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Register a new userEncoding and Decoding Mixed Bandlimited Signals using Spiking Integrate-and-Fire Neurons
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Added by
Karen Adam
Publication date
2019
fields
Electronic Engineering
and research's language is
English
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Conventional sampling focuses on encoding and decoding bandlimited signals by recording signal amplitudes at known time points. Alternately, sampling can be approached using biologically-inspired schemes. Among these are integrate-and-fire time encoding machines (IF-TEMs). They behave like simplifi
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Sampling is classically performed by recording the amplitude of an input signal at given time instants; however, sampling and reconstructing a signal using multiple devices in parallel becomes a more difficult problem to solve when the devices have an unknown shift in their clocks. Alternatively, one can record the times at which a signal (or its integral) crosses given thresholds. This can model integrate-and-fire neurons, for example, and has been studied by Lazar and Toth under the name of ``Time Encoding Machines. This sampling method is closer to what is found in nature. In this paper, we show that, when using time encoding machines, reconstruction from multiple channels has a more intuitive solution, and does not require the knowledge of the shifts between machines. We show that, if single-channel time encoding can sample and perfectly reconstruct a $mathbf{2Omega}$-bandlimited signal, then $mathbf{M}$-channel time encoding with shifted integrators can sample and perfectly reconstruct a signal with $mathbf{M}$ times the bandwidth. Furthermore, we present an algorithm to perform this reconstruction and prove that it converges to the correct unique solution, in the noiseless case, without knowledge of the relative shifts between the integrators of the machines. This is quite unlike classical multi-channel sampling, where unknown shifts between sampling devices pose a problem for perfect reconstruction.
Collective oscillations and their suppression by external stimulation are analyzed in a large-scale neural network consisting of two interacting populations of excitatory and inhibitory quadratic integrate-and-fire neurons. In the limit of an infinite number of neurons, the microscopic model of this network can be reduced to an exact low-dimensional system of mean-field equations. Bifurcation analysis of these equations reveals three different dynamic modes in a free network: a stable resting state, a stable limit cycle, and bistability with a coexisting resting state and a limit cycle. We show that in the limit cycle mode, high-frequency stimulation of an inhibitory population can stabilize an unstable resting state and effectively suppress collective oscillations. We also show that in the bistable mode, the dynamics of the network can be switched from a stable limit cycle to a stable resting state by applying an inhibitory pulse to the excitatory population. The results obtained from the mean-field equations are confirmed by numerical simulation of the microscopic model.
We derive analytical formulae for the firing rate of integrate-and-fire neurons endowed with realistic synaptic dynamics. In particular we include the possibility of multiple synaptic inputs as well as the effect of an absolute refractory period into the description.
We analyze the dynamics of two coupled identical populations of quadratic integrate-and-fire neurons, which represent the canonical model for class I neurons near the spiking threshold. The populations are heterogeneous; they include both inherently spiking and excitable neurons. The coupling within and between the populations is global via synapses that take into account the finite width of synaptic pulses. Using a recently developed reduction method based on the Lorentzian ansatz, we derive a closed system of equations for the neurons firing rates and the mean membrane potentials in both populations. The reduced equations are exact in the infinite-size limit. The bifurcation analysis of the equations reveals a rich variety of non-symmetric patterns, including a splay state, antiphase periodic oscillations, chimera-like states, also chaotic oscillations as well as bistabilities between various states. The validity of the reduced equations is confirmed by direct numerical simulations of the finite-size networks.
Complementary metal oxide semiconductor (CMOS) devices display volatile characteristics, and are not well suited for analog applications such as neuromorphic computing. Spintronic devices, on the other hand, exhibit both non-volatile and analog features, which are well-suited to neuromorphic computing. Consequently, these novel devices are at the forefront of beyond-CMOS artificial intelligence applications. However, a large quantity of these artificial neuromorphic devices still require the use of CMOS, which decreases the efficiency of the system. To resolve this, we have previously proposed a number of artificial neurons and synapses that do not require CMOS for operation. Although these devices are a significant improvement over previous renditions, their ability to enable neural network learning and recognition is limited by their intrinsic activation functions. This work proposes modifications to these spintronic neurons that enable configuration of the activation functions through control of the shape of a magnetic domain wall track. Linear and sigmoidal activation functions are demonstrated in this work, which can be extended through a similar approach to enable a wide variety of activation functions.
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