Related papers: Explicit construction of recurrent neural networks…

In this paper, we develop a compositional scheme for the construction of continuous approximations for interconnections of infinitely many discrete-time switched systems. An approximation (also known as abstraction) is itself a…

Reverse engineering of complex dynamical networks is important for a variety of fields where uncovering the full topology of unknown networks and estimating parameters characterizing the network structure and dynamical processes are of…

Recurrent Networks are one of the most powerful and promising artificial neural network algorithms to processing the sequential data such as natural languages, sound, time series data. Unlike traditional feed-forward network, Recurrent…

Time series forecasting is difficult. It is difficult even for recurrent neural networks with their inherent ability to learn sequentiality. This article presents a recurrent neural network based time series forecasting framework covering…

Recommender systems objectives can be broadly characterized as modeling user preferences over short-or long-term time horizon. A large body of previous research studied long-term recommendation through dimensionality reduction techniques…

We present a framework for constructing physics and causally constrained neural models of turbulent dynamical systems from data. We first formulate a finite-time flow map with strict energy-preserving nonlinearities for stable modeling of…

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…

While deep feature learning has revolutionized techniques for static-image understanding, the same does not quite hold for video processing. Architectures and optimization techniques used for video are largely based off those for static…

The neural network techniques are developed for artificial sequences based on approximate models of proteins. We only encode the hydrophobicity of the amino acid side chains without attempting to model the secondary structure. We use our…

It is difficult to describe in mathematical terms what a neural network trained on data represents. On the other hand, there is a growing mathematical understanding of what neural networks are in principle capable of representing.…

With an increasing amount of observations on the dynamics of many complex systems, it is required to reveal the underlying mechanisms behind these complex dynamics, which is fundamentally important in many scientific fields such as climate,…

Designing mechanically efficient geometry for architectural structures like shells, towers, and bridges, is an expensive iterative process. Existing techniques for solving such inverse problems rely on traditional optimization methods,…

We present a computational algebra solution to reverse engineering the network structure of discrete dynamical systems from data. We use monomial ideals to determine dependencies between variables that encode constraints on the possible…

Detecting structure in noisy time series is a difficult task. One intuitive feature is the notion of trend. From theoretical hints and using simulated time series, we empirically investigate the efficiency of standard recurrent neural…

This book explores an alternative to the current dominant paradigm where a discrete computer model is constructed as an attempt to approximate some continuum theory. We focus on a class of discrete computer models that are based on simple…

In this work, we propose a deep neural network architecture motivated by primal-dual splitting methods from convex optimization. We show theoretically that there exists a close relation between the derived architecture and residual…

The key component in forecasting demand and consumption of resources in a supply network is an accurate prediction of real-valued time series. Indeed, both service interruptions and resource waste can be reduced with the implementation of…

Recently, Neural Networks have been proven extremely effective in many natural language processing tasks such as sentiment analysis, question answering, or machine translation. Aiming to exploit such advantages in the Ontology Learning…

We address the efficiency issue for the construction of a deep graph neural network (GNN). The approach exploits the idea of representing each input graph as a fixed point of a dynamical system (implemented through a recurrent neural…

The topology of social networks can be understood as being inherently dynamic, with edges having a distinct position in time. Most characterizations of dynamic networks discretize time by converting temporal information into a sequence of…