A SUPERVISED STDP-BASED TRAINING ALGORITHM FOR LIVING NEURAL
NETWORKS
Yuan Zeng∗ Kevin Devincentis† Yao Xiao‡ Zubayer Ibne Ferdous∗
Xiaochen Guo∗ Zhiyuan Yan∗ Yevgeny Berdichevsky∗§

arXiv:1710.10944v3 [] 21 Mar 2018

Lehigh University, ∗ Electrical and Computer Engineering Department § Bioengineering Department
†
Carnegie Mellon University, Electrical and Computer Engineering Department
‡
University of Science and Technology of China, School of Gifted Young
ABSTRACT
Neural networks have shown great potential in many
applications like speech recognition, drug discovery, image
classification, and object detection. Neural network models are inspired by biological neural networks, but they are
optimized to perform machine learning tasks on digital computers. The proposed work explores the possibility of using
living neural networks in vitro as the basic computational elements for machine learning applications. A new supervised
STDP-based learning algorithm is proposed in this work,
which considers neuron engineering constraints. A 74.7% accuracy is achieved on the MNIST benchmark for handwritten
digit recognition.
Index Terms— Spiking neural network, Spike timing dependent plasticity, Supervised learning, Biological neural network
1. INTRODUCTION AND MOTIVATION
Artificial Neural Network (ANN) and Spiking Neural
Network (SNN) are two brain inspired computational models, which have shown promising capabilities for solving
problems such as face detection [1] and image classification
[2]. Computer programs based on neural networks can defeat
professional players in the board game Go [3] [4]. ANN relies on numerical abstractions to represent both the states of
the neurons and the connections among them, whereas SNN
uses spike trains to represent inputs and outputs and mimics
computations performed by neurons and synapses [5]. Both
ANN and SNN are models extracted from biological neuron
behaviors and optimized to perform machine learning tasks
on digital computers.
In contrast, the proposed work explores whether biological living neurons in vitro can be directly used as basic computational elements to perform machine learning tasks. Living neurons can perform “computation” naturally by transferring spike information through synapses. The energy consumption is 100000× more efficient than hardware evaluation
[6]. Living neurons have small sizes (4 to 100 micrometers
diameter) [7], and adapt to changes.
While precise control of living neural networks is challenging, recent advances in optogenetics, genetically encoded
neural activity indicators, and cell-level micropatterning open
up possibilities in this area [8] [9] [10]. Optogenetics can
label individual neurons with different types of optically
This work is supported in part by a CORE grant from Lehigh University
and in part by the National Science Foundation under Grant ECCS-1509674.

controlled channels, which equip in vitro neural networks
with optical interfaces. Patterned optical stimulation and
high-speed optical detection allow simultaneous access to
thousands of in vitro neurons. In addition, the invention of
micropattern [11] enables modularized system design.
To the best of our knowledge, this work is the first to
explore the possibility of using living neurons for machine
learning applications. By considering neuron engineering design constraints, a new algorithm is proposed for easy training
in future biological experiments. A fully connected spiking
neural network is evaluated on MNIST dataset using NEURON simulator [12]. A 74.7% accuracy is obtained based on
a biologically-plausible SNN model, which is a promising result that demonstrates the feasibility of using living neuron
networks to compute.
2. METHODS
Spiking neural network is a model that closely represents
biological neuron behavious. In biological neural network,
neurons are connected through plastic synapses. A spike of
a pre-synaptic neuron will change the membrane potential of
a post-synaptic neuron. The impact of the spikes at different time from all of the pre-synaptic neurons will be accumulated at the post-synaptic neuron. Post synaptic spikes are
generated when the membrane voltage of a neuron exceeds a
certain threshold. In SNN, information is represented as a series of spikes, and the accumulative effect of the pre-synaptic
spikes are also modeled.
This work models biological neural networks using the
Hodgkin-Huxley (HH) neuron model [13] and spike-based
data representation. One major difference between the proposed work and prior SNN based models [14] [15] [16] [17]
[18] [19] is that this work aims to explore the potential of using biological living neurons as the functional devices, while
prior works focused on the computational capability of the
neuron model. Neuron engineering design constraints lead to
different design choice for input encoding, network topology,
neuron model, learning rule, and model parameters.
2.1. Network topology
Neural connectivity in human brain is complex and has
different types of topologies in different parts of the nervous
system. To understand the network functionality, a simple
network topology is built, where all input neurons are connected to all output neurons through synapses (Fig. 1).

apse

1

Black

1

.
.

White

.
.
.
.

.
.
.
.

1
.
.

