Related papers: Efficient low-dimensional approximation of continu…

Modeling the locations of nodes as a uniform binomial point process (BPP), we present a generic mathematical framework to characterize the performance of an arbitrarily-located reference receiver in a finite wireless network. Different from…

Deep neural networks have proven to be particularly effective in visual and audio recognition tasks. Existing models tend to be computationally expensive and memory intensive, however, and so methods for hardware-oriented approximation have…

Modeling brain dynamics to better understand and control complex behaviors underlying various cognitive brain functions are of interests to engineers, mathematicians, and physicists from the last several decades. With a motivation of…

Recurrent neural networks have seen widespread use in modeling dynamical systems in varied domains such as weather prediction, text prediction and several others. Often one wishes to supplement the experimentally observed dynamics with…

Line attractors in neuronal networks have been suggested to be the basis of many brain functions, such as working memory, oculomotor control, head movement, locomotion, and sensory processing. In this paper, we make the connection between…

Reduced order models are computationally inexpensive approximations that capture the important dynamical characteristics of large, high-fidelity computer models of physical systems. This paper applies machine learning techniques to improve…

We study dropout regularization in continuous-time models through the lens of random-batch methods -- a family of stochastic sampling schemes originally devised to reduce the computational cost of interacting particle systems. We construct…

For many tasks of data analysis, we may only have the information of the explanatory variable and the evaluation of the response values are quite expensive. While it is impractical or too costly to obtain the responses of all units, a…

Contemporary modeling approaches to the dynamics of neural networks consider two main classes of models: biologically grounded spiking neurons and functionally inspired rate-based units. The unified simulation framework presented here…

Recent progress in deep learning has been driven by increasingly larger models. However, their computational and energy demands have grown proportionally, creating significant barriers to their deployment and to a wider adoption of deep…

Qualitatively, some real networks in the brain could be characterized as 'small worlds', in the sense that the structure of their connections is intermediate between the extremes of an orderly geometric arrangement and of a…

Attractor networks are an influential theory for memory storage in brain systems. This theory has recently been challenged by the observation of strong temporal variability in neuronal recordings during memory tasks. In this work, we study…

Neural processes (NPs) learn stochastic processes and predict the distribution of target output adaptively conditioned on a context set of observed input-output pairs. Furthermore, Attentive Neural Process (ANP) improved the prediction…

We propose a hierarchical training algorithm for standard feed-forward neural networks that adaptively extends the network architecture as soon as the optimization reaches a stationary point. By solving small (low-dimensional) optimization…

In this lecture I will present some models of neural networks that have been developed in the recent years. The aim is to construct neural networks which work as associative memories. Different attractors of the network will be identified…

Spiking neural networks (SNNs) have closer dynamics to the brain than current deep neural networks. Their low power consumption and sample efficiency make these networks interesting. Recently, several deep convolutional spiking neural…

Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. The topologies of random Boolean networks with one input per…

Attractor neural networks consider that neural information is stored as stationary states of a dynamical system formed by a large number of interconnected neurons. The attractor property empowers a neural system to encode information…

We extend a recently introduced class of exactly solvable models for recurrent neural networks with competition between 1D nearest neighbour and infinite range information processing. We increase the potential for further frustration and…

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…