As computers are getting more pervasive, software becomes transferable to di erent types of hardware and, at the extreme, being bio-compatible. Recent e orts in Arti cial Intelligence propose that software can be trained and taught instead of \hard-coded" sequences. This paper addresses the learnability of software in the context of platforms integrating biological components. A method for training Spiking Neural Networks (SNNs) for pattern recognition is proposed, based on spike timing dependent plasticity (STDP) of connections. STDP corresponds to the way connections between neurons change according to the spiking activity in the network, and we use STDP to stimulate outputs of the network shortly after feeding it with a pattern as input, thus creating speci c pathways in the network. The computational model used to test this method through simulations is developed to t the behaviour of biological neural networks, showing the potential for training neural cells into biological processors.
Software is everywhere: the human environment is populated by more and more software-driven intelligent devices, connected by Internet and other networks. With the apparition of wearables and implantables, computers are getting more and more pervasive and close to the biological world. In such systems, software is expected to expand on various types of platforms.
In the current information technology, the interplay between biology and
software has been indirect. Humans use software through various user interfaces,
rather than with direct communication links. Concepts from biological systems
have inspired various heuristic algorithms to solve computer science problems
(typically optimization and search), or inspired software for communication
systems to mimic the adaptive behavior of biological systems [
The work reported in this paper is a rst step in a project aiming at developing techniques to support the direct run-time interaction of biological entities and software. Our vision is that eventually software interacts directly with the biological world: software controls biological entities, and biological entities control software systems. Thus, rather than using the biological world as a model of new algorithms, we intend to let biological entities communicate directly with software. In this way, software systems and biological entities form co-operational organizations in which both parties solve problems suitable for them, contributing to a common goal. Typically, biological entities are superior in e cient massive parallel processing of fuzzy data and resilient to damage, while traditional software systems are better suited for making discrete, well-de ned logical decisions. Biological entities are also far more energy-e cient than traditional computing devices.
The project focuses on integrating real neural cultures with software systems.
A central problem then is the training of biological neural structures for a
particular task and the connection of the trained neural culture to the software system.
However, to experiment with di erent approaches to solve these problems,
available biological neural cultures impose many practical problems: their detailed
structure is di cult to study, their lifetime is limited, and they need constant
nutrition. Luckily, for the past decades, Arti cial Neural Networks (ANNs) have
evolved to the point of being currently very close in behaviour to biological neural
structures [
In this paper we study the basic training problem of biological neural networks using a biologically realistic model of spiking neurons. A simple pattern recognition problem is applied to this model. We demonstrate that a training technique based on Spike-Timing-Dependent-Plasticity (STDP) appears to be su cient for these kinds of tasks.
The rest of this paper is structured as follows. In Section 2, we discuss related work. In Section 3, we introduce the computational model used in this paper. In Section 4, we evaluate the results we have obtained. In Section 5, we draw some nal conclusions. 2
In [
In their chapter on computing with SNNs [
To a certain extent, the simple training method proposed in this paper follows
the idea of training only the output layer as STDP will act alone for reinforcing
the positive pathways of the network. However, the network studied in this paper
is simply a feed-forward network modeled with the BRIAN simulator [
The training method presented in this paper is studied with the computational
model presented in this section because it provides a rst test of feasibility before
testing this method on biological Neural Networks (bioNNs). The model used for
this research is composed of two basic elements: neurons and synapses. Neurons
are built based on the ring model of Izhikevich which is shown to be very
realistic in [
The model of a spiking neuron used in this study is from Izhikevich [
u)
C
= k(v
vr)(v
vt)
u + I
where v represents the membrane potential, u the recovery current of the
