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We present diffusion-convolutional neural networks (DCNNs), a new model for graph-structured data. Through the introduction of a diffusion-convolution operation, we show how diffusion-based representations can be learned from…
Recently, graph neural networks (GNNs) have proved to be suitable in tasks on unstructured data. Particularly in tasks as community detection, node classification, and link prediction. However, most GNN models still operate with static…
This paper builds on the connection between graph neural networks and traditional dynamical systems. We propose continuous graph neural networks (CGNN), which generalise existing graph neural networks with discrete dynamics in that they can…
Identifying critical nodes and links in graphs is a crucial task. These nodes/links typically represent critical elements/communication links that play a key role in a system's performance. However, a majority of the methods available in…
We introduce a multimodal deep learning framework, Prescriptive Neural Networks (PNNs), that combines ideas from optimization and machine learning, and is, to the best of our knowledge, the first prescriptive method to handle multimodal…
Our brain consists of biological neurons encoding information through accurate spike timing, yet both the architecture and learning rules of our brain remain largely unknown. Comparing to the recent development of backpropagation-based…
Conditional belief networks introduce stochastic binary variables in neural networks. Contrary to a classical neural network, a belief network can predict more than the expected value of the output $Y$ given the input $X$. It can predict a…
Graph Neural Networks (GNNs) have recently become increasingly popular due to their ability to learn complex systems of relations or interactions arising in a broad spectrum of problems ranging from biology and particle physics to social…
In this paper we propose a novel neural network model for learning stochastic Hamiltonian systems (SHSs) from observational data, termed the stochastic generating function neural network (SGFNN). SGFNN preserves symplectic structure of the…
We investigate the functioning of a classifying biological neural network from the perspective of statistical learning theory, modelled, in a simplified setting, as a continuous-time stochastic recurrent neural network (RNN) with identity…
Despite the recent successes of probabilistic programming languages (PPLs) in AI applications, PPLs offer only limited support for random variables whose distributions combine discrete and continuous elements. We develop the notion of…
Structured stochastic processes evolving in continuous time present a widely adopted framework to model phenomena occurring in nature and engineering. However, such models are often chosen to satisfy the Markov property to maintain…
Bayesian Neural Networks (BNNs) provide a promising framework for modeling predictive uncertainty and enhancing out-of-distribution robustness (OOD) by estimating the posterior distribution of network parameters. Stochastic Gradient Markov…
We introduce a novel neural network structure called Strongly Constrained Theory-Guided Neural Network (SCTgNN), to investigate the behaviours of the localized solutions of the generalized nonlinear Schr\"{o}dinger (NLS) equation. This…
In this paper we present a language for finite state continuous time Bayesian networks (CTBNs), which describe structured stochastic processes that evolve over continuous time. The state of the system is decomposed into a set of local…
Turbulence modeling is a classical approach to address the multiscale nature of fluid turbulence. Instead of resolving all scales of motion, which is currently mathematically and numerically intractable, reduced models that capture the…
Deep neural networks (DNNs) have delivered a remarkable performance in many tasks of computer vision. However, over-parameterized representations of popular architectures dramatically increase their computational complexity and storage…
Current statistical models for structured prediction make simplifying assumptions about the underlying output graph structure, such as assuming a low-order Markov chain, because exact inference becomes intractable as the tree-width of the…
Data-driven approaches are increasingly popular for identifying dynamical systems due to improved accuracy and availability of sensor data. However, relying solely on data for identification does not guarantee that the identified systems…
In recent years, spiking neural networks (SNNs) have attracted substantial interest due to their potential to replicate the energy-efficient and event-driven processing of biological neurons. Despite this, the application of SNNs in graph…