of temporal sets prediction aims to predict the elements in the subsequent set. In practice, temporal sets prediction is much more complex than…

A longstanding goal in computational educational research is to develop explainable knowledge tracing (KT) models. Deep Knowledge Tracing (DKT), which leverages a Recurrent Neural Network (RNN) to predict student knowledge and performance…

We examine two recent artificial intelligence (AI) based deep learning algorithms for visual blending in convolutional neural networks (Mordvintsev et al. 2015, Gatys et al. 2015). To investigate the potential value of these algorithms as…

Hyperbolic models are known to produce networks with properties observed empirically in most network datasets, including heavy-tailed degree distribution, high clustering, and hierarchical structures. As a result, several embeddings…

We present hyper-connections, a simple yet effective method that can serve as an alternative to residual connections. This approach specifically addresses common drawbacks observed in residual connection variants, such as the seesaw effect…

Despite a lack of theoretical understanding, deep neural networks have achieved unparalleled performance in a wide range of applications. On the other hand, shallow representation learning with component analysis is associated with rich…

It has been shown that deep learning models can under certain circumstances outperform traditional statistical methods at forecasting. Furthermore, various techniques have been developed for quantifying the forecast uncertainty (prediction…

Complex network topologies and hyperbolic geometry seem specularly connected, and one of the most fascinating and challenging problems of recent complex network theory is to map a given network to its hyperbolic space. The Popularity…

We construct a family of hyperbolic link complements by gluing tangles along totally geodesic four-punctured spheres, then investigate the commensurability relation among its members. Those with different volume are incommensurable,…