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The network embedding task is to represent the node in the network as a low-dimensional vector while incorporating the topological and structural information. Most existing approaches solve this problem by factorizing a proximity matrix,…
The Hopfield model is a pioneering neural network model with associative memory retrieval. The analytical solution of the model in mean field limit revealed that memories can be retrieved without any error up to a finite storage capacity of…
The Hopfield network has been applied to solve optimization problems over decades. However, it still has many limitations in accomplishing this task. Most of them are inherited from the optimization algorithms it implements. The computation…
Despite a lot of research efforts devoted in recent years, how to efficiently learn long-term dependencies from sequences still remains a pretty challenging task. As one of the key models for sequence learning, recurrent neural network…
Reasoning is the ability to integrate internal states and external inputs in a meaningful and semantically consistent flow. Contemporary machine learning (ML) systems increasingly rely on such sequential reasoning, from language…
We consider a general class of stochastic networks and ask which network nodes need to be controlled, and how, to stabilize and switch between desired metastable (target) states in terms of the first and second statistical moments of the…
We show how a Hopfield network with modifiable recurrent connections undergoing slow Hebbian learning can extract the underlying geometry of an input space. First, we use a slow/fast analysis to derive an averaged system whose dynamics…
Understanding how the brain learns to compute functions reliably, efficiently and robustly with noisy spiking activity is a fundamental challenge in neuroscience. Most sensory and motor tasks can be described as dynamical systems and could…
Cyclic patterns of neuronal activity are ubiquitous in animal nervous systems, and partially responsible for generating and controlling rhythmic movements such as locomotion, respiration, swallowing and so on. Clarifying the role of the…
The state space of a conventional Hopfield network typically exhibits many different attractors of which only a small subset satisfy constraints between neurons in a globally optimal fashion. It has recently been demonstrated that combining…
Real-world networks in technology, engineering and biology often exhibit dynamics that cannot be adequately reproduced using network models given by smooth dynamical systems and a fixed network topology. Asynchronous networks give a…
This paper introduces a novel unsupervised learning paradigm inspired by Gerald Edelman's theory of neuronal group selection ("Neural Darwinism"). The presented automaton learns to recognize arbitrary symbols (e.g., letters of an alphabet)…
The mechanisms responsible for contention of activity in systems represented by networks are crucial in various phenomena, as in diseases such as epilepsy that affects the neuronal networks, and for information dissemination in social…
In this paper we developed a hierarchical network model, called Hierarchical Prediction Network (HPNet), to understand how spatiotemporal memories might be learned and encoded in the recurrent circuits in the visual cortical hierarchy for…
This paper proposes a novel topological learning framework that integrates networks of different sizes and topology through persistent homology. Such challenging task is made possible through the introduction of a computationally efficient…
A model of sensory information processing is presented. The model assumes that learning of internal (hidden) generative models, which can predict the future and evaluate the precision of that prediction, is of central importance for…
Local bifurcation analysis plays a central role in understanding qualitative transitions in networked nonlinear dynamical systems, including dynamic neural network and opinion dynamics models. In this article we establish explicit bounds of…
Neuronal networks constitute a special class of dynamical systems, as they are formed by individual geometrical components, namely the neurons. In the existing literature, relatively little attention has been given to the influence of…
The Hopfield network (HN) is a classical model of associative memory whose dynamics are closely related to the Ising spin system with 2-body interactions. Stored patterns are encoded as minima of an energy function shaped by a Hebbian…
While many neural networks focus on layers to process information, the GAIN model uses a grid-based structure to improve biological plausibility and the dynamics of the model. The grid structure helps neurons to interact with their closest…