Related papers: Strongly nonlinear age structured equation,time-el…
Recent advances in autoregressive neural surrogate models have enabled orders-of-magnitude speedups in simulating dynamical systems. However, autoregressive models are generally prone to distribution drift: compounding errors in…
Temporal networks model a variety of important phenomena involving timed interactions between entities. Existing methods for machine learning on temporal networks generally exhibit at least one of two limitations. First, time is assumed to…
When investigating the spreading of a piece of information or the diffusion of an innovation, we often lack information on the underlying propagation network. Reconstructing the hidden propagation paths based on the observed diffusion…
The principle of linearized stability and instability is established for a classical model describing the spatial movement of an age-structured population with nonlinear vital rates. It is shown that the real parts of the eigenvalues of the…
Recurrent neural networks are a powerful means to cope with time series. We show how autoregressive linear, i.e., linearly activated recurrent neural networks (LRNNs) can approximate any time-dependent function f(t). The approximation can…
We consider two neuronal networks coupled by long-range excitatory interactions. Oscillations in the gamma frequency band are generated within each network by local inhibition. When long-range excitation is weak, these oscillations…
Behavior can be described as a temporal sequence of actions driven by neural activity. To learn complex sequential patterns in neural networks, memories of past activities need to persist on significantly longer timescales than the…
A neural network with fixed topology can be regarded as a parametrization of functions, which decides on the correlations between functional variations when parameters are adapted. We propose an analysis, based on a differential geometry…
Learning models of dynamical systems characterized by specific stability properties is of crucial importance in applications. Existing results mainly focus on linear systems or some limited classes of nonlinear systems and stability…
Empirical data, on which deep learning relies, has substantial internal structure, yet prevailing theories often disregard this aspect. Recent research has led to the definition of structured data ensembles, aimed at equipping established…
Deep learning models have proven to be exceptionally useful in performing many machine learning tasks. However, for each new dataset, choosing an effective size and structure of the model can be a time-consuming process of trial and error.…
Networks of model neurons with balanced recurrent excitation and inhibition produce irregular and asynchronous spiking activity. We extend the analysis of balanced networks to include the known dependence of connection probability on the…
Underpinning the past decades of work on the design, initialization, and optimization of neural networks is a seemingly innocuous assumption: that the network is trained on a \textit{stationary} data distribution. In settings where this…
A single dynamical system with time-delayed feedback can emulate networks. This property of delay systems made them extremely useful tools for Machine Learning applications. Here we describe several possible setups, which allow emulating…
Graph processes exhibit a temporal structure determined by the sequence index and and a spatial structure determined by the graph support. To learn from graph processes, an information processing architecture must then be able to exploit…
We study synchronization for linearly coupled temporal networks of heterogeneous time-dependent nonlinear agents via the convergence of attracting trajectories of each node. The results are obtained by constructing and studying the…
We derive key features of the Age-of-Information distribution in a system whose activities are strictly limited to periodic instances on a global time grid. In particular, one agent periodically generates updates while the other agent…
Neural networks can emulate nonlinear physical systems with high accuracy, yet they may produce physically-inconsistent results when violating fundamental constraints. Here, we introduce a systematic way of enforcing nonlinear analytic…
We model acoustic dynamics in space and time from synthetic sensor data. The tasks are (i) to predict and extrapolate the spatiotemporal dynamics, and (ii) reconstruct the acoustic state from partial observations. To achieve this, we…
Deep neural networks are often used to implement powerful generative models for real-world data. Notable applications include image denoising, as well as other classical inverse problems like compressed sensing and super-resolution. To…