IEEE Computational Intelligence Magazine - November 2022 - 33

FIGURE 6 Illustration of the relationship between two spike trains
which are learned by the proposed network.
letters to digits. The input and output information ofthe spiking
BAM network can be encoded and decoded with the proposed
XOR-phase coding method. The spiking BAM
network employs spiking neurons for its processing units,
where auxiliary neurons are used to fill the previous time
points.
A. LIFNeuron and PSD Learning Rule
The neuron model of the spiking BAM network is the Leaky
Integrate-and-Fire (LIF) [24] model:
tm
dVm
dt
¼ðVmVrestÞþ RmðIsyn þ InoiseÞ
(9)
where Vm is the membrane potential ofthe neuron, Vrest is the
resting potential, tm ¼ RmCm is the membrane time constant,
Rm and Cm are the membrane resistance and capacitance, Isyn
and Inoise are the synaptic current and background current
noise, respectively. When Vm exceeds the threshold Vthr, the
neuron will fire a spike and the Vm is reset to Vreset.
In the LIF model, each spike from the afferent neuron will
lead to a postsynaptic current (PSC), and Isyn is the weighted
sum ofall arriving PSCs:
IsynðtÞ¼
X
i
wiIi
PSCðtÞ
(10)
where wi is the synaptic efficacy of the i-th afferent neuron.
Ii
Ii
PSCðtÞ¼
X
tj
Kðt tjÞHðt tjÞ
(11)
where tj is the time of the j-th spike obtained from the i-th
afferent neuron, and HðtÞ is the Heaviside function. Kðt tjÞ
is calculated from Kðt tjÞ¼ V0ðexpððt tjÞ=tsÞ
expððt tjÞ=tfÞÞ, and V0 is the normalization factor. ts and
tf are the slow and fast decay constants, respectively.
Tempotron learning rule focuses on firing statuses of output
neurons rather than the time of output spikes. However,
the firing time of output spikes is important for decoding the
recalled memories. Compared with tempotron learning rule,
PSD learning rule focus on the precise firing time. It can train
the output neuron to fire spikes at the same time of the target
train. Thus, we use PSD learning rule to train synaptic weights
ofthe spiking BAM network.
The PSD rule for synaptic adaptations ofthe spiking BAM
network can be described as:
PSCðtÞ is the postsynaptic current and can be calculated
from:
FIGURE 7 Illustration of the variation of the patterns which are decoded
from spike trains with different epochs.
Dwi ¼ h ½sdðtÞ soðtÞ Ii
Z1
PSCðtÞdt
(12)
where h is the positive constant referring to the learning rate,
sd and so are the desired and actual postsynaptic spike trains.
The errors between sd and so
lead to the weight adaptation,
while Long-Term Potentiation (LTP) is caused by positive
errors, and Long-Term Depression (LTD) is caused by negative

IEEE Computational Intelligence Magazine - November 2022

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