.
.

0

Black
.
.

0

Group 9
30 neurons

Syn

Group 0
30 neurons

Due to bioengineering constraints, images from the
MNIST dataset, which have 28 × 28 pixels, are compressed
to 14 × 14 pixels. As a result of this simplification, the network has 196 input neurons, each corresponding to one pixel.
Only black pixels generate spikes, and all input spikes occur
simultaneously.
Output for the network is a vector of spiking state for output neurons, “1” represents a spike, “0” means no spike. Each
output neuron is associated with a group index from 0 to 9,
which can be defined artificially. The index of the group with
the largest number of spiking neurons will be considered as
the network output. In our experiment, 300 output neurons
are used. Every 30 consecutive neurons belong to one group,
for example, the first 30 belong to group 0.

1
MNIST image

196 input

300 output

Fig. 1. Network topology.
2.2. Neuron model
To capture the realistic neuron dynamics, the HodgkinHuxley (HH) model [13] is used in the simulation, which
models the electro-chemical information transmission of biological neurons with electrical circuit. HH model has been
successfully verified by numerous biological experimental
data and it is more biologically accurate than other simplified
model such as Integrate and Fire model [20].
A spike will be generated if the membrane potential for
a neuron exceeds a certain threshold. However, after a strong
current pulse excites a spike, there will be a period during
which current pulse at the same amplitude cannot generate another spike,which is referred to as the refractory period [21].
2.3. Learning rule
The plasticity of synapses between neurons is important for learning. Connection strength changes based on
precise timing between pre- and post-synaptic spikes. This
phenomenon is called Spike Timing Dependent Plasticity
(STDP) [22].
Eqs. (1)-(4) describe the STDP rule [23] used in this
work. In this rule, the weight changes are proportional to
spike trace [24]. tpre and tpost denote the time a pre- and
post-synaptic, respectively, spikes arrive; tpre 0 and tpost 0
represent the arrival time of previous pre- and post-synaptic
spikes respectively. ALT P and ALT D are the amplitudes of
trace updating for potentiation and depression respectively;
and aLT P and aLT D are the potentiation and depression

learning rate respectively. Each pre-synaptic spike arrival will
update the pre-synaptic trace P according to Eq. (1), postsynaptic spike changes the post-synaptic trace Q according to
Eq. (2). If a pre-synaptic spike happens after a post-synaptic
spike, weight will decrease by δW q , which is given by (3). If
a post-synaptic spike occurs after a pre-synaptic spike, weight
will increase by δW p given by (4).
tpre 0 − tpre
P = P × exp(
) + ALT P
(1)
τLT P
Q = Q × exp(

tpost 0 − tpost
) + ALT D
τLT D

δW q = aLT D × Q × exp(

(2)

tpost − tpre
), tpost < tpre (3)
τLT D

tpre − tpost
), tpre < tpost (4)
τLT P
The STDP rule itself is not enough for learning. Both unsupervised [14] [15] [16] and supervised [17] [18] training algorithms based on the STDP rule have been proposed, which
focus on computational aspect of the neuron model. These algorithms use Poisson based spike trains as input and include
other bio-inspired mechanisms like winner-take-all [25] and
homoeostasis [26].
Since artificial stimuli can be precisely applied to optically stimulated neurons, synchronous inputs are used for the
proposed work. Considering a feedforward network, the synchronous inputs will lead to a problem. There will be no
weight decrease for the network based on the basic STDP
rule and all of the neurons will fire eventually. That is because when all of the input neurons fire at the same time, no
post-synaptic neuron will fire before any pre-synaptic spike.
In order to solve this problem and make the living neural
network easy to train, we propose a new supervised STDP
training algorithm. Four basic operations in this algorithm
are shown in Fig. 2 and discussed below.
In this algorithm, stimuli can be applied to both input and
output neurons artificially to generate a spike. In Fig. 2, external stimuli that generate a spike for input and output neurons
are shown in pink and blue respectively.
Without artificial output stimuli, an output neuron can
reach its action potential and fire in response to the network
inputs, which is shown in yellow. Because the output neuron
spikes after the input stimuli, weights between those in-out
pairs will be naturally potentiated. This is referred to as the
network’s “natural increase”, with tpre − tpost = T 2 − T 4.
Besides this natural increase, stimuli can be directly applied to the input and output neuron pairs to artificially change
the weights. If an output stimulus is given at T3 and an input
stimulus is given at T2, weight between this pair will be increased, which is referred to as “artificial increase”. If an output stimulus is given at T1, which is before an input stimulus,
“artificial decrease” will happen and weight will decrease.
In this work, these timing-based rules of applying external stimuli are the essential mechanisms to change synaptic
weights. For the digit recognition task, groups of weights are
δW p = aLT P × P × exp(

