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Versatile stochastic dot product circuits based on nonvolatile memories for high performance neurocomputing and neurooptimization.
The key operation in stochastic neural networks, which have become the state-of-the-art approach for solving problems in machine learning, information theory, and statistics, is a stochastic dot-product. While there have been many demonstrations of dot-product circuits and, separately, of stochastic neurons, the efficient hardware implementation combining both functionalities is still missing. Here we report compact, fast, energy-efficient, and scalable stochastic dot-product circuits based on either passively integrated metal-oxide memristors or embedded floating-gate memories. The circuit's high performance is due to mixed-signal implementation, while the efficient stochastic operation is achieved by utilizing circuit's noise, intrinsic and/or extrinsic to the memory cell array. The dynamic scaling of weights, enabled by analog memory devices, allows for efficient realization of different annealing approaches to improve functionality. The proposed approach is experimentally verified for two representative applications, namely by implementing neural network for solving a four-node graph-partitioning problem, and a Boltzmann machine with 10-input and 8-hidden neurons
Chaos and Asymptotical Stability in Discrete-time Neural Networks
This paper aims to theoretically prove by applying Marotto's Theorem that
both transiently chaotic neural networks (TCNN) and discrete-time recurrent
neural networks (DRNN) have chaotic structure. A significant property of TCNN
and DRNN is that they have only one fixed point, when absolute values of the
self-feedback connection weights in TCNN and the difference time in DRNN are
sufficiently large. We show that this unique fixed point can actually evolve
into a snap-back repeller which generates chaotic structure, if several
conditions are satisfied. On the other hand, by using the Lyapunov functions,
we also derive sufficient conditions on asymptotical stability for symmetrical
versions of both TCNN and DRNN, under which TCNN and DRNN asymptotically
converge to a fixed point. Furthermore, generic bifurcations are also
considered in this paper. Since both of TCNN and DRNN are not special but
simple and general, the obtained theoretical results hold for a wide class of
discrete-time neural networks. To demonstrate the theoretical results of this
paper better, several numerical simulations are provided as illustrating
examples.Comment: This paper will be published in Physica D. Figures should be
requested to the first autho
Probing the dynamics of identified neurons with a data-driven modeling approach
In controlling animal behavior the nervous system has to perform within the operational limits set by the requirements of each specific behavior. The implications for the corresponding range of suitable network, single neuron, and ion channel properties have remained elusive. In this article we approach the question of how well-constrained properties of neuronal systems may be on the neuronal level. We used large data sets of the activity of isolated invertebrate identified cells and built an accurate conductance-based model for this cell type using customized automated parameter estimation techniques. By direct inspection of the data we found that the variability of the neurons is larger when they are isolated from the circuit than when in the intact system. Furthermore, the responses of the neurons to perturbations appear to be more consistent than their autonomous behavior under stationary conditions. In the developed model, the constraints on different parameters that enforce appropriate model dynamics vary widely from some very tightly controlled parameters to others that are almost arbitrary. The model also allows predictions for the effect of blocking selected ionic currents and to prove that the origin of irregular dynamics in the neuron model is proper chaoticity and that this chaoticity is typical in an appropriate sense. Our results indicate that data driven models are useful tools for the in-depth analysis of neuronal dynamics. The better consistency of responses to perturbations, in the real neurons as well as in the model, suggests a paradigm shift away from measuring autonomous dynamics alone towards protocols of controlled perturbations. Our predictions for the impact of channel blockers on the neuronal dynamics and the proof of chaoticity underscore the wide scope of our approach
Hopf Bifurcation and Chaos in a Single Inertial Neuron Model with Time Delay
A delayed differential equation modelling a single neuron with inertial term
is considered in this paper. Hopf bifurcation is studied by using the normal
form theory of retarded functional differential equations. When adopting a
nonmonotonic activation function, chaotic behavior is observed. Phase plots,
waveform plots, and power spectra are presented to confirm the chaoticity.Comment: 12 pages, 7 figure
Chaotic Neural Network with Radial Basis Function Disturbance
This novel chaotic neural network bases on the Chen’s transiently chaotic neural network. It is proposed by introducing radial basis function as disturbance item into the inside state. Analyze the dynamics behavior of the single chaotic neuron and the chaotic search capability of the network. Research the capability of the novel network for resisting the disturbance. This chaotic neural network with radial basis function disturbance is used to solve TSP. The simulation result indicates that this network can avoid the limit of being trapped into the local minima and the capability of resisting the disturbance is perfect
Multiscale Computations on Neural Networks: From the Individual Neuron Interactions to the Macroscopic-Level Analysis
We show how the Equation-Free approach for multi-scale computations can be
exploited to systematically study the dynamics of neural interactions on a
random regular connected graph under a pairwise representation perspective.
Using an individual-based microscopic simulator as a black box coarse-grained
timestepper and with the aid of simulated annealing we compute the
coarse-grained equilibrium bifurcation diagram and analyze the stability of the
stationary states sidestepping the necessity of obtaining explicit closures at
the macroscopic level. We also exploit the scheme to perform a rare-events
analysis by estimating an effective Fokker-Planck describing the evolving
probability density function of the corresponding coarse-grained observables
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