Related papers: Boundary solution based on rescaling method: recou…

The inclusion of a macroscopic adaptive threshold is studied for the retrieval dynamics of both layered feedforward and fully connected neural network models with synaptic noise. These two types of architectures require a different method…

Recurrent networks of dynamic elements frequently exhibit emergent collective oscillations, which can display substantial regularity even when the individual elements are considerably noisy. How noise-induced dynamics at the local level…

Task-trained recurrent neural networks (RNNs) are widely used in neuroscience and machine learning to model dynamical computations. To gain mechanistic insight into how neural systems solve tasks, prior work often reverse-engineers…

The boundary control problem is a non-convex optimization and control problem in many scientific domains, including fluid mechanics, structural engineering, and heat transfer optimization. The aim is to find the optimal values for the…

Spiking neural networks can compensate for quantization error by encoding information either in the temporal domain, or by processing discretized quantities in hidden states of higher precision. In theory, a wide dynamic range state-space…

With the increasing application of deep learning in mission-critical systems, there is a growing need to obtain formal guarantees about the behaviors of neural networks. Indeed, many approaches for verifying neural networks have been…

Dynamical balance of excitation and inhibition is usually invoked to explain the irregular low firing activity observed in the cortex. We propose a robust nonlinear balancing mechanism for a random network of spiking neurons, which works…

This work studies approximation based on single-hidden-layer feedforward and recurrent neural networks with randomly generated internal weights. These methods, in which only the last layer of weights and a few hyperparameters are optimized,…

We analyze transport on a graph with multiple constraints and where the weight of the edges connecting the nodes is a dynamical variable. The network dynamics results from the interplay between a nonlinear function of the flow, dissipation,…

The accurate treatment of outflow boundary conditions remains a critical challenge in computational fluid dynamics when predicting aerodynamic forces and/or acoustic emissions. This is particularly evident when employing the lattice…

Many iterative and non-iterative methods have been developed for inverse problems associated with Ising models. Aiming to derive an accurate non-iterative method for the inverse problems, we employ the tree-reweighted approximation. Using…

In this paper, we elaborate over the well-known interpretability issue in echo state networks. The idea is to investigate the dynamics of reservoir neurons with time-series analysis techniques taken from research on complex systems.…

This paper is concerned with the approximation of high-dimensional functions in a statistical learning setting, by empirical risk minimization over model classes of functions in tree-based tensor format. These are particular classes of…

The increasing availability of time --and space-- resolved data describing human activities and interactions gives insights into both static and dynamic properties of human behavior. In practice, nevertheless, real-world datasets can often…

We deal with the problem of bridging the gap between two scales in neuronal modeling. At the first (microscopic) scale, neurons are considered individually and their behavior described by stochastic differential equations that govern the…

We propose dynamic scaling in temporal networks with heterogeneous activities and memory, and provide a comprehensive picture for the dynamic topologies of such networks, in terms of the modified activity-driven network model [H. Kim…

Numerical homogenization of multiscale equations typically requires taking an average of the solution to a microscale problem. Both the boundary conditions and domain size of the microscale problem play an important role in the accuracy of…

Neurons in the brain communicate with spikes, which are discrete events in time and value. Functional network models often employ rate units that are continuously coupled by analog signals. Is there a qualitative difference implied by these…

We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a…

Various deep neural network architectures (DNNs) maintain massive vital records in computer vision. While drawing attention worldwide, the design of the overall structure lacks general guidance. Based on the relationship between DNN design…