Training phase 1

Training phase 2

Natural increase
Artificial increase
Artificial decrease

in

Stimulus

out

Stimulus

out

Artificial hold
Time axis
0

T0

T1

T2

T3

T4

Tn Tn+T0

Tn+T1

Tn+T2

Tn+T3

Tn+T4

2Tn

Fig. 2. Four mechanisms in the supervised STDP training.
increased or decreased to make the network converge. Some
weights that are already reaching convergence need to be kept
same. However, if the weight of a synapse is large enough to
make the output neuron fire, the weight will increase naturally during the training process, which will move the network away from convergence. Therefore, each training step
is separated into two phases, and the input stimuli corresponding to the input image are given once for each phase. During
the first phase, if a weight that should be kept the same actually increased, a stimulus will be added to the corresponding
output neurons at Tn+T0, which is before the input stimulus at Tn+T2 for the second phase to decrease the increased
weight. Because of the refractory period, there will not be a
natural increase at the second phase. The time interval between input and the stimuli (T2-T0) is adjusted with the time
interval between natural output spike and input stimuli (T4T2) at the first phase, so that the amount of decrease and increase matches. Through this approach, the weight can be
kept roughly the same. This process is referred to as “artificial hold”.
The new STDP training algorithm is described in Algorithm 1. For each new image observed by the network, a
prediction is made by applying the input stimuli to the network and checking the natural response of the outputs (Algorithm 1 lines 3-5). The index of the group that contain the
largest number of spiking neurons is the predicted result (if
two groups have the same number of spikes, the smaller group
index is chosen). To train the network, the correct label (ID)
for the input image and the actual spike pattern for output
neurons are compared to generate the control signals to select
neurons into different lists that require external stimuli (lines
7-14). Based on the selected neurons, stimuli are applied to
the network to update weights (lines 16-22).
Three tunable parameters can be set for the training process. trainStep is the number of training steps the network
goes through for one image. A larger trainStep means higher
effective learning rate. In order for the correct group to have
more firing neurons than the other groups, inTarget and deTarget are targets of the number of firing neurons in each group.
inTarget represents the desired number of firing neurons to
be observed in the output group that matches the correct label. deTarget represents the desired number of firing neurons
to be observed in the incorrect groups. numSpike[id] is the
number of spiking neurons in group id. When id matches
ID, all spiking neurons in this group will be added to the
holdList to keep their weights since they respond correctly

(line 8). If the number of firing neurons is less than inTarget, inTarget-numSpike[id] neurons will be randomly chosen
among the non-spiking ones and added to the inList (lines
9-11). For other output groups, if the number of firing neurons is more than deTarget, numSpike[id]-deTarget neurons
will be randomly chosen among the spiking ones and added
to the deList (lines 12-14). After selecting inList, deList, and
holdList, corresponding stimuli are applied in time sequence
shown in Fig. 2 for each training step (lines 16-22).
Algorithm 1 Supervised STDP Training
1: // Tunable parameters: trainStep, inTarget, deTarget
2: for each image do
3:
Clear inList, deList and holdList
4:
Apply stimuli to input neurons based on pixel values
5:
Record spike pattern for output neurons
6:
for each output group (id = 0 to 9) do
7:
if id == ID then
8:
Add all spiking neurons to holdList
9:
if numSpike[id]<inT arget then
10:
x = inT arget − numSpike[id]
11:
Add x non-spiking neurons to inList
12:
if id 6= ID and numSpike[id]>deT arget then
13:
y = numSpike[id] − deT arget
14:
Add y spiking neurons to deList
15:
for each trainStep do
16:
Apply stimuli to the deList at T1
17:
Apply stimuli to input neurons at T2
18:
Apply stimuli to the inList at T3
19:
Apply stimuli to the holdList at Tn+T0
20:
Apply stimuli to the deList at Tn+T1
21:
Apply stimuli to input neurons at Tn+T2
22:
Apply stimuli to the inList at Tn+T3
3. SIMULATION
3.1. Parameters
Parameters used for the network are listed in Table 1.
Timing parameters in Fig. 2 impact the learning rate for each
trainStep. Small time interval between pre- and post-synaptic
neuron spikes (e.g., T3-T2) leads to greater weight changes.
However, the optical stimuli cannot be spaced arbitrarily close
to each other. In this work, a fixed 5 ms interval is used between pre- and post-synaptic spikes for artificial increase and
decrease. The pre- and post-synaptic spike interval for the

