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Artificial Development of Neural-Symbolic Networks

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Artificial Development of Neural-Symbolic Networks University of Exeter Department of Computer Science Artificial Development of Neural-Symbolic Networks Joseph Paul Townsend March 2014 Supervised by Dr. Ed Keedwell and Dr. Antony Galton Submitted by Joseph Paul Townsend, to the University of Exeter as a thesis for the degree of Doctor of Philosophy in Computer Science , March 2014. This thesis is available for Library use on the understanding that it is copyright material and that no quotation from the thesis may be published without proper acknowledgement. I certify that all material in this thesis which is not my own work has been identi- fied and that no material has previously been submitted and approved for the award of a degree by this or any other University. (signature) ................................................................................................. 1 Abstract Artificial neural networks (ANNs) and logic programs have both been suggested as means of modelling human cognition. While ANNs are adaptable and relatively noise resis- tant, the information they represent is distributed across various neurons and is therefore difficult to interpret. On the contrary, symbolic systems such as logic programs are in- terpretable but less adaptable. Human cognition is performed in a network of biological neurons and yet is capable of representing symbols, and therefore an ideal model would combine the strengths of the two approaches. This is the goal of Neural-Symbolic In- tegration [4, 16, 21, 40], in which ANNs are used to produce interpretable, adaptable representations of logic programs and other symbolic models. One neural-symbolic model of reasoning is SHRUTI [89, 95], argued to exhibit biological plausibility in that it captures some aspects of real biological processes. SHRUTI's original developers also suggest that further biological plausibility can be ascribed to the fact that SHRUTI networks can be represented by a model of genetic development [96, 120]. The aims of this thesis are to support the claims of SHRUTI's developers by producing the first such genetic representation for SHRUTI networks and to explore biological plausibility further by investigating the evolvability of the proposed SHRUTI genome. The SHRUTI genome is developed and evolved using principles from Generative and De- velopmental Systems and Artificial Development [13, 105], in which genomes use indirect encoding to provide a set of instructions for the gradual development of the phenotype just as DNA does for biological organisms. This thesis presents genomes that develop SHRUTI representations of logical relations and episodic facts so that they are able to correctly answer questions on the knowledge they represent. The evolvability of the SHRUTI genomes is limited in that an evolutionary search was able to discover genomes for simple relational structures that did not include conjunction, but could not discover structures that enabled conjunctive relations or episodic facts to be learned. Experiments were performed to understand the SHRUTI fitness landscape and demonstrated that this landscape is unsuitable for navigation using an evolutionary search. Complex SHRUTI structures require that necessary substructures must be discovered in unison and not individually in order to yield a positive change in objective fitness that informs the evolutionary search of their discovery. The requirement for multiple substructures to be in place before fitness can be improved is probably owed to the localist representation of concepts and relations in SHRUTI. Therefore this thesis concludes by making a case for switching to more distributed repre- sentations as a possible means of improving evolvability in the future. 