membrane, I the input current through the membrane, C the membrane capacitance,
vr the resting potential of the membrane, vt the threshold potential for the
membrane to re a spike, k, a and b parameters adjusted according to the ring
pattern required. The variables v and u of equation 1 are reset after v reaches a
peak value vpeak, as follows:
if v
vpeak, then
(v
u
c
u + d
STDP is a rule for neurons to strengthen or weaken their connections according
to their degree of synchronous ring [
N N wj = X X W (tlj with the function W (x) de ning the order of decrease or increase of strength depending on the synchrony of spiking between pre- and post-synaptic neurons, expressed as:
W (x) = (A+ exp( x ) if x > 0 + A exp( x ) otherwise. (4)
In equations 3 and 4, tlj represents the lth spiking time of neuron j; similarly, tik stands for the kth spike timing of neuron i; A+ and A are constants de ning the amplitude of change in weight (at t = 0+ and t = 0 , respectively); and, + and are time constants of the exponential decrease in weight change. The network developed in this study as an example of pattern recognition is presented in Fig. 3. This network is dedicated at recognizing patterns from a 5x5 pixels image. It is composed of: { 25 input neurons corresponding to each pixel of the image, { a hidden layer of 5 neurons, and { 2 output neurons (1 corresponding to the neuron reacting when a circle appears in the image, the other one being a test neuron for comparison between learning and no stimulation). 4
This section goes more into the details of the simple learning method using STDP rule for training the network. A pattern recognition task is used as a case study for testing the learning method proposed. 4.1
The pattern recognition task evaluated during this simple case study consists in making the di erence between a circle given as input stimuli and other inputs (in that case an X-cross shape). These shapes are represented as coming from a 25 pixels image (5x5 matrix), each pixel being binary: black or white. Figure 4 presents the input circle and X-cross patterns and their respective representations as input stimuli to the network.
(a) Circle pattern (b) X-cross pattern After initial tests on the learning ability of the network, the training period was adjusted to be 15s during which the input layer is stimulated every 100ms with a circle pattern. 10ms after stimulating the input layer, the output neuron is given an external stimulation making it to spike. This spiking, in relation with the preliminary spiking of neurons from the input layer, reinforces the paths between activated neurons of the input layer and the trained neuron of the output layer. This training can be seen in the rst phase of the time diagrams (top and middle) of Figure 5 from t = 0 to 15s. The testing phase is composed of 6 stimuli with circle pattern and 7 stimuli with a di erent pattern (in that case representing an X-cross). These stimuli of the input layer happen without any external stimulation of the output layer. The neuron trained for recognizing a circle res on its own after the learning phase. These test patterns are sent between t = 15; 5 to 25s with the following sequence: fcircle, circle, cross, cross, circle, cross, cross, cross, cross, circle, circle, cross, circleg at the respective times f15.5, 16, 16.5, 17, 17.5, 18, 18.5, 19, 20, 21, 23, 24, 24.5g seconds. The two upper time diagrams of Figure 5 show this test phase.
The third time diagram of Figure 5 (down) presents the evolution of strength of synapses between neurons from the hidden layer and neurons from the output layer. This evolution shows rst a stabilization period from the random strengths given as initial condition to lower values. Secondly, learning can be seen as the strengths of certain synapses increase to high levels of connectivity (i.e. to levels higher than 0.8 times the maximum connectivity and often reaching this maximum). 4.3
The 1000 simulations of this experiment revealed a success rate of 80.3% in recognizing a circle from a cross. This rate was computed after the execution of a thousand experiments. From these experiments, ve di erent cases were observed: { correct learning: output res only when a circle is given as input (80.3%) { some mistakes: output res sometimes when input is a cross (5.7%) { always ring: output always res whatever the input may be (12.8%) { no learning: output never res (1.1%)
{ wrong learning: output res only when input is a cross (0.1%) These di erent cases are represented in Figure 6.
These results show a high learning rate, i.e. a high rate of correct experiments (80.3%), meaning that such learning method has correct grounds. Indeed, there is space for improving this rate and a lot to learn from the analysis of failed experiments.
First, we can notice that the network keeps on learning even after the training phase has stopped. Each time a pattern is fed as input to the network, small increase in synaptic weights take place.
