IEEE Circuits and Systems Magazine - Q2 2022 - 8

For example, we will discuss the implications that neuron
models and learning algorithms may impose on hardware
design, how the hardware architecture limits software
and algorithm, and the design trade-offs between algorithm
and hardware.
The rest of the survey is organized as the following.
Section II reviews neuron and synapse models, network topologies,
information encoding schemes and learning algorithms.
Their impact on hardware implementation will be
discussed in Section III, followed by a detailed discussion of
the hardware and software ecosystems of several selected
neuromorphic computing systems in Section IV. The outlook
of future research directions will be given in Section V.
II. Neuromorphic Computing Models
Biological neurons communicate with each other by generating
and propagating electrical pulses called spikes
[19], [20]. At the high abstraction level, all spiking models
share the following common properties: (1) they process
information coming from many inputs and produce single
or multiple spikes; (2) the probability of spike generation
is increased by excitatory inputs and decreased by
inhibitory inputs; (3) at least one state variable is used to
characterize their dynamics and the model is supposed
to generate one or more spikes when the internal variables
of the model reach a certain state. Neurons connect
and communicate with one another through specialized
junctions called synapses [21], [22]. Similar to the neuron
models, synapse models also vary in the complexity and
biological plausibility.
The details of some popular spiking neuron models
and synapse models are reviewed in Sections II-A and II-B.
Different spike coding techniques are reviewed in Section
II-C. In Section II-D, we discuss various network architectures
and in Section II-E we show how learning is accomplished
in the networks of spiking neurons.
A. Neuron Models in Ordinary
Differential Equations (ODE)
The existing neuron models can be categorized into two
groups, conductance-based models and spike-based models.
The former includes the Hodgkin-Huxley (HH) model
[23], the Fitz-Hugh-Nagumo (FHN) model [24] and the Morris-Lecar
[25] model, while the latter includes the Izhikevich
model [26], the Integrate and Fire (IF) model and the
Leaky-Integrate and Fire (LIF) [27] model.
Conductance-based models are based on an equivalent
circuit representation of a cell membrane, as first put
forth by Hodgkin and Huxley [23]. These models apply
a set of nonlinear differential equations to provide a biophysical
interpretation of an excitable cell in which current
flows across the membrane due to the charging of
the membrane capacitance ()Ic
and the movement of ions
across ion channels (), such that the total membrane
current () is the sum of the capacitive current and the
ionic current () =+ The membrane potential Vm
of the cell with capacitance Cm
Iion
Itm
It II .mc ion
is related to the capacitance
current based on the following equation
IC
cm
=
The ion current Iion
Vm
dVm
dt
(1)
is a function of the difference of the
and the ion potential, whose conduction is time varying
and modeled by a set of differential equations. Based
on the model, positive surges (i.e. spikes) are formed on
the membrane potential at constant or time varying input
current. The conductance-base models consider neuron
input, output, and state as continuous-time continuousvalued
variables; hence they have a high computational
complexity. Due to their high fidelity to the biological neuron,
the conductance-based models are more widely used
in computational neuroscience.
The spike-based model simplifies the neuron input and
output into spikes. A sequence of the spike events, i.e. a
spike train, can be described as the following
() (),
Application
St =-d ttf
f
/
3
3
d td . The ba()
t 1
=
(2)
where f ,,= 12 f is the label of the spike and (.)d is a Dirac
function with ()td =Y for t 0= and #Machine
Intelligence
Computational
Neuroscience
Hardware
Analog
Digital
Figure
1. Different aspects in neuromorphic computing.
8
IEEE CIRCUITS AND SYSTEMS MAGAZINE
C
d ()
ut
dt
=- ++/
1 ut it
R
() (()())wi toj j
(3)
SECOND QUARTER 2022
This
Review
Model
Non-Spiking
Spiking
sic assumption underlying most spiking neuron models is
that it is the timing of spikes rather than the specific shape
of spikes that carries neural information [28].
Among the spike-based models, the Integrate-and-Fire
(IF) model, and Leaky Integrate-and-Fire (LIF) model [28]
are the most widely used. Both models abstract biological
neurons as point dynamical systems. The dynamics of the
LIF unit is described by the following formula:
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