Supervising an unsupervised neural network

The Duy Bui Duy Khuong Nguyen Tien Dat Ngo

Human Machine Interaction LaboratoryCollege of Technology, Vietnam National University, Hanoi

Abstract

Machine learning is the field that is dedicated to thedesign and development of algorithms and techniques thatallow computers to “learn”. Two common types of learningthat are often mentioned are supervised learning and unsu-pervised learning. One often understands that in supervisedlearning, the system is given the desired output, and it isrequired to produce the correct output for the given input,while in unsupervised learning the system is given onlythe input and the objective is to find the natural structureinherent in the input data. We, however, suggest that evenwith unsupervised learning, the information inside the input,the structure of the input, and the sequence that the input isgiven to the system actually make the learning “supervised”in some way. Therefore, we recommend that in order tomake the machine learn, even in a “supervised” manner,we should use an “unsupervised learning” model togetherwith an appropriate way of presenting the input. We proposein this paper a simple plasticity neural network model thathas the ability of storing information as well as storingthe association between a pair of inputs. We then introducetwo simple unsupervised learning rules and a framework tosupervise our neural network.

1. Introduction

Machine learning is the field that is dedicated to the designand development of algorithms and techniques that allowcomputers to “learn”. Two common types of learning that areoften mentioned are supervised learning and unsupervisedlearning. From a system perspective, in supervised learning,the system is given the desired output, and it is requiredto produce the correct output for the given input, while inunsupervised learning the system is given only the input andthe objective is to find the natural structure inherent in theinput data [1]. From this perspective, one often understandsthat it requires a teacher in supervised learning and it doesnot in unsupervised learning. However, this seems to benot a very logical perspective on the meaning of “super-vised” and “unsupervised”. Thus, even with unsupervisedlearning, the information inside the input, the structure ofthe input, and the sequence that the input is given to thesystem actually make the learning “supervised” in some way.

So, differentiating “unsupervised learning” from “supervisedlearning” can be understood as a way of explaining existinglearning models in the field of machine learning. Froma model perspective, while unsupervised learning tries toreflex the given sets of input in a model, supervised learningtries to build an input-output connection model from anumber of given pairs of input and output [2]. In order toobtain the connection between pairs of input and output,supervised learning often interfere cruelly and unnaturallyinto the model, for example changing the weights in Back-propagation Multiple Layer Neural Networks.

We, however, suggest that “supervised learning” shouldbe obtained at a higher abstract level rather at the modellevel. Let us analyze an example of biting a lemon. Whenwe bite a lemon, our tongue tastes sour. The concepts of“lemon” and “sour” are then bound together. After that,whenever we see a lemon without biting it, we may still feelsour. Let us see another example of a child learning how to“add one to one”. Obviously, the teacher does not directlychange the brain of the child so it can produce “two” as theanswer to the problem. Also, from the research results inneuroscience, there is not any back propagation of errors inthe brain so that it can adapt its synapse weights to producecorrect answer. Actually, both “one plus one” and “two”are feeded to brain as input (maybe in different time) sothat the brain learns to associate them together. After theassociation is created, the brain can still recall “two” whenonly “one plus one” is present. In fact, the way a humanlearns how to solve a problem also relates very much tothe learning of association. By seeing the consequences ofperformed actions either randomly or in a supervised way,a human learns the association between consequences andactions. This association will then be used to solve newsimilar problems. We believe that similarity can also belearnt, however, we will not discuss this issue in the scopeof this paper.

We recommend that in order to make the machine learn,even in a “supervised” manner, we should use an “unsu-pervised learning” model in a way of imitating the humanbrain. The system is actually “supervised” by the way theinput is given rather than by the “supervised learning”model itself. With supervised learning model, the difficultyof the learning task increases exponentially in the numberof steps between the input and output. On the other hands,

2009 First Asian Conference on Intelligent Information and Database Systems

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Figure 1. The structure of a synapse.

unsupervised learning model allows the learning of largerand more complex models with the learning time increasesapproximately linearly in the number of levels in the modelhierarchy.

