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Many applications, such as optimization, uncertainty quantification and inverse problems, require repeatedly performing simulations of large-dimensional physical systems for different choices of parameters. This can be prohibitively…
The activity of neurons is correlated, and this correlation affects how the brain processes information. We study the neural circuit mechanisms of correlations by analyzing a network model characterized by strong and heterogeneous…
Recurrent neural networks (RNNs) are capable of learning features and long term dependencies from sequential and time-series data. The RNNs have a stack of non-linear units where at least one connection between units forms a directed cycle.…
Reverberating dynamics of neural network is modelled on PC in order to illustrate possible role of inhibition as binding controller in the network. The network is composed of binding neurons. In the binding neuron model the degree of…
We present a morphological-symmetry-equivariant heterogeneous graph neural network, namely MS-HGNN, for robotic dynamics learning, that integrates robotic kinematic structures and morphological symmetries into a single graph network. These…
The relation between neural activity and behaviorally relevant variables is at the heart of neuroscience research. When strong, this relation is termed a neural representation. There is increasing evidence, however, for partial…
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…
Viewing recurrent neural networks (RNNs) as continuous-time dynamical systems, we propose a recurrent unit that describes the hidden state's evolution with two parts: a well-understood linear component plus a Lipschitz nonlinearity. This…
In this paper, we introduces a Pseudo-Symplectic Neural Network (PSNN) for learning general Hamiltonian systems (both separable and non-separable) from data. To address the limitations of existing structure-preserving methods (e.g.,…
We study a rate-model neural network composed of excitatory and inhibitory neurons in which neuronal input-output functions are power laws with a power greater than 1, as observed in primary visual cortex. This supralinear input-output…
Continuous-Time Recurrent Neural Networks (CTRNNs) have been widely used for their capacity to model complex temporal behaviour. However, their internal dynamics often remain difficult to interpret. In this paper, we propose a new class of…
Spiking Neural Networks (SNNs) offer energy-efficient and biologically plausible alternatives to traditional artificial neural networks, but their performance depends critically on the tuning of neuron model parameters. In this work, we…
We study heteroclinic networks in $\mathbb{R}^4$, made of a certain type of simple robust heteroclinic cycle. In simple cycles all the connections are of saddle-sink type in two-dimensional fixed-point spaces. We show that there exist only…
Recurrently coupled oscillators that are sufficiently heterogeneous and/or randomly coupled can show an asynchronous activity in which there are no significant correlations among the units of the network. The asynchronous state can…
We present a formal, mathematical foundation for modeling and reasoning about the behavior of $synchronous$, $stochastic$ $Spiking$ $Neural$ $Networks$ $(SNNs)$, which have been widely used in studies of neural computation. Our approach…
Efficient and robust control using spiking neural networks (SNNs) is still an open problem. Whilst behaviour of biological agents is produced through sparse and irregular spiking patterns, which provide both robust and efficient control,…
We study the asymptotic behavior for asymmetric neuronal dynamics in a network of linear Hopfield neurons. The interaction between the neurons is modeled by random couplings which are centered i.i.d. random variables with finite moments of…
Spiking activity of neurons engaged in learning and performing a task show complex spatiotemporal dynamics. While the output of recurrent network models can learn to perform various tasks, the possible range of recurrent dynamics that…
Tunnelling from a chaotic potential well is explained in terms of a set of complex periodic orbits which contain information about the real dynamics inside the well as well as the complex dynamics under the confining barrier. These orbits…
This paper describes how realistic neuromorphic networks can have their connectivity fully characterized in analytical fashion. By assuming that all neurons have the same shape and are regularly distributed along the two-dimensional…