Related papers: Harnessing and modulating chaos to sample from neu…
The generalization properties of an attractive network of non monotonic neurons which infers concepts from samples are studied. The macroscopic dynamics for the overlap between the state of the neurons with the concepts, well as the…
The use of artificial neural networks as models of chaotic dynamics has been rapidly expanding. Still, a theoretical understanding of how neural networks learn chaos is lacking. Here, we employ a geometric perspective to show that neural…
Chaos control techniques have been applied to a wide variety of experimental systems, including magneto-elastic ribbons, lasers, chemical reactions, arrhythmic cardiac tissue, and spontaneously bursting neuronal networks. An underlying…
Chaos presents complex dynamics arising from nonlinearity and a sensitivity to initial states. These characteristics suggest a depth of expressivity that underscores their potential for advanced computational applications. However,…
Dynamical networks are important models for the behaviour of complex systems, modelling physical, biological and societal systems, including the brain, food webs, epidemic disease in populations, power grids and many other. Such dynamical…
Stable chaos is a generalization of the chaotic behaviour exhibited by cellular automata to continuous-variable systems and it owes its name to an underlying irregular and yet linearly stable dynamics. In this review we discuss analogies…
We present a perception model of ambiguous patterns based on the chaotic neural network and investigate the characteristics through computer simulations. The results induced by the chaotic activity are similar to those of psychophysical…
The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying…
The practical success of widely used machine learning (ML) and deep learning (DL) algorithms in Artificial Intelligence (AI) community owes to availability of large datasets for training and huge computational resources. Despite the…
It is widely accepted that the complex dynamics characteristic of recurrent neural circuits contributes in a fundamental manner to brain function. Progress has been slow in understanding and exploiting the computational power of recurrent…
Highly connected recurrent neural networks often produce chaotic dynamics, meaning their precise activity is sensitive to small perturbations. What are the consequences for how such networks encode streams of temporal stimuli? On the one…
In neural information processing, an input modulates neural dynamics to generate a desired output. To unravel the dynamics and underlying neural connectivity enabling such input-output association, we proposed an exactly soluble…
Chaos and Noise are ubiquitous in the Brain. Inspired by the chaotic firing of neurons and the constructive role of noise in neuronal models, we for the first time connect chaos, noise and learning. In this paper, we demonstrate Stochastic…
Generative modeling aims at producing new datapoints whose statistical properties resemble the ones in a training dataset. In recent years, there has been a burst of machine learning techniques and settings that can achieve this goal with…
Diluted neural networks with continuous neurons and nonmonotonic transfer function are studied, with both fixed and dynamic synapses. A noisy stimulus with periodic variance results in a mechanism for controlling chaos in neural systems…
This study shows that a mixture of RNN experts model can acquire the ability to generate sequences combining multiple primitive patterns by means of self-organizing chaos. By training of the model, each expert learns a primitive sequence…
How chaos is useful in the brain information processing is greatly unknown. Here, we show that the statistical property of chaos such as invariant measures naturally organized under a great number of iterations of chaotic mappings can be…
Further analysis and experimentation is carried out in this paper for a chaotic dynamic model, viz. the Nonlinear Dynamic State neuron (NDS). The analysis and experimentations are performed to further understand the underlying dynamics of…
Large networks of sparsely coupled, excitatory and inhibitory cells occur throughout the brain. A striking feature of these networks is that they are chaotic. How does this chaos manifest in the neural code? Specifically, how variable are…
We introduce a model of randomly connected neural populations and study its dynamics by means of the dynamical mean-field theory and simulations. Our analysis uncovers a rich phase diagram, featuring high- and low-dimensional chaotic…