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Neural circuits in the brain perform a variety of essential functions, including input classification, pattern completion, and the generation of rhythms and oscillations that support processes such as breathing and locomotion. There is also…

Generative adversarial nets (GAN) has been successfully introduced for generating text to alleviate the exposure bias. However, discriminators in these models only evaluate the entire sequence, which causes feedback sparsity and mode…

The past decade has seen tremendous growth in the field of Complex Social Networks. Several network generation models have been extensively studied to develop an understanding of how real world networks evolve over time. Two important…

Biological neural networks can operate in qualitatively distinct dynamical regimes, and transitions between these regimes are thought to underlie changes in computation and behavior. The seminal work of Sompolinsky, Crisanti, and Sommers…

The concept of structured occurrence nets is an extension of that of occurrence nets which are directed acyclic graphs that represent causality and concurrency information concerning a single execution of a distributed system. The formalism…

Over the last years, a great deal of attention has been focused on complex networked systems, characterized by intricate structure and dynamics. The latter has been often represented in terms of overall statistics (e.g. average and standard…

We propose a new framework for the study of continuous time dynamical systems on networks. We view such dynamical systems as collections of interacting control systems. We show that a class of maps between graphs called graph fibrations…

Dynamic neural network is an emerging research topic in deep learning. Compared to static models which have fixed computational graphs and parameters at the inference stage, dynamic networks can adapt their structures or parameters to…

Neural receivers have demonstrated strong performance in wireless communication systems. However, their effectiveness typically depends on access to large-scale, scenario-specific channel data for training, which is often difficult to…

Neural networks have been shown to perform incredibly well in classification tasks over structured high-dimensional datasets. However, the learning dynamics of such networks is still poorly understood. In this paper we study in detail the…

Networks of fast-spiking interneurons are crucial for the generation of neural oscillations in the brain. Here we study the synchronous behavior of interneuronal networks that are coupled by delayed inhibitory and fast electrical synapses.…

We present a natural language generator based on the sequence-to-sequence approach that can be trained to produce natural language strings as well as deep syntax dependency trees from input dialogue acts, and we use it to directly compare…

We analyze the control of frequency for a synchronized inhibitory neuronal network. The analysis is done for a reduced membrane model with a biophysically-based synaptic influence. We argue that such a reduced model can quantitatively…

In this article, we review the literature on statistical theories of neural networks from three perspectives: approximation, training dynamics and generative models. In the first part, results on excess risks for neural networks are…

Generative models using neural network have opened a door to large-scale studies for various application domains, especially for studies that suffer from lack of real samples to obtain statistically robust inference. Typically, these…

We present a general computational theory of stem cell networks and their developmental dynamics. Stem cell networks are special cases of developmental control networks. Our theory generates a natural classification of all possible stem…

The dynamics and the stationary states for the competition between pattern reconstruction and asymmetric sequence processing are studied here in an exactly solvable feed-forward layered neural network model of binary units and patterns near…

This paper considers a network of infinite-server queues with the special feature that, triggered by specific events, the network population vector may undergo a linear transformation (a `multiplicative transition'). For this model we…

Small disturbances can trigger functional breakdowns in complex systems. A challenging task is to infer the structural cause of a disturbance in a networked system, soon enough to prevent a catastrophe. We present a graph neural network…

Recent genomic and bioinformatic advances have motivated the development of numerous random network models purporting to describe graphs of biological, technological, and sociological origin. The success of a model has been evaluated by how…