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Recent advancements in graph learning have revolutionized the way to understand and analyze data with complex structures. Notably, Graph Neural Networks (GNNs), i.e. neural network architectures designed for learning graph representations,…

Deep neural networks (DNNs) are the workhorses of deep learning, which constitutes the state of the art in numerous application domains. However, DNN-based decision rules are notoriously prone to poor generalization, i.e., may prove…

When several models have similar training scores, classical model selection heuristics follow Occam's razor and advise choosing the ones with least capacity. Yet, modern practice with large neural networks has often led to situations where…

Deep neural networks (DNNs) play a crucial role in the field of machine learning, demonstrating state-of-the-art performance across various application domains. However, despite their success, DNN-based models may occasionally exhibit…

The ubiquity of neural networks (NNs) in real-world applications, from healthcare to natural language processing, underscores their immense utility in capturing complex relationships within high-dimensional data. However, NNs come with…

Learning deep representations to solve complex machine learning tasks has become the prominent trend in the past few years. Indeed, Deep Neural Networks are now the golden standard in domains as various as computer vision, natural language…

The predominant success of diffusion models in generative modeling has spurred significant interest in understanding their theoretical foundations. In this work, we propose a feature learning framework aimed at analyzing and comparing the…

Recent breakthroughs in AI have shown the remarkable power of deep learning and deep reinforcement learning. These developments, however, have been tied to specific tasks, and progress in out-of-distribution generalization has been limited.…

Randomized Neural Networks explore the behavior of neural systems where the majority of connections are fixed, either in a stochastic or a deterministic fashion. Typical examples of such systems consist of multi-layered neural network…

This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the…

The methods of extracting image features are the key to many image processing tasks. At present, the most popular method is the deep neural network which can automatically extract robust features through end-to-end training instead of…

Combining machine learning with logic-based expert systems in order to get the best of both worlds are becoming increasingly popular. However, to what extent machine learning can already learn to reason over rule-based knowledge is still an…

Deep neural networks have achieved great success both in computer vision and natural language processing tasks. However, mostly state-of-art methods highly rely on external training or computing to improve the performance. To alleviate the…

Inspired by the brain, deep neural networks (DNN) are thought to learn abstract representations through their hierarchical architecture. However, at present, how this happens is not well understood. Here, we demonstrate that DNN learn…

Graph representation learning aims to effectively encode high-dimensional sparse graph-structured data into low-dimensional dense vectors, which is a fundamental task that has been widely studied in a range of fields, including machine…

The random neural network (RNN) is a mathematical model for an "integrate and fire" spiking network that closely resembles the stochastic behaviour of neurons in mammalian brains. Since its proposal in 1989, there have been numerous…

A challenging open question in deep learning is how to handle tabular data. Unlike domains such as image and natural language processing, where deep architectures prevail, there is still no widely accepted neural architecture that dominates…

In this work, we describe a new approach that uses deep neural networks (DNN) to obtain regularization parameters for solving inverse problems. We consider a supervised learning approach, where a network is trained to approximate the…

In this paper, we study the problem of learning probabilistic logical rules for inductive and interpretable link prediction. Despite the importance of inductive link prediction, most previous works focused on transductive link prediction…

Signal processing, communications, and control have traditionally relied on classical statistical modeling techniques. Such model-based methods utilize mathematical formulations that represent the underlying physics, prior information and…