In this paper, we propose a simple plasticity neural net-work model that has the ability of storing information as wellas storing the association between a pair of inputs by tryingto simulate the concept of long term potentiation (LTP) [3].We then introduce two simple unsupervised learning rulesthat make the network learns very fast. Finally, we introducea framework to supervise our neural network. We thendemonstrate an example network that can solve the XORproblem.

The rest of the paper is organized as follows. We summa-rize several related concepts in biological neural network andartificial neural network in Section 2. Section 3.1 presentsour proposal on a simple plasticity neural network togetherwith unsupervised learning rules. An example network isdescribed in Section 4. Finally, we give some discussions inSection 5.

2. Related Work

2.1. Biological Neural Network

A biological neural network expresses a population ofphysically interconnected neurons. Communication betweenneurons often involves an electrochemical process throughan interface which consists of several dendrites connectedto other neurons via synapses (see Figure 1), and one axon.One principle by which neurons work is neural summation,i.e. potentials at the post synaptic membrane will sum up inthe cell body. If the depolarization of the neuron at the axongoes above threshold, the neuron sends an action potential(AP) at the axon hillock and transmits this electrical signalalong the axon to other neurons.

There are various phenomena which alter the efficacy ofsynaptic transmission, which is called synaptic plasticity.Synaptic plasticity refers to changes at synapses that aresensitive to the timing of action potentials in connected neu-rons. Synaptic plasticity can result from presynaptic spikes

preceding postsynaptic spikes (known as pre-post spiking)and postsynaptic spikes preceding presynaptic spikes (knownas post-pre spiking). Usually, pre-post spiking causes long-term potentiation (LTP) of the synapse, and post-pre spikingcauses long-term depression (LTD).

2.2. Theory of learning

It has been discovered for a long time that the numberof neurons in the adult brain did not increase did notincrease significantly with age. Scientist, therefore, has sug-gested that a mechanism of learning that did not requirethe formation of new neurons [4]. In his 1894 CroonianLecture, the Spanish neuroanatomist Santiago Ram’on yCajal proposed that memories might instead be formedby strengthening the connections between existing neuronsto improve the effectiveness of their communication [4].Hebbian theory [5], introduced by Donald Hebb in 1949,echoed Ramn y Cajal’s ideas, further proposing that cellsmay grow new connections or undergo metabolic changesthat enhance their ability to communicate. The theory isoften summarized as “cells that fire together, wire together”.In 1966, Terje Lømo discovered the presence of long termpotentiation (LTP) in rabbit hippocampus [6]. Since neuronscommunicate via chemical synapses, and because memoriesare believed to be stored within these synapses [7], LTPand its opposing process, long-term depression, are widelyconsidered the major cellular mechanisms that underlielearning and memory. LTP exhibits three main properties:input specificity, associativity, and cooperativity.

• Input specificity. This means LTP happens only atactive synapse. LTP at one synapse only propagates tothose synapses according to the rules of associativityand cooperativity but not any other synapse.

• Associativity. When weak stimulation of a single path-way is insufficient for the induction of LTP, simultane-ous strong stimulation of another pathway will induceLTP at both pathways.

• Cooperativity. When weak stimuli are applied to manypathways that converge on a single patch of postsy-naptic membrane, the individual postsynaptic depo-larizations generated may collectively depolarize thepostsynaptic cell enough to induce LTP cooperatively.

Although the concept of LTP has been investigated for along time in the field of neuroscience, until present, there isnot any artificial neural network that can simulate the idea ofLTP to create an effective learning mechanism for machines.

2.3. Unsupervised Artificial Neural Networks

Inspired from biological neuron, several neuron modelsfor artificial neural networks have been proposed. However,the philosophies used for artificial neural networks (ANN)

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are still much different from those used in neuron models forneuroscience studies. Freeman [8] has pointed out that whilebrains and artificial neural networks share certain structuralfeatures, biological networks solve complex problems easilyand creatively, but existing artificial neural networks do not.

