Related papers: A Generalized Kahn Principle for Abstract Asynchro…
We introduce an abstract neural flow framework for neural networks and neural operators. The framework contains two continuous-depth models, namely neural flows with composition and separation structures, and covers both finite-dimensional…
In this paper, a Neural network is derived from first principles, assuming only that each layer begins with a linear dimension-reducing transformation. The approach appeals to the principle of Maximum Entropy (MaxEnt) to find the posterior…
Even the most sophisticated artificial neural networks are built by aggregating substantially identical units called neurons. A neuron receives multiple signals, internally combines them, and applies a non-linear function to the resulting…
Graph neural networks (GNNs) have recently exploded in popularity thanks to their broad applicability to graph-related problems such as quantum chemistry, drug discovery, and high energy physics. However, meeting demand for novel GNN models…
Network modeling is a fundamental tool in network research, design, and operation. Arguably the most popular method for modeling is Queuing Theory (QT). Its main limitation is that it imposes strong assumptions on the packet arrival…
Artificial networks have been studied through the prism of statistical mechanics as disordered systems since the 80s, starting from the simple models of Hopfield's associative memory and the single-neuron perceptron classifier. Assuming…
Dynamical networks are important models for the behaviour of complex systems, modelling physical, biological and societal systems, including the brain, food webs, epidemic disease in populations, power grids and many other. Such dynamical…
Networks are a useful representation for data on connections between units of interests, but the observed connections are often noisy and/or include missing values. One common approach to network analysis is to treat the network as a…
We report on all- to- all chaos synchronization in a network of networks based on the Ikeda model. We consider one of the simplest cases. We find the existence and stability conditions for such a synchronization regime. Numerical…
Attaining prototypical features to represent class distributions is well established in representation learning. However, learning prototypes online from streaming data proves a challenging endeavor as they rapidly become outdated, caused…
Networks are fundamental models for data used in practically every application domain. In most instances, several implicit or explicit choices about the network definition impact the translation of underlying data to a network…
Networks are ubiquitous throughout science and engineering. A number of methods, including some from our own group, have explored how one goes about computing or predicting the dynamics of networks given information about internal models of…
For highly distributed environments such as edge computing, collaborative learning approaches eschew the dependence on a global, shared model, in favor of models tailored for each location. Creating tailored models for individual learning…
Neural networks are a revolutionary but immature technique that is fast evolving and heavily relies on data. To benefit from the newest development and newly available data, we want the gap between research and production as small as…
Comparative analyses of graph structured datasets underly diverse problems. Examples of these problems include identification of conserved functional components (biochemical interactions) across species, structural similarity of large…
In-network computation represents a transformative approach to addressing the escalating demands of Artificial Intelligence (AI) workloads on network infrastructure. By leveraging the processing capabilities of network devices such as…
Datalog$^\neg$ is a central formalism used in a variety of domains ranging from deductive databases and abstract argumentation frameworks to answer set programming. Its model theory is the finite counterpart of the logical semantics…
Based on a natural connection between ResNet and transport equation or its characteristic equation, we propose a continuous flow model for both ResNet and plain net. Through this continuous model, a ResNet can be explicitly constructed as a…
We propose a new model for networks of time series that influence each other. Graph structures among time series are found in diverse domains, such as web traffic influenced by hyperlinks, product sales influenced by recommendation, or…
Quantum graphs model processes in complex systems represented as spatial networks in various fields of natural science and technology. An example is the oscillations of elastic string networks, the nodes of which, besides the continuity…