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Traditional mathematical approaches to studying analytically the dynamics of neural networks rely on the mean-field approximation, which is rigorously applicable only to networks of infinite size. However, all existing real biological…

The article is a lightly edited version of my habilitation thesis at the University Wuerzburg. My aim is to give a self contained, if concise, introduction to the formal methods used when off-line learning in feedforward networks is…

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…

The recent success of Deep Neural Networks (DNNs) has drastically improved the state of the art for many application domains. While achieving high accuracy performance, deploying state-of-the-art DNNs is a challenge since they typically…

In this paper, we are introducing a novel model of artificial intelligence, the functional neural network for modeling of human decision-making processes. This neural network is composed of multiple artificial neurons racing in the network.…

Inference and prediction are fundamental to the study of complex systems, where network data are often incomplete, inaccurate or obtained indirectly. In this paper, we review recent advances in network sampling and comparison, as well as in…

Recent research in artificial intelligence and machine learning has largely emphasized general-purpose learning and ever-larger training sets and more and more compute. In contrast, I propose a hybrid, knowledge-driven, reasoning-based…

Advances in deep learning over the last decade have led to a flurry of research in the application of deep artificial neural networks to robotic systems, with at least thirty papers published on the subject between 2014 and the present.…

We currently witness the spectacular success of artificial intelligence in both science and public life. However, the development of a rigorous mathematical foundation is still at an early stage. In this survey article, which is based on an…

Artificial Neural Networks (ANNs) inspired by biology are beginning to be widely used to model behavioral and neural data, an approach we call neuroconnectionism. ANNs have been lauded as the current best models of information processing in…

Artificial neural networks (ANN), typically referred to as neural networks, are a class of Machine Learning algorithms and have achieved widespread success, having been inspired by the biological structure of the human brain. Neural…

Artificial Neural Networks (ANNs) have demonstrated remarkable utility in various challenging machine learning applications. While formally verified properties of their behaviors are highly desired, they have proven notoriously difficult to…

In biological evolution complex neural structures grow from a handful of cellular ingredients. As genomes in nature are bounded in size, this complexity is achieved by a growth process where cells communicate locally to decide whether to…

Artificial Neural Networks (ANNs) implement a specific form of multi-variate extrapolation and will generate an output for any input pattern, even when there is no similar training pattern. Extrapolations are not necessarily to be trusted,…

While machine learning techniques have been successfully applied in several fields, the black-box nature of the models presents challenges for interpreting and explaining the results. We develop a new framework called Adaptive Explainable…

The Approximate Near Neighbor (ANN) problem is a cornerstone in high-dimensional data analysis, with applications ranging from information retrieval to data mining. Among the most successful paradigms for solving ANN in high-dimensional…

Artificial neural networks (ANNs) are increasingly used as research models, but questions remain about their generalizability and representational invariance. Biological neural networks under social constraints evolved to enable…

Artificial Neuronal Networks are models widely used for many scientific tasks. One of the well-known field of application is the approximation of high-dimensional problems via Deep Learning. In the present paper we investigate the Deep…

The field of neuroscience and the development of artificial neural networks (ANNs) have mutually influenced each other, drawing from and contributing to many concepts initially developed in statistical mechanics. Notably, Hopfield networks…

Understanding neural networks is challenging due to their high-dimensional, interacting components. Inspired by human cognition, which processes complex sensory data by chunking it into recurring entities, we propose leveraging this…