The second important thing noticed due to this continuous learning is that the output neuron trained to recognize a circle also gets trained when receiving another pattern as input. As the synaptic levels may already be high, it requires only few X-cross stimulation signals for the output neuron to start spiking and we notice that when it has learned to spike for a cross pattern, it will then re each time a cross appears. This is what happens for the cases where some mistakes are found (57 cases out of 1000 simulations).
Third, for 128 simulations the synaptic levels are high from the beginning of the training due to the initial random value of synaptic weights. This causes the network to be \over-trained" and thus to re for every kind of patterns from the beginning of the test phase. In the contrary, for 11 simulations the output neuron does not re at all when given any input. These 11 tests show clearly low rates in synaptic weights and low increase in synaptic weights during training expressing the fact that the network does not have time to learn during this period of time. The only simulation where the output neuron res only and always when given the wrong input could not be explained. 5
We have studied a central problem in using biological neural networks as computing resources: how to train the neural culture for a particular task. The SNN presented in this paper shows reasonable success rate in learning (80.3%) to di erentiate between two patterns. As the behavior of the simulated network is very close to that of real biological neural networks (bioNNs), this experiment gives preliminary insight for using bioNNs to process complex tasks requiring massive parallelism.
However, there is still possibility for improvement in performing such recognition tasks. In the case where pathways did not have time to form during initial training, it is indeed possible to continue training the network until synaptic level reaches the appropriate levels. On the opposite case, when the network res for any type of input pattern, meaning that it is \over-trained", training the network with negative output stimulation should help restoring the di erentiation
(a) Correct learning (rate 80.3%) (b) Some mistakes (rate 5.7%) (c) Always ring (rate 12.8%) (d) No learning (rate 1.1%) (e) Wrong learning (rate 0.1%) Fig. 6. Example of the 5 di erent cases found in experiments 306 between input patterns. Such negative stimulation can be realized by stimulating the output neuron just prior to the input pattern, when an input pattern is to be discarded by the network. This way, the synaptic pathways related to this input pattern would decrease due to the STDP rule, thus de-correlating the output neuron with this input pattern.
The proximity in behavior of SNNs from bioNNs should not require e orts to transfer computations from silicon platforms into biological platforms. From this point, transferring the various tasks developed for the past sixty years with ANNs (e.g. classi ers, generators, etc.) to small bio-computers will be possible. Research directions for such transfer lead to the following questions: { Can a taxonomy of the various tasks performed with ANNs and their hierarchical relations be developed? { Can we classify tasks as unitary/atomic to some higher level? On the other hand, can tasks be broken down into summation of unitary tasks? { Is it possible to automatically associate tasks to network structures (number of nodes, number of layers etc.) ? { Can training also be automatically generated for these speci c tasks?
These questions could lead to the construction of a compiler deriving the number of biological neural networks used for an application, their structural parameters and the training associated to each task required for the application. 6
In this paper, we presented a simple learning method using STDP for training pathways of a SNN. This method was tested on a SNN model trained to di erentiate between two patterns given as input to the network. The results of this test (80.3% success rate) combined with the fact that the behaviour of the simulated network is very close to the one of a real biological network gives promising expectations for the future of this project. This rst test is still a preliminary test towards applying bioNNs to the computation of more complex tasks such as handwritten digit and character recognition 1. Expectations on the results to such test should give similar success rate as to the test conducted in this paper. Next experiments will be conducted on real biological cells in order to validate the possibility of training bioNNs for pattern recognition tasks. In the nal stage we intend to connect such trained bioNNs with software applications requiring pattern recognition capability such as classi cation of moving objects.
This research is funded by the Academy of Finland under project named \Biointegrated Software Development for Adaptive Sensor Networks", project number 278882. 1 Such training is usually tested on the http://yann.lecun.com/exdb/mnist/ MNIST
dataset available from