An artificial neural network consists of an interconnectedgroup of artificial neurons. The common models of artificialneuron are the McCulloch-Pitts model [9] and perceptronmodel [10]. In that model, the artificial neuron receives oneor more inputs (representing the one or more dendrites) andsums them to produce an output (synapse). Usually the sumsof each node are weighted, and the sum is passed through afunction known as an activation function or transfer function.

Beside the ability to represent biological activities, ar-tificial neural networks, especially supervised ones, oftenconcentrate in achieving also some mathematical propertiese.g.; its capability as a universal function approximator. Thatphilosophy seems to prevent artificial neural networks frombeing able to solve complex problems like a human.

There are three major learning paradigms for artificialneural networks, which are supervised learning, unsuper-vised learning and reinforcement learning. In this paper,we will consider only the unsupervised learning paradigms.A number of unsupervised learning methods have beenproposed. They include competitive learning [11], adaptiveresonance theory [12] and Self-Organizing Maps with a wellknown type is a Kohonen network [13].

With competitive learning, the Hopfield network [11] isa recurrent neural network in which all connections aresymmetric.With Hebbian learning, the Hopfield networkcan perform as robust content-addressable (or associative)memory, resistant to connection alteration.

In an adaptive resonance theory system [12], an input vec-tor is feeded into the comparison field and then transferredto its best match in the recognition field which is the singleneuron whose set of weights most closely matches the inputvector is the best match. The recognition field exhibits lateralinhibition, allowing each neuron in it to represent a categoryto which input vectors are classified.

A self-organizing map (SOM) [13] uses unsupervisedlearning to produce a low-dimensional, discretized represen-tation of the input space of the training samples by mappingpoints in an input space to coordinates in an output space. Aself-organizing map preserves the topological properties ofthe input space. The dimensions and topology of the inputspace can be different from those of the output space.

3. A Simple Plasticity Neural Network Model

In this section, we describe our proposal on a simpleplasticity neural network model. Our neural network is afeed-forward network of simple plasticity neurons. We thenintroduce two unsupervised learning rules with the objectivethat the network can store the input pattern as well as

Figure 2. A Simple Plasticity Neuron model.

store the association between two input patterns that areintroduced to the network preceding each other. Finally, weintroduce a framework to supervise our neural network.

3.1. A Simple Plasticity Neuron model

In our neuron model, each neuron contains a soma andmany input connection, which corresponds to synapsein biological neurons (see Figure 2). The inputs of eachneuron are action pontentials (APs). In biological neuron,APs are pulse-like waves of voltage where they are differentfrom each other only in frequency. We therefore representeach AP by its value. Different from McCulloch-Pitts orperceptron model, the value of each AP in our model doesnot play a role of intensity for that input to jointly activatethe neuron with other inputs. Thus, in our model, the APwith value of 0.5 or 1.0 plays the same role in activatingthe neuron. We assume that the value of AP sent to inputconnection i is a positive real number xi. When it is 0, itis considered there is no AP sent to the neuron via thatinput connection. We model the plasticity of each inputconnection i of the neuron via its long term potentiation(LTP) with two components: a value vi and an intensitywi. Each input connection also contains a filter that allowsonly values in a certain range (V lowi to V highi) to pass.This is inspired by fact that any given biological neurononly responds to a subset of stimuli within its receptivefield. The main idea behind the introducing of filters isto redirect the input pattern into certain regions of theneural networks based on the values in the input pattern.When there is an AP in filter range sending to an inputconnection, it is activated and send to the soma an amountof neurotransmitters with value of Nvi and intensity of Nwi:

if V lowi ≤ xi ≤ V highi

Nvi = vi,Nwi = wi

elseNvi = 0,Nwi = 0.

