Neural Symbol Grounding


Human thought has a dual nature. Some cognitive tasks involve manipulating symbols while others do not. These modes of thought are mirrored by classical AI systems and connectionist systems respectively. Over the last decade considerable work has been done in integrating symbolic and connectionist systems, yet the relationship between symbolic and connectionist representation is not well defined. In this paper we present the view that symbolic representations can emerge from connectionist representations. This is demonstrated with a modified feed-forward network which has the property that, when trained, directly produces a representation in propositional logic. We use an example dataset with which we demonstrate that our methodology can ground both new and predefined symbols in experience. Symbolism and Connectionism First we will very briefly review some of the philosophical work which is pertinent to this research. First, John Searle(Searle 1980) made the claim that strong AI is impossible, using his well known Chinese room example. The original form of the argument was that classical AI systems were merely following syntactic rules, mindlessly shuffling symbols without any understanding of what they meant. This was certainly the case with the various systems he reviewed at that time. What was missing was a connection between the systems’ representations and external reality. The way out is to ground the system’s symbols in experience, as has been pointed out by Harnad(Preston & Bishop 2002) and Chalmers(Chalmers 1992). The last decade has seen considerable controversy over whether the classical (symbolic) approach or the connectionist approach is superior for building intelligent systems. Much of this controversy was provoked by a paper by Fodor and Pylyshyn(Fodor & Pylyshyn 1988) which claimed that connectionist systems cannot exhibit certain properties required for human-like thought. Humans exhibit both types of processing so it is sensible to try to build systems that do the same. Smolensky (Smolensky 1987) calls this dual nature of thought ’the paradox’. He describes five ways in which people resolve this paradox: denial of the soft (connectionist), denial of the hard (symbolic), fuzziness, softness emerging from the hard, and hardness emerging from the soft. This last approach is investigated in this paper. While numerous persuasive arguments have been made and examples devised in an attempt to refute Fodor and Pylyshyn, including (Chalmers 1990), (McMillan, Mozer, & Smolensky 1991),(Plate 1995),(Pollack 1990), (Smolensky 1990),(Touretzky 1990),(Touretzky & Hinton 1985), the symbolic processing abilities of connectionist systems to date have not been so impressive to completely refute Fodor and Pylyshyn’s argument. Symbolic systems also have been lacking in various ways. In particular, there is no explanation as to where the symbols manipulated by these systems