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Deep learning (DL) enables deep neural networks (DNNs) to automatically learn complex tasks or rules from given examples without instructions or guiding principles. As we do not engineer DNNs' functions, it is extremely difficult to…

In recent years, deep learning using neural network architecture, i.e. deep neural networks, has been on the frontier of computer science research. It has even lead to superhuman performance in some problems, e.g., in computer vision, games…

While deep ensembles are widely considered to be the default method for uncertainty quantification in deep learning, their effectiveness for graph-structured data is often simply assumed based on successes in domains like computer vision.…

Why does Deep Learning work? What representations does it capture? How do higher-order representations emerge? We study these questions from the perspective of group theory, thereby opening a new approach towards a theory of Deep learning.…

Algorithms based on deep network models are being used for many pattern recognition and decision-making tasks in robotics and AI. Training these models requires a large labeled dataset and considerable computational resources, which are not…

It is widely believed that learning good representations is one of the main reasons for the success of deep neural networks. Although highly intuitive, there is a lack of theory and systematic approach quantitatively characterizing what…

Deep learning algorithms demonstrate a surprising ability to learn high-dimensional tasks from limited examples. This is commonly attributed to the depth of neural networks, enabling them to build a hierarchy of abstract, low-dimensional…

Machine learning is advancing towards a data-science approach, implying a necessity to a line of investigation to divulge the knowledge learnt by deep neuronal networks. Limiting the comparison among networks merely to a predefined…

State-of-the-art deep neural networks have achieved impressive results on many image classification tasks. However, these same architectures have been shown to be unstable to small, well sought, perturbations of the images. Despite the…

The world is structured in countless ways. It may be prudent to enforce corresponding structural properties to a learning algorithm's solution, such as incorporating prior beliefs, natural constraints, or causal structures. Doing so may…

Current deep neural networks suffer from two problems; first, they are hard to interpret, and second, they suffer from overfitting. There have been many attempts to define interpretability in neural networks, but they typically lack…

Artificial neural networks (ANNs) are at the core of most Deep learning (DL) algorithms that successfully tackle complex problems like image recognition, autonomous driving, and natural language processing. However, unlike biological brains…

Over the last decade, adversarial attack algorithms have revealed instabilities in deep learning tools. These algorithms raise issues regarding safety, reliability and interpretability in artificial intelligence; especially in high risk…

Deep learning has powered recent successes of artificial intelligence (AI). However, the deep neural network, as the basic model of deep learning, has suffered from issues such as local traps and miscalibration. In this paper, we provide a…

At present, artificial intelligence in the form of machine learning is making impressive progress, especially the field of deep learning (DL) [1]. Deep learning algorithms have been inspired from the beginning by nature, specifically by the…

Neural machine learning methods, such as deep neural networks (DNN), have achieved remarkable success in a number of complex data processing tasks. These methods have arguably had their strongest impact on tasks such as image and audio…

The last decade of machine learning has seen drastic increases in scale and capabilities. Deep neural networks (DNNs) are increasingly being deployed in the real world. However, they are difficult to analyze, raising concerns about using…

Deep neural networks are powerful machines for visual pattern recognition, but reasoning tasks that are easy for humans may still be difficult for neural models. Humans possess the ability to extrapolate reasoning strategies learned on…

In this thesis, we develop various techniques for working with sets in machine learning. Each input or output is not an image or a sequence, but a set: an unordered collection of multiple objects, each object described by a feature vector.…

We show how the success of deep learning could depend not only on mathematics but also on physics: although well-known mathematical theorems guarantee that neural networks can approximate arbitrary functions well, the class of functions of…