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This survey provides a comprehensive exploration of applications of Topological Data Analysis (TDA) within neural network analysis. Using TDA tools such as persistent homology and Mapper, we delve into the intricate structures and behaviors…

The usual figure of merit characterizing the performance of neural networks applied to problems in the quantum domain is their accuracy, being the probability of a correct answer on a previously unseen input. Here we append this parameter…

Topological deep learning is a formalism that is aimed at introducing topological language to deep learning for the purpose of utilizing the minimal mathematical structures to formalize problems that arise in a generic deep learning…

Diversity of environments is a key challenge that causes learned robotic controllers to fail due to the discrepancies between the training and evaluation conditions. Training from demonstrations in various conditions can mitigate---but not…

Bayesian neural networks utilize probabilistic layers that capture uncertainty over weights and activations, and are trained using Bayesian inference. Since these probabilistic layers are designed to be drop-in replacement of their…

Bayesian neural networks allow us to keep track of uncertainties, for example in top tagging, by learning a tagger output together with an error band. We illustrate the main features of Bayesian versions of established deep-learning…

Techniques for understanding the functioning of complex machine learning models are becoming increasingly popular, not only to improve the validation process, but also to extract new insights about the data via exploratory analysis. Though…

Deep neural networks are increasingly being used for the analysis of medical images. However, most works neglect the uncertainty in the model's prediction. We propose an uncertainty-aware deep kernel learning model which permits the…

Artificial neural networks will always make a prediction, even when completely uncertain and regardless of the consequences. This obliviousness of uncertainty is a major obstacle towards their adoption in practice. Techniques exist,…

Topology learning of networked dynamical systems is an important problem with implications to optimal control, decision-making over networks, cybersecurity and safety. The majority of prior work in consistent topology estimation relies on…

Existing methods for estimating uncertainty in deep learning tend to require multiple forward passes, making them unsuitable for applications where computational resources are limited. To solve this, we perform probabilistic reasoning over…

Deep unrolling is an emerging deep learning-based image reconstruction methodology that bridges the gap between model-based and purely deep learning-based image reconstruction methods. Although deep unrolling methods achieve…

Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…

Deep neural networks have achieved impressive results on a wide variety of tasks. However, quantifying uncertainty in the network's output is a challenging task. Bayesian models offer a mathematical framework to reason about model…

Deep neural networks has been increasingly applied in fault diagnostics, where it uses historical data to capture systems behavior, bypassing the need for high-fidelity physical models. However, despite their competence in prediction tasks,…

Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs,…

Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a…

End-to-end trained neural networks (NNs) are a compelling approach to autonomous vehicle control because of their ability to learn complex tasks without manual engineering of rule-based decisions. However, challenging road conditions,…

In many real applications that use and analyze networked data, the links in the network graph may be erroneous, or derived from probabilistic techniques. In such cases, the node classification problem can be challenging, since the…

Despite significant advances in the field of deep learning in applications to various fields, explaining the inner processes of deep learning models remains an important and open question. The purpose of this article is to describe and…