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Randomly connected neural networks have long served as a theoretical tool for studying collective dynamics in neural populations, yet quantitative comparisons to experiments remain limited. Recent technological advances have made it…
The formation of dynamical patterns is one of the most striking features of nonequilibrium physical systems. Recent work has shown that such patterns arise generically from forces that violate Newton's third law, known as nonreciprocal…
We study graded response attractor neural networks with asymmetrically extremely dilute interactions and Langevin dynamics. We solve our model in the thermodynamic limit using generating functional analysis, and find (in contrast to the…
Many networks in nature and applications have an approximate low-rank structure in the sense that their connectivity structure is dominated by a few dimensions. It is natural to expect that dynamics on such networks would also be…
We investigate recurrent neural networks with asymmetric interactions and demonstrate that the inclusion of self-couplings or sparse excitatory inter-module connections leads to the emergence of a densely connected manifold of dynamically…
Given a population of interconnected input-output agents repeatedly exposed to independent random inputs, we talk of correlated variability when agents' outputs are variable (i.e., they change randomly at each input repetition) but…
Inhibitory neurons play a crucial role in maintaining persistent neuronal activity. Although connected extensively through electrical synapses (gap-junctions), these neurons also exhibit interactions through chemical synapses in certain…
Recording simultaneous activity of hundreds of neurons is now possible. Existing methods can model such population activity, but do not directly reveal the computations used by the brain. We present a fully unsupervised method that models…
Brain areas' functional repertoires are shaped by their incoming and outgoing structural connections. In empirically measured networks, most connections are short, reflecting spatial and energetic constraints. Nonetheless, a small number of…
It is well-known that population structure is a catalyst for the evolution of cooperation since individuals can reciprocate with their neighbors through local interactions defined by network structures. Previous research typically relies on…
In a complex system, the interactions between individual agents often lead to emergent collective behavior like spontaneous synchronization, swarming, and pattern formation. The topology of the network of interactions can have a dramatic…
Synchronization is an important behavior that characterizes many natural and human made systems composed by several interacting units. It can be found in a broad spectrum of applications, ranging from neuroscience to power-grids, to mention…
We analyze the input-output behavior of residual networks from a dynamical system point of view by disentangling the residual dynamics from the output activities before the classification stage. For a network with simple skip connections…
We introduce and solve a general model of dynamic response under external perturbations. This model captures a wide range of systems out of equilibrium including Ising models of physical systems, social opinions, and population genetics.…
Pattern formation and evolution in unsynchronizable complex networks are investigated. Due to the asymmetric topology, the synchronous patterns formed in complex networks are irregular and nonstationary. For coupling strength immediately…
Previous work has shown that the dynamical regime of Recurrent Neural Networks (RNNs) - ranging from oscillatory to chaotic and fixpoint behavior - can be controlled by the global distribution of weights in connection matrices with…
Inspired by measurement incompatibility and Bell-family inequalities in quantum mechanics, we propose the Non-Classical Network (NCnet), a simple classical neural architecture that stably exhibits non-classical statistical behaviors under…
The ability to create linear systems that manifest broadband nonreciprocal wave propagation would provide for exquisite control over acoustic signals for electronic filtering in communication and noise control. Until now, acoustic…
Complex systems in the real world can be modeled as a network of connected components. The human brain, as a network of neurons among which the interactions cause perception, is a complex network. Synchronization is a dynamical phenomenon…
Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…