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We study the phase synchronization of Kuramoto's oscillators in small parts of networks known as motifs. We first report on the system dynamics for the case of a scale-free network and show the existence of a non-trivial critical point. We…
Brain networks typically exhibit characteristic synchronization patterns where several synchronized clusters coexist. On the other hand, neurological disorders are considered to be related to pathological synchronization such as excessive…
Learning or memory formation are associated with the strengthening of the synaptic connections between neurons according to a pattern reflected by the input. According to this theory a retained memory sequence is associated to a dynamic…
We study a system of coupled oscillators of the Sakaguchi-Kuramoto type with interactions including a phase delay. We consider the case of a coupling matrix such that oscillators with large natural frequencies drive all slower ones but not…
Reservoir computing is a powerful tool to explain how the brain learns temporal sequences, such as movements, but existing learning schemes are either biologically implausible or too inefficient to explain animal performance. We show that a…
The slowing of Moore's law and the increasing energy demands of machine learning present critical challenges for both the hardware and machine learning communities, and drive the development of novel computing paradigms. Of particular…
This Letter investigates the transition to synchronization of oscillator ensembles encoded by simplicial complexes in which pairwise and higher-order coupling weights alter with time through a rate-based adaptive mechanism inspired by the…
In neural circuits, synaptic strengths influence neuronal activity by shaping network dynamics, and neuronal activity influences synaptic strengths through activity-dependent plasticity. Motivated by this fact, we study a recurrent-network…
We study the associative-memory network of Kuramoto-type oscillators that stores a set of memorized patterns (memories). In [Phys. Rev. Lett., 92 (2004), 108101], Nishikawa, Lai and Hoppensteadt showed that the capacity of this system for…
Leveraging recent advances in neuroscience and control theory, this paper presents a neuromimetic network model with dynamic symmetric connections governed by Hebbian learning rules. Formal analysis grounded in graph theory and classical…
A family of stochastic processes has quasi-cycle oscillations if the oscillations are sustained by noise. For such a family we define a Kuramoto-type coupling of both phase and amplitude processes. We find that synchronization, as measured…
Hebbian and anti-Hebbian plasticity are widely observed in the biological brain, yet their theoretical understanding remains limited. In this work, we find that when a learning method is regularized with L2 weight decay, its learning signal…
Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent…
Physical networks, such as biological neural networks, can learn desired functions without a central processor, using local learning rules in space and time to learn in a fully distributed manner. Learning approaches such as equilibrium…
Intracortical brain-machine interfaces require decoders that adapt continuously to neural signal instability while operating within strict memory budgets. We introduce a dual-timescale Hebbian accumulator learning rule for spiking neural…
The brain performs unsupervised learning and (perhaps) simultaneous supervised learning. This raises the question as to whether a hybrid of supervised and unsupervised methods will produce better learning. Inspired by the rich space of…
The standard Hopfield model for associative neural networks accounts for biological Hebbian learning and acts as the harmonic oscillator for pattern recognition, however its maximal storage capacity is $\alpha \sim 0.14$, far from the…
Representation learning from complex data typically involves models with a large number of parameters, which in turn require large amounts of data samples. In neural network models, model complexity grows with the number of inputs to each…
Humans can learn several tasks in succession with minimal mutual interference but perform more poorly when trained on multiple tasks at once. The opposite is true for standard deep neural networks. Here, we propose novel computational…
In this work, we study the synchronization of coupled phase oscillators on the underlying topology of scale-free networks. In particular, we assume that each network's component is an oscillator and that each interacts with the others…