2 Acknowledgements I would like to thank my supervisors Dr. Ed Keedwell and Dr. Antony Galton for all the help they have provided throughout my research and for encouraging me to share my work with the wider research community through various publications. Furthermore, I would like to thank them for taking an interest in my research in the first place and for their willingness to supervise it. I would also like to thank my parents, Derek William and Margaret Townsend, and my brother Martyn Townsend, for supporting, advising and encouraging every single decision I have made to date regarding my education, work and life in general. Finally, I would like to acknowledge my friends James Gould, David Singeisen, Marjorie Gehrhardt and Rachel Warren. Over the past few years we have shared the joys and hardships of academia together and supported each other in doing so. I would like to thank these people for their support, particularly for encouraging me to keep going. I would like to encourage them to do the same and wish them all the best in their future work, be it in academia or elsewhere. 3 Contents List of tables 7 List of figures 9 Publications 14 Definitions 15 1 Introduction 18 1.1 Aims . 24 1.2 Claims . 24 1.3 Contributions . 24 1.4 Thesis overview . 25 2 Background 27 2.1 Biological preliminaries . 27 2.1.1 The biological neuron . 27 2.1.2 Neural learning mechanisms . 28 2.1.3 Representation of reasoning in the brain . 28 2.1.4 Localist and distributed representation . 29 2.1.5 Temporal coding . 31 2.1.6 Genetic development . 31 2.1.7 Biological plausibility . 32 2.2 Psychological preliminaries . 33 2.3 Neural-symbolic integration . 34 2.3.1 Logic programs . 35 2.3.2 Artificial neural networks . 37 2.3.3 General relational structure . 38 2.3.4 Connectionist models . 38 2.3.5 SHRUTI . 43 2.3.6 Distributed representations . 52 2.3.7 Summary of neural-symbolic reasoning . 57 2.4 Evolutionary algorithms . 58 2.5 Generative and developmental systems . 60 2.5.1 Grammatical encodings . 61 2.5.2 Cellular development models . 64 2.5.3 GDS and objective fitness . 66 2.6 Evolution of neural-symbolic networks . 68 4 Contents 3 Evolution with Hebbian learning 69 3.1 Hebbian learning . 70 3.1.1 Logic programs without negation . 72 3.1.2 Logic programs with negation . 74 3.2 SHRUTI genome . 78 3.2.1 Learning and development cycle . 78 3.2.2 Genome structure . 79 3.2.3 Testing the genome model . 82 3.2.4 Discussion . 88 3.3 Method for evolving SHRUTI genomes . 90 3.3.1 Parameters . 91 3.3.2 Variation . 91 3.3.3 Training and test data . 93 3.3.4 Evaluating error . 94 3.3.5 Alternative objectives . 94 3.3.6 Sampling evolved genomes . 96 3.4 Evolution of networks . 97 3.4.1 Selection of objectives . 97 3.4.2 Performance on training data . 101 3.4.3 Performance on test data . 109 3.5 Larger Predicates . 114 3.6 Discussion . 116 4 Evolution with recruitment learning 119 4.1 Recruitment learning . 120 4.2 Genome model . 121 4.3 Mediator structures . 126 4.3.1 Learning mediator structures . 127 4.3.2 Developing mediator structures . 130 4.3.3 Testing development . 134 4.3.4 Method for evolving mediator structures . 136 4.3.5 Results of evolving mediator structures . 140 4.3.6 Fitness landscape . 146 4.4 Fact structures . 154 4.4.1 Learning fact structures . 154 4.4.2 Developing fact structures . 156 4.4.3 Testing development . 160 4.4.4 Evolving fact structures . 161 4.4.5 Fitness landscape . 165 4.5 Discussion . 172 5 Distributed SHRUTI Networks 175 5.1 Generalising the problem to all localist models . 177 5.2 Distributed neural-symbolic reasoning systems . 179 5.3 Distributed SHRUTI: preliminary results . 180 5 Contents 5.3.1 Distributed relational structure . 180 5.3.2 Error and ambiguity . 182 5.3.3 Probability of θ-overlap: method . 184 5.3.4 Probability of θ-overlap: results . 185 5.3.5 Organising distributed representations . 188 5.3.6 Other nodes . 189 5.3.7 Other SHRUTI structures . 190 5.3.8 Evolvability . 190 5.4 Visuospatial and linguistic systems . 191 5.5 Summary . 191 6 Conclusions 194 6.1 Overview of findings . 195 6.2 Contributions . 197 6.3 Future work . 198 6.3.1 Distributed SHRUTI model . 199 6.3.2 Localist SHRUTI model . 200 6.3.3 Biological plausibility . 201 6.3.4 The goals of neural-symbolic integration . 201 Appendices 204 A Question sets and event sequences 205 A.1 NoNeg data sets . 206 A.1.1 NoNeg1 . 206 A.1.2 NoNeg2 . 206 A.1.3 NoNeg3 . 207 A.1.4 NoNeg4 . 207 A.1.5 NoNeg5 . ..
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