Related papers: Dissipative Deep Neural Dynamical Systems

This paper considers distributed optimization algorithms, with application in binary classification via distributed support-vector-machines (D-SVM) over multi-agent networks subject to some link nonlinearities. The agents solve a…

Deep Neural Networks (DNNs) are being deployed in a wide range of settings today, from safety-critical applications like autonomous driving to commercial applications involving image classifications. However, recent research has shown that…

One of the outstanding problems in complexity science and dynamical system theory is understanding the dynamic behavior of high-dimensional networked systems and their susceptibility to transitions to undesired states. Because of varied…

In real-world networks the interactions between network elements are inherently time-delayed. These time-delays can not only slow the network but can have a destabilizing effect on the network's dynamics leading to poor performance. The…

Despite the widespread practical success of deep learning methods, our theoretical understanding of the dynamics of learning in deep neural networks remains quite sparse. We attempt to bridge the gap between the theory and practice of deep…

In this paper we consider complex dynamical networks modeled by means of state space systems running in discrete time. We assume that the dependency structure of the variables within the (nonlinear) network equations is known and use…

We analyze the complexity of classically simulating continuous-time dynamics of locally interacting quantum spin systems with a constant rate of entanglement breaking noise. We prove that a polynomial time classical algorithm can be used to…

Implicit layer deep learning techniques, like Neural Differential Equations, have become an important modeling framework due to their ability to adapt to new problems automatically. Training a neural differential equation is effectively a…

We study the time-asymptotic behavior of linear hyperbolic systems under partial dissipation which is localized in suitable subsets of the domain. More precisely, we recover the classical decay rates of partially dissipative systems…

Classical network embeddings create a low dimensional representation of the learned relationships between features across nodes. Such embeddings are important for tasks such as link prediction and node classification. In the current paper,…

Dynamic neural network is an emerging research topic in deep learning. Compared to static models which have fixed computational graphs and parameters at the inference stage, dynamic networks can adapt their structures or parameters to…

Considering a network of dissipative quantum harmonic oscillators we deduce and analyze the optimum topologies which are able to store, for the largest period of time, a quantum superposition previously prepared in one of the network…

We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To…

Recurrent Neural Networks (RNNs) are widely used for modelling neural activity, yet the mathematical interplay of core procedures is used to analyze them (temporal rescaling, discretization, and linearization) remain uncharacterized. This…

This paper introduces a network architecture, called dynoNet, utilizing linear dynamical operators as elementary building blocks. Owing to the dynamical nature of these blocks, dynoNet networks are tailored for sequence modeling and system…

To be effective in sequential data processing, Recurrent Neural Networks (RNNs) are required to keep track of past events by creating memories. While the relation between memories and the network's hidden state dynamics was established over…

Deep learning is finding its way into the embedded world with applications such as autonomous driving, smart sensors and aug- mented reality. However, the computation of deep neural networks is demanding in energy, compute power and memory.…

We analyse the stability of linear dynamical systems defined on sparse, random graphs with predator-prey, competitive, and mutualistic interactions. These systems are aimed at modelling the stability of fixed points in large systems defined…

The notion of a part of phase space containing desired (or allowed) states of a dynamical system is important in a wide range of complex systems research. It has been called the safe operating space, the viability kernel or the sunny…

Given a dynamic network, where edges appear and disappear over time, we are interested in finding sets of edges that have similar temporal behavior and form a dense subgraph. Formally, we define the problem as the enumeration of the maximal…