Abstract

In neuromorphic engineering, neural populations are generally modeled in a bottom-up manner, where individual neuron models are connected through synapses to form large-scale spiking networks. Alternatively, a top-down approach treats the process of spike generation and neural representation of excitation in the context of minimizing some measure of network energy. However, these approaches usually define the energy functional in terms of some statistical measure of spiking activity (ex. firing rates), which does not allow independent control and optimization of neurodynamical parameters. In this paper, we introduce a new spiking neuron and population model where the dynamical and spiking responses of neurons can be derived directly from a network objective or energy functional of continuous-valued neural variables like the membrane potential. The key advantage of the model is that it allows for independent control over three neuro-dynamical properties: (a) control over the steady-state population dynamics that encodes the minimum of an exact network energy functional; (b) control over the shape of the action potentials generated by individual neurons in the network without affecting the network minimum; and (c) control over spiking statistics and transient population dynamics without affecting the network minimum or the shape of action potentials. At the core of the proposed model are different variants of Growth Transform dynamical systems that produce stable and interpretable population dynamics, irrespective of the network size and the type of neuronal connectivity (inhibitory or excitatory). In this paper, we present several examples where the proposed model has been configured to produce different types of single-neuron dynamics as well as population dynamics. In one such example, the network is shown to adapt such that it encodes the steady-state solution using a reduced number of spikes upon convergence to the optimal solution. In this paper, we use this network to construct a spiking associative memory that uses fewer spikes compared to conventional architectures, while maintaining high recall accuracy at high memory loads.

Highlights

  • Spiking neural networks that emulate neural ensembles have been studied extensively within the context of dynamical systems (Izhikevich, 2007), and modeled as a set of differential equations that govern the temporal evolution of its state variables

  • For a network of M neurons with state variables v = {vi} ∈ RM, where the trans-conductance coupling matrix is denoted by Q = {Qij} ∈ RM × RM and the external stimulus vector is denoted by b = {bi} ∈ RM, the time-evolution of the network under bound constraints on the state variables vi(t) ≤ vc ∀t, is governed by the following continuous-time dynamical system: τi (t) dvi (t) dt

  • This paper introduces the theory behind a new spiking neuron and population model based on the Growth Transform dynamical system

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Summary

Introduction

Spiking neural networks that emulate neural ensembles have been studied extensively within the context of dynamical systems (Izhikevich, 2007), and modeled as a set of differential equations that govern the temporal evolution of its state variables. Individual neuron models are connected through synapses, bottom-up, to form large-scale spiking neural networks An alternative to this bottom-up approach is a topdown approach that treats the process of spike generation and neural representation of excitation in the context of minimizing some measure of network energy. The rationale for this approach is that physical processes occurring in nature have a tendency to self-optimize toward a minimum-energy state. As a result in these models, it is difficult to independently control different neuro-dynamical parameters, for example the shape of the action-potential, bursting activity or adaptation in neural activity, without affecting the network solution

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