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Deep learning's performance has been extensively recognized recently. Graph neural networks (GNNs) are designed to deal with graph-structural data that classical deep learning does not easily manage. Since most GNNs were created using…

Recent researches on complex systems highlighted the so-called super-linear growth phenomenon. As the system size $P$ measured as population in cities or active users in online communities increases, the total activities $X$ measured as GDP…

Deep Neural Networks (DNNs) have become very popular for prediction in many areas. Their strength is in representation with a high number of parameters that are commonly learned via gradient descent or similar optimization methods. However,…

Graph neural networks (GNNs) are designed to process data associated with graphs. They are finding an increasing range of applications; however, as with other modern machine learning techniques, their theoretical understanding is limited.…

We characterize the exact solutions to neural network descrambling--a mathematical model for explaining the fully connected layers of trained neural networks (NNs). By reformulating the problem to the minimization of the Brockett function…

This paper introduces a scale-invariant methodology employing \textit{Fractal Geometry} to analyze and explain the nonlinear dynamics of complex connectionist systems. By leveraging architectural self-similarity in Deep Neural Networks…

Graph neural networks (GNNs) have attracted much attention due to their ability to leverage the intrinsic geometries of the underlying data. Although many different types of GNN models have been developed, with many benchmarking procedures…

This paper introduces Graph Convolutional Recurrent Network (GCRN), a deep learning model able to predict structured sequences of data. Precisely, GCRN is a generalization of classical recurrent neural networks (RNN) to data structured by…

Deep learning and convolutional neural networks in particular are powerful and promising tools for cosmological analysis of large-scale structure surveys. They are already providing similar performance to classical analysis methods using…

Graph Neural Networks (GNNs) are powerful models for graph-structured data, with broad applications. However, the interplay between GNN parameter optimization, expressivity, and generalization remains poorly understood. We address this by…

In recent years, there has been a resurgence in methods that use distributed (neural) representations to represent and reason about semantic knowledge for robotics applications. However, while robots often observe previously unknown…

In this paper, we propose DeepTree, a novel method for modeling trees based on learning developmental rules for branching structures instead of manually defining them. We call our deep neural model situated latent because its behavior is…

Graph Neural Networks (GNNs) have emerged as an efficient alternative to convolutional approaches for vision tasks such as image classification, leveraging patch-based representations instead of raw pixels. These methods construct graphs…

The local geometry of high dimensional neural network loss landscapes can both challenge our cherished theoretical intuitions as well as dramatically impact the practical success of neural network training. Indeed recent works have observed…

Graph neural networks (GNNs) have demonstrated a significant boost in prediction performance on graph data. At the same time, the predictions made by these models are often hard to interpret. In that regard, many efforts have been made to…

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…

Deep learning's success has been widely recognized in a variety of machine learning tasks, including image classification, audio recognition, and natural language processing. As an extension of deep learning beyond these domains, graph…

This work bridges two important concepts: the Neural Tangent Kernel (NTK), which captures the evolution of deep neural networks (DNNs) during training, and the Neural Collapse (NC) phenomenon, which refers to the emergence of symmetry and…

We introduce Graph-Structured Sum-Product Networks (GraphSPNs), a probabilistic approach to structured prediction for problems where dependencies between latent variables are expressed in terms of arbitrary, dynamic graphs. While many…

Recent deep learning approaches for representation learning on graphs follow a neighborhood aggregation procedure. We analyze some important properties of these models, and propose a strategy to overcome those. In particular, the range of…