平成23年度 電気関係学会四国支部連合大会

161-16

Multi-Layer Perceptron Introducing
Glial Pulse Propagating to Two Directions†Yoko UWATE†
Yoshifumi NISHIO†(Tokushima University)

1. Introduction
The glia is one of nervous cells in a brain. Recently, theglia attracts researchers’ attentions, because this cell cantransmit signals each other. The glias have some ions’channels, thus the glias possess important relationshipwith neurons for the brain works [1].
In the previous study, we proposed the pulse glial chain
which was inspired from the features of the glias. The glia
generates a pulse by a connecting neuron and the pulse
excites the glias on one side.
In this study, we propose the Multi-Layer Perceptron(MLP) introducing glial pulse propagating to two directions. We broaden the deﬁnition of the pulse glial chain
to the glial pulse propagating to two directions. In the
proposed MLP, all glias are excited by the connecting neurons’ outputs and aﬀects its neighborhood glias on bothsides. We conﬁrm that the proposed MLP has better
learning performance than the conventional methods bythe simulation.

2. Proposed methodThe glial pulse propagating to two directions is deﬁnedby Eq. (1).
ψi (t + 1) ={ 1, {(θ < y ∪ ψnii+1,i−1 (t − i ∗ D) = 1)

∩ (θg > ψi (t))} ,(1)γψi (t), else,
where ψ is an output of a glia, γ is an attenuated parameter, y is an output of a connecting neuron, θn is a glia
threshold of excitation, θg is a period of inactivity, and D
is a delay time of a glia’s eﬀect. In the proposed MLP,
the glias are excited by the connecting neuron or glias onboth side. After that, the exciting glias generate outputs
pulse.
We connect glial pulse propagating to two directions to
the thresholds of hidden layer’s neurons in the MLP. Because, the biological glia can change the neuron membranepotentials. The neuron updating rule of the hidden layer’s
is given by Eq. (2).
yi (t) =N∑(wij xj (t) − θ + ψi (t))

(2)

j=1

where y is an output, w is a weight parameter of neurons
and x is an input. In general, the MLP is learned byback propagation (BP), however, this algorithm often falls
into local minimum. In proposed MLP, the glias’ eﬀects
give energies to the MLP for escaping out from the local
minima. We show an example of an output of the glial
pulse propagating to two directions in Fig. 1. We can seethat the 5th glia is excited by the connecting neuron andexcites glias on both sides. After that, the glias pulses aregenerated into a chain reaction. Moreover, the exciting
glias pattern can be dynamically changed during learning

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time. Because, the glias watch the neurons’ outputs which
are changed by the BP learning.

10.8

Glia output

Chihiro IKUTA†

0.6
0.4
0.2
0151
10151
1Figure 1: Example of glias’ pulses as proposed method.

3. Simulation
In this simulation, the MLPs learn classiﬁcation of twoskew tent maps which are given by Eq. (3). We choose
diﬀerent A (0.1 and −0.1) of the skew tent maps, thus, thechaotic oscillation pattern changes. The MLP classiﬁes
the two diﬀerent time series.

{ 2ϕ(t)+1−A (−1 ≤ ϕ(t) ≤ A)
1+A

ϕi (t + 1) =,−2ϕ(t)+1+A
1−A(3)(A < ϕ(t) ≤ 1)

Table 1 is a statistic results of the MLPs which are anaverage of error (Avg. Err.), a minimum error as trials(Min.), a maximum as trials (Max.), and a standard deviation of error (St. Dev.). The number of trials are 100.
We compare the four MLPs which are the conventional
MLP (1), the MLP introducing glial pulse propagating to
two directions (2), the MLP with pulse glial chain, and theMLP adding random noise (4). From this table, we can seethat the proposed MLP has better learning performance
than the others.

Table 1: Learning performance.
(1)
(2)
(3)
(4)

Avg. Err.
0.00850.00120.00480.0067Min.
0.00010.00010.00010.0005Max.
0.06120.06020.0641
0.0620St. Dev.
0.02010.00600.01450.0132

4. Conclusions
In this article, we have proposed the MLP introducing
glial pulse propagating to two directions. The proposed
method is inspired from features of the biological glia. Theglias generate pulse by neurons’ outputs and the pulse isaﬀecting other glias and neurons. We showed that theproposed MLP has the better performance than the conventional MLPs by the simulation. We conﬁrmed thatthe proposed method improved the MLP learning performance.
References[1] P.G. Haydon, “Glia: Listening and Talking to the Synapse,”
Nature Reviews Neuroscience, vol. 2, pp. 844-847, 2001.