Accuracy

Accuracy

Accuracy
75%

75%

75%
60%

60%

60%

45%

45%

45%

30%

30%

30%

15%

15%

15%

0%

1

2

3

4

trainStep (inTarget=20, deTarget=0)

0%

5

10

15

20

25

30

inTarget (trainStep=2, deTarget=0)

0%

0

5

10

15

20

25

deTarget (trainStep=2, inTarget=20)

Fig. 3. Sensitivity of the image recognition accuracy to different parameters.
hold mechanism matches the natural increase interval, which
is 10 ms according to empirical data.
Parameter
τLT P / τLT D
ALTP / ALTD
aLTP / aLTD
max weight
refractory period
T3-T2 / T2-T1
T4-T2 / T2-T0
Tn

Value
20ms / 20ms
1 / -1
6 × 10−5 / 6.3 × 10−5
0.02
25ms
5ms / 5ms
10ms / 10ms
30ms

Table 1. Simulation parameters, [27][28][29][14].
3.2. Results and analysis
Three tunable parameters for the network are: trainStep,
inTarget and deTarget. trainStep is kept at 2, inTarget is set
at 20, and deTarget is configured as 0 as the base line. A
sensitivity study is done by tuning one parameter at a time.
For this sensitivity study, 1000 images from the MNIST
dataset are used for training, another 1000 images are used for
testing. Training time for each trainStep is 60 ms. Simulation
results are shown in Fig. 3.
When trainStep increases from 1 to 2, the prediction accuracy increases. However, when learning rate is too large
(beyond 3 steps), the accuracy drops. This is because a larger
effective learning rate may lead to fast convergence, but if it is
too large, overshooting will happen when moving towards the
global optimum point, which leads to oscillations and hurts
the performance.
For inTarget, better results are achieved in the middle
range, which shows that, training nearly half of the neurons to
fire can provide enough information while avoid divergence.
For example, if two images have a large set of overlapping
firing neurons in the inputs but have different labels, strengthening the connections between all of the firing inputs and
the corresponding outputs for one image will likely lead to
mis-prediction for the other image. The best performance is
achieved at inTarget=20.
Decreasing weights associated with all firing neurons in
all incorrect groups (deTarget=0) achieves the best performance. When deTarget is larger than 10, performance drops
dramatically. This is because inTarget is 20 for this set of results. The number of firing neurons in the incorrect group
needs to be below 20 to make sure that the correct group

has the greatest number of firing neurons. However, training 2 steps cannot guarantee both inTarget and deTarget are
reached. The best accuracy for the sensitivity study is 72.7%.
A larger dataset (10000 images from MNIST) is evaluated
based on the best parameters: trainStep=2, inTarget=20 and
deTarget=0. The accuracy for this larger dataset is 74.7%.
Compared to a single-layer fully connected ANN, which
achieves 88% [30] accuracy on MNIST dataset, the proposed
supervised STDP-based SNN still has an accuracy gap. Unlike the ANN, where weights and inputs can be directly used
in the prediction, most SNN models only rely on the output
spikes other than the exact membrane potential to make a prediction. The loss of information leads to the accuracy drops.
The only single-layer SNN work in our knowledge [31] derives an extra mathematical function to extract more informations through the timing relationships for output spikes,
which does not consider biological properties of neurons and
synapses and hence is an unrealistic scheme for living neuron
experiment.
For SNN works based on neuron science simulations, a
three-layer design with supervised STDP achieved an accuracy of 75.93% for 10 digit recognition task on a MNIST
dataset [18]. That is similar to the proposed single-layer network in this paper. There are other SNN works that have better results on MNIST [14] [15] [16] [17] [19]. However, those
networks have at least two layers and a larger number of neurons (e.g. 71,026 in [19]). Some works also preprocess the
input images to achieve better accuracy [17]. The major difference between the proposed work and prior works is that
prior works are optimized for solid state computers. For the
proposed supervised scheme, bioengineering constraints are
considered. Input data are compressed and applied as synchronous spike trains, HH model are used instead of the integrate and fire model. The biological limitations on maintaining the synaptic weights lead to the design of two training
phases and multiple training steps.
4. CONCLUSION
To explore the possibility of using living neuron for machine learning tasks, a new supervised STDP training algorithm has been proposed and simulated on a fully-connected
neural network based on the HH model. A 74.7% accuracy
is achieved on digit recognition task for the MNIST dataset.
This result demonstrates the feasibility of using living neurons as computation elements for machine learning tasks.

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