The output of a synapse does not depend on its input value,but depend only on its LTP and on whether there is input ornot. At the soma, if the total intensity of neurotransmitters

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from its synapse exceed a threshold θ:

n∑

i=1

Nwi > θ

the neuron will send an AP to other neurons. The value ofthis AP is calculated by:

V alue =∑n

i=1 Nvi ∗ Nwi∑ni=1 Nwi

where n is the number of input connections of the neuron.

3.2. Learning rule

Our unsupervised learning rule is inspired from the con-cept of spike timing dependent plasticity (STDP). Recallthat STDP means the changes of synaptic plasticity thatare sensitive to the timing of action potentials in connectedneurons. Presynaptic spikes preceding postsynaptic spikes(known as pre-post spiking) and postsynaptic spikes preced-ing presynaptic spikes (known as post-pre spiking) can causeSTDP. Usually, pre-post spiking causes long-term potentia-tion (LTP) of the synapse, and post-pre spiking causes long-term depression (LTD). This rule actually conforms with theHebbian principle of “cells that fire together, wire together”.In this paper, we only concentrate on the pre-post spikingwhich causes LTP.

We introduce two learning rules that alter the plasticitiesin our neuron model. Our learning rules reflect the inputspecificity properties of LTP, that is only LTP of the inputconnections that receive AP will be updated. The firstlearning rule is that when there are several APs sent to theinput connections of a neuron at the same time and activatethat neuron, the LTP intensity of these input connectionswill be altered in a way that in the future they are requiredto be activated together in order to activate the neuron:

wi = (1 − η) ∗ wi + η ∗ θ

C

where η is learning rate and C is the number of activatedinput connections. This rule, to some extent, reflects thecooperativity properties of LTP.

The second learning rule is that when the neuron isactivated in both time t and time t + 1, the LTP value ofactivated input connections at time t will be altered by thevalue of APs sent to the neuron at time t + 1:

vi = (1 − η) ∗ vi + η ∗ targetV

for all activated input connections i at time t where

targetV =∑

xj ∗ wj∑wj

Figure 3. An example of a neuron that will fire 0.9 whenfeed 0.5 as input.

for all activated input connections j at time t + 1. With thislearning rule, if one input pattern is introduced to the neuronpreceding to another input pattern repeatedly, the LTP valuesof corresponding input connections will converge to the thevalues in the second pattern. This learning rule, to someextent, reflects the associativity properties of LTP.

3.3. Supervising the network

We will now describe a supervising framework for ourneural network model for storing information and for storingassociation between two input patterns.

For storing a single input value P in the network, feed thenetwork with P repeatedly. The LTP value of an activatedinput connection of an activated neuron by P will approachthe value of P by the second learning rule. Thus, the neuronwill store P in one of its connections. When this connectionis activated, the neuron will fire the value P .

For storing the association of an input value P with a setof input values Q1,Q2, . . .,Qk, feed the network with theset of Qi. By the first learning rule, the LTP intensities ofactivated input connections of an activated neuron by theset of Qi will be altered so that in the future that neuron isonly activated when there are all Qi together. By the secondlearning rule, the LTP values of activated input connectionsof the activated neuron by the set of Qi will approach thevalue of P . As a result, after learning, that neuron will firethe value of P when it is feeded with the set of Qi together.If we consider P as the desired output of the input set Qi,then our unsupervised neural network model can producethe output in a way of supervised models.

4. Example Neurons and Networks

In this section, we introduce an example of networkcontaining a single neuron based on our model that can firea value p whenever a value q is introduced as the input ofthe neuron. We then describe an example network that canlearn the solution of the XOR problem.

The first example is described in Figure 3. In this example,we want the network to fire 0.9 when 0.5 is feeded to the

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Figure 4. The network for the XOR problem.

first input connection. The LTP value and intensity of theinput connections are initiated with random values. First,we feed the second input connection 1000 times with thevalue of 0.9. The LTP value of the second input connectionconverges to 0.9. Then we feed the network step by step:first time step, first input connection with 0.5, second timestep, second input connection with 0.9, and third time step,0 to both input connections so values will affect the LTPvalue the second connection. We repeated this 1000 times.The LTP value of the first input connection converges to 0.9.After the learning phase, this network fires 0.9 whenever thefirst input connection is activated (with 0.5) even when thesecond input connection is not activated. When both inputconnections are activated, the network still fires 0.9. If wewant values closing to 0.5 can activate network, we just haveto change the filter range of the first input connection.

The second example is described in Figure 4. For thisnetwork, we represent the value of 0 and 1 in the XORproblem with the input value of 0.5 and 1.0 respectively (tomake positive input for the network). The filter ranges ofthe input connections are presented in Table 1. We first feedthe value 0.5 into the third input of the network 1000 times,and then the value of 1.0 into the third input of the network1000 times. With these steps, the network can rememberthe possible outputs of the XOR problem. We then feedthe first and second input of the network with the valuescorresponding to each case of the XOR problem, then itsdesired output to the third input in the next time, and thenall 0 to all input in the next time. We repeat this process 1000times. After learning phase, the network can now producethe solution of the XOR problem when feeding the valuesinto the first and second input of the network. As can be seenfrom the network, neuron 4 actually stores the solution of 0XOR 0, which is 0, neuron 5 stores the solution of 0 XOR1, and so on. When 0.5 and 0.5 (corresponding to 0 and 0in XOR problem) are feeded into input 1 and 2 respectively,only neuron 4 is activated. Neuron 5 is not activated becauseonly one of its input connections is activated.

Because of the unsupervised learning rule with the learn-ing time depending linearly on the number of connections,

From To Vlow 4 Vhigh

Input 1 Neuron 4 0.5 0.5Input 2 Neuron 4 0.5 0.5Input 3 Neuron 4 0.5 0.5Input 1 Neuron 5 0.5 0.5Input 2 Neuron 5 0.9 0.9Input 3 Neuron 5 0.5 0.5Input 1 Neuron 6 0.9 0.9Input 2 Neuron 6 0.5 0.5Input 3 Neuron 6 0.9 0.9Input 1 Neuron 7 0.9 0.9Input 2 Neuron 7 0.9 0.9Input 3 Neuron 7 0.5 0.5

Table 1. Filter ranges of the input connections in theXOR network.

the network learn very fast. Note that, these two examplesabove are pre-designed networks in order to demonstrate thelearning ability of our proposed model. For a large randomlyconnected network, the information will store in some partof the network based on the filters of input connections ofneurons.

5. Discussion

The proposed learning rules in our neural network modelare very simple. However, with appropriate supervising,complicated information processing still can be achievedwith a complex network by:

• the redirection of different input patterns into differentparts of the network,

• the ability to remember the input,• and the ability to recall one input from another associ-

ated input after they are presented together (after eachother) to the network many times.

One more thing we want to discuss is the auto-associationability. Our first learning rule requires that all componentsof an input pattern must be present for associated neuron tofire. This seems to remove the auto-association ability of theneuron that enables the neuron to retrieve entire pattern fromits incomplete sample. However, the auto-association abilitycan be obtained for the network by learning the associationbetween components of the pattern. When some componentsof the pattern are missing, the rest can recover them.

6. Conclusion

In this paper, we proposed that in order to make themachine learn, we should use an “unsupervised learning”model in a way of imitating the human brain. The systemis actually “supervised” by the way the input. A simpleplasticity neural network model that has the ability of storing

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information as well as storing the association between apair of input was introduced. We showed this ability in anexample network that solves the XOR problem.

There are many things that can be done with our pro-posed model. We intend to investigate the problem ofauto-association and classification with our network. Wealso want to perform experiments with a large randomly-connected network.

7. Acknowledgement

This work is financially supported by the Research Grantfrom Vietnam National University, Hanoi No. QG.07.47and The Research Fund of College of Technology, VietnamNational University, Hanoi.

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