Related papers: Isospectral Reductions of Dynamical Networks

Two networks are equivalent if they produce the same output for any given input. In this paper, we study the possibility of transforming a deep neural network to another network with a different number of units or layers, which can be…

To cope with the complexity of large networks, a number of dimensionality reduction techniques for graphs have been developed. However, the extent to which information is lost or preserved when these techniques are employed has not yet been…

In this manuscript, we show that any neural network with any activation function can be represented as a decision tree. The representation is equivalence and not an approximation, thus keeping the accuracy of the neural network exactly as…

We present a new computational scheme aimed at reducing the complexity of the chemical networks in astrophysical models, one which is shown to markedly improve their computational efficiency. It contains a flux-reduction scheme that permits…

We introduce a new method for predicting the formation of links in real-world networks, which we refer to as the method of effective transitions. This method relies on the theory of isospectral matrix reductions to compute the probability…

An increasing number of models require the control of the spectral norm of convolutional layers of a neural network. While there is an abundance of methods for estimating and enforcing upper bounds on those during training, they are…

Many real world networks are very large and constantly change over time. These dynamic networks exist in various domains such as social networks, traffic networks and biological interactions. To handle large dynamic networks in downstream…

Deep convolutional neural networks have revolutionized many machine learning and computer vision tasks, however, some remaining key challenges limit their wider use. These challenges include improving the network's robustness to…

Random matrix theory is finding an increasing number of applications in the context of information theory and communication systems, especially in studying the properties of complex networks. Such properties include short-term and long-term…

A large variety of dynamical processes that take place on networks can be expressed in terms of the spectral properties of some linear operator which reflects how the dynamical rules depend on the network topology. Often such spectral…

The widespread relevance of complex networks is a valuable tool in the analysis of a broad range of systems. There is a demand for tools which enable the extraction of meaningful information and allow the comparison between different…

While gradient descent has proven highly successful in learning connection weights for neural networks, the actual structure of these networks is usually determined by hand, or by other optimization algorithms. Here we describe a simple…

This paper describes how realistic neuromorphic networks can have their connectivity properties fully characterized in analytical fashion. By assuming that all neurons have the same shape and are regularly distributed along the…

Introduced is a methodology for adapting the topology of dense neural networks, enabled by isotropic activation functions. Achieved through prescribed reparameterisation symmetries and singular-value decomposition of affine maps, this…

We formulate a reduction theory that describes the response of an oscillator network as a whole to external forcing applied nonuniformly to its constituent oscillators. The phase description of multiple oscillator networks coupled weakly is…

This paper considers the problem of designing a dynamical system to solve constrained optimization problems in a distributed way and in an anytime fashion (i.e., such that the feasible set is forward invariant). For problems with separable…

The process of training an artificial neural network involves iteratively adapting its parameters so as to minimize the error of the network's prediction, when confronted with a learning task. This iterative change can be naturally…

In this paper, we propose a novel implicit semantic data augmentation (ISDA) approach to complement traditional augmentation techniques like flipping, translation or rotation. Our work is motivated by the intriguing property that deep…

Complex networks are frequently employed to model physical or virtual complex systems. When certain entities exist across multiple systems simultaneously, unveiling their corresponding relationships across the networks becomes crucial. This…

Dynamic networks are ubiquitous for modelling sequential graph-structured data, e.g., brain connectome, population flows and messages exchanges. In this work, we consider dynamic networks that are temporal sequences of graph snapshots, and…