MoL-2011-04: Variable Binding in Biologically Plausible Neural Networks

MoL-2011-04: Kiela, Douwe (2011) Variable Binding in Biologically Plausible Neural Networks. [Report]

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One of the most essential aspects of logic is the ability to bind variables. Without that ability, we cannot represent generic rules in a logical form. In the past decades there has been a lot of interest in implementing logic on neural networks, but this was largely restricted to propositional logic. There have been attempts to implement more sophisticated logics on neural networks, with mixed success. So far, there have been no results that conclusively (and non-theoretically) show that first-order logic can successfully be implemented on neural networks. The most important step towards doing just that, or at least doing so for a fragment, is implementing variable binding on neural networks. In the study of logic and neural networks, the connectionist paradigm has been of pivotal importance all across the domains of cognitive science. However, one might consider traditional connectionism slightly outdated or oversimplified compared to our current knowledge of the workings of neurons and the brain. Since the advent of the original artificial neural networks, the discipline of computational neuroscience has made significant progress. The fine-grained dynamics in such models may provide new insight into the relative standstill that the study of logic (using variables) and neural networks has suffered from in recent years. This interrelation has, so far, been largely unexplored for these biologically more plausible models. The purpose of the thesis at hand is to unite these two points, insofar as that it aims to show that biologically plausible neural networks are capable of representing predicates and are capable of performing variable binding on the predicate’s variables. The results presented in the current thesis are preliminary, meaning that they are merely meant to show that exploring the combination between logic and computational neuroscience can be a fruitful approach and that it should be pursued much further. The outline of the thesis is as follows. First we will establish a solid foundation, covering the background of the study of logic and neural networks in depth, from the inception of artificial neurons to the representation of predicates. In chapter 3, the binding problem–one of the major hurdles to be taken before variable binding can even be attempted–is discussed, along with the solutions that have been proposed over the years. Chapter 4 makes explicit the distinction between connectionism and computational neuroscience, in order to draw attention to biologically plausible neurons. Chapter 5 briefly describes the methodology. The correlation between spike times as a measure for binding is described and the software chosen to perform the simulations is introduced, as well as the software used to analyze the results. Since biologically plausible networks are necessarily highly parameterized, the chosen parameters are discussed as well. The next chapter will turn to the actual experiments used to show that such networks are indeed capable of performing variable binding. Several criteria have been set in the preceding chapters, which will be addressed in the models. Chapter 7 will briefly discuss these results and shed light on some of the remaining issues. Moreover, it discusses the conception of logic that is at the base of what the thesis proposes; and discusses some important aspects of extending the research presented. The closing chapter will look back on what has been covered in the thesis and provides a brief roadmap towards achieving the final goal of implementing first-order logic in full.

Item Type: Report
Report Nr: MoL-2011-04
Series Name: Master of Logic Thesis (MoL) Series
Year: 2011
Date Deposited: 12 Oct 2016 14:38
Last Modified: 12 Oct 2016 14:38

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