Related papers: Topological Deep Learning: Classification Neural N…
Persistent topological properties of an image serve as an additional descriptor providing an insight that might not be discovered by traditional neural networks. The existing research in this area focuses primarily on efficiently…
Deep neural network has recently shown very promising applications in different research directions and attracted the industry attention as well. Although the idea was introduced in the past but just recently the main limitation of using…
The unwavering success of deep learning in the past decade led to the increasing prevalence of deep learning methods in various application fields. However, the downsides of deep learning, most prominently its lack of trustworthiness, may…
In recent years, with the rapid development of information on the Internet, the number of complex texts and documents has increased exponentially, which requires a deeper understanding of deep learning methods in order to accurately…
The techniques of deep learning have become the state of the art methodology for executing complicated tasks from various domains of computer vision, natural language processing, and several other areas. Due to its rapid development and…
Social network analysis is an important problem in data mining. A fundamental step for analyzing social networks is to encode network data into low-dimensional representations, i.e., network embeddings, so that the network topology…
Deep Learning refers to a set of machine learning techniques that utilize neural networks with many hidden layers for tasks, such as image classification, speech recognition, language understanding. Deep learning has been proven to be very…
Using tools from topology and functional analysis, we provide a framework where artificial neural networks, and their architectures, can be formally described. We define the notion of machine in a general topological context and show how…
Deep learning has recently become one of the most popular sub-fields of machine learning owing to its distributed data representation with multiple levels of abstraction. A diverse range of deep learning algorithms are being employed to…
Deep learning (DL) is a high dimensional data reduction technique for constructing high-dimensional predictors in input-output models. DL is a form of machine learning that uses hierarchical layers of latent features. In this article, we…
As both machine learning models and the datasets on which they are evaluated have grown in size and complexity, the practice of using a few summary statistics to understand model performance has become increasingly problematic. This is…
Deep learning is a powerful tool for solving nonlinear differential equations, but usually, only the solution corresponding to the flattest local minimizer can be found due to the implicit regularization of stochastic gradient descent. This…
In this work we use the persistent homology method, a technique in topological data analysis (TDA), to extract essential topological features from the data space and combine them with deep learning features for classification tasks. In TDA,…
Deep neural networks are powerful tools to detect hidden patterns in data and leverage them to make predictions, but they are not designed to understand uncertainty and estimate reliable probabilities. In particular, they tend to be…
This paper presents the first approach to visualize the importance of topological features that define classes of data. Topological features, with their ability to abstract the fundamental structure of complex data, are an integral…
In artificial-intelligence-aided signal processing, existing deep learning models often exhibit a black-box structure, and their validity and comprehensibility remain elusive. The integration of topological methods, despite its relatively…
Probabilistic deep learning is deep learning that accounts for uncertainty, both model uncertainty and data uncertainty. It is based on the use of probabilistic models and deep neural networks. We distinguish two approaches to probabilistic…
Deep learning relies on a very specific kind of neural networks: those superposing several neural layers. In the last few years, deep learning achieved major breakthroughs in many tasks such as image analysis, speech recognition, natural…
The unprecedented pace of machine learning research has lead to incredible advances, but also poses hard challenges. At present, the field lacks strong theoretical underpinnings, and many important achievements stem from ad hoc design…
With the growth of deep learning, how to describe deep neural networks unifiedly is becoming an important issue. We first formalize neural networks mathematically with their directed graph representations, and prove a generation theorem…