Related papers: Explicit construction of recurrent neural networks…

The network structure (or topology) of a dynamical network is often unavailable or uncertain. Hence, we consider the problem of network reconstruction. Network reconstruction aims at inferring the topology of a dynamical network using…

Large-scale recurrent networks have drawn increasing attention recently because of their capabilities in modeling a large variety of real-world phenomena and physical mechanisms. This paper studies how to identify all authentic connections…

Spatial and temporal resource constraints are critical for both biological and artificial intelligent systems. Here we define differentiable cost terms for breadth, depth, and time within a recurrent convolutional neural network conceived…

We consider a class of systems over finite alphabets, namely discrete-time systems with linear dynamics and a finite input alphabet. We formulate a notion of finite uniform bisimulation, and motivate and propose a notion of regular finite…

This paper is concerned with fundamental limits on the approximation of nonlinear dynamical systems. Specifically, we show that recurrent neural networks (RNNs) can approximate nonlinear systems -- that satisfy a Lipschitz property and…

Time-reversal symmetry arises naturally as a structural property in many dynamical systems of interest. While the importance of hard-wiring symmetry is increasingly recognized in machine learning, to date this has eluded time-reversibility.…

Precise timing of spikes and temporal locking are key elements of neural computation. Here we demonstrate how even strongly heterogeneous, deterministic neural networks with delayed interactions and complex topology can exhibit periodic…

Substring kernels are classical tools for representing biological sequences or text. However, when large amounts of annotated data are available, models that allow end-to-end training such as neural networks are often preferred. Links…

We investigate recurrent neural networks with asymmetric interactions and demonstrate that the inclusion of self-couplings or sparse excitatory inter-module connections leads to the emergence of a densely connected manifold of dynamically…

We investigate what can be learned from translating numerical algorithms into neural networks. On the numerical side, we consider explicit, accelerated explicit, and implicit schemes for a general higher order nonlinear diffusion equation…

We construct compositional continuous approximations for an interconnection of infinitely many discrete-time switched systems. An approximation (known as abstraction) is itself a continuous-space system, which can be used as a replacement…

The structure of a complex network plays a crucial role in determining its dynamical properties. In this work, we show that the the degree to which a network is directed and hierarchically organised is closely associated with the degree to…

Many reinforcement learning algorithms are built on an assumption that an agent interacts with an environment over fixed-duration, discrete time steps. However, physical systems are continuous in time, requiring a choice of…

Learning with recurrent neural networks (RNNs) on long sequences is a notoriously difficult task. There are three major challenges: 1) complex dependencies, 2) vanishing and exploding gradients, and 3) efficient parallelization. In this…

Temporal networks model how the interaction between elements in a complex system evolve over time. Just like complex systems display collective dynamics, here we interpret temporal networks as trajectories performing a collective motion in…

This paper studies the problem of recursively estimating the weighted adjacency matrix of a network out of a temporal sequence of binary-valued observations. The observation sequence is generated from nonlinear networked dynamics in which…

We study the approximation properties of convolutional architectures applied to time series modelling, which can be formulated mathematically as a functional approximation problem. In the recurrent setting, recent results reveal an…

Dynamical processes on complex networks such as information propagation, innovation diffusion, cascading failures or epidemic spreading are highly affected by their underlying topologies as characterized by, for instance, degree-degree…

Recurrent neural networks (RNNs) are a class of nonlinear dynamical systems often used to model sequence-to-sequence maps. RNNs have excellent expressive power but lack the stability or robustness guarantees that are necessary for many…

While deep neural networks take loose inspiration from neuroscience, it is an open question how seriously to take the analogies between artificial deep networks and biological neuronal systems. Interestingly, recent work has shown that deep…