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Oscillatory dynamics of complex networks has recently attracted great attention. In this paper we study pattern formation in oscillatory complex networks consisting of excitable nodes. We find that there exist a few center nodes and small…
Neural network models in neuroscience allow one to study how the connections between neurons shape the activity of neural circuits in the brain. In this chapter, we study Combinatorial Threshold-Linear Networks (CTLNs) in order to…
We describe a recurrent neural network (RNN) based architecture to learn the flow function of a causal, time-invariant and continuous-time control system from trajectory data. By restricting the class of control inputs to piecewise constant…
Continual Graph Learning (CGL), which aims to accommodate new tasks over evolving graph data without forgetting prior knowledge, is garnering significant research interest. Mainstream solutions adopt the memory replay-based idea, ie,…
The global asymptotic behavior of a stochastic Hopfield neural network model (HNNM) with delays is explored by studying the existence and structure of random attractors. It is first proved that the trajectory field of the stochastic delayed…
Grid cells in the rodent entorhinal cortex display strikingly regular firing responses to the animal's position in 2-D space, and have been hypothesized to form the neural substrate for dead-reckoning. However, in previous models suggested…
In exploring the simulation of human rhythmic perception and synchronization capabilities, this study introduces a computational model inspired by the physical and biological processes underlying rhythm processing. Utilizing a reservoir…
Networks of neurons in the brain encode preferred patterns of neural activity via their synaptic connections. Despite receiving considerable attention, the precise relationship between network connectivity and encoded patterns is still…
Central Pattern Generators (CPGs) have several properties desirable for locomotion: they generate smooth trajectories, are robust to perturbations and are simple to implement. Although conceptually promising, we argue that the full…
Sequential learning involves learning tasks in a sequence, and proves challenging for most neural networks. Biological neural networks regularly conquer the sequential learning challenge and are even capable of transferring knowledge both…
Traditional artificial neural networks consist of nodes with non-oscillatory dynamics. Biological neural networks, on the other hand, consist of oscillatory components embedded in an oscillatory environment. Motivated by this feature of…
Identifying stimulus-driven neural activity patterns is critical for studying the neural basis of cognition. This can be particularly challenging in intracranial datasets, where electrode locations typically vary across patients. This…
Models based on deep convolutional networks have dominated recent image interpretation tasks; we investigate whether models which are also recurrent, or "temporally deep", are effective for tasks involving sequences, visual and otherwise.…
Neural networks promote a distributed representation with no clear place for symbols. Despite this, we propose that symbols are manufactured simply by training a sparse random noise as a self-sustaining attractor in a feedback spiking…
A variety of nonlinear models of biological systems generate complex chaotic behaviors that contrast with biological homeostasis, the observation that many biological systems prove remarkably robust in the face of changing external or…
The recurrent neural networks (RNN) can be used to solve the sequence to sequence problem, where both the input and the output have sequential structures. Usually there are some implicit relations between the structures. However, it is hard…
We present a model for capturing musical features and creating novel sequences of music, called the Convolutional Variational Recurrent Neural Network. To generate sequential data, the model uses an encoder-decoder architecture with latent…
Oscillatory activity is ubiquitous in natural and engineered network systems. The interaction scheme underlying interdependent oscillatory components governs the emergence of network-wide patterns of synchrony that regulate and enable…
Neural coupling in both neuroscience and artificial intelligence emerges as dynamic oscillatory patterns that encode abstract concepts. To this end, we hypothesize that a deeper understanding of the neural mechanisms governing brain rhythms…
How do humans and animals perform trial-and-error learning when the space of possibilities is infinite? In a previous study, we used an interval timing production task and discovered an updating strategy in which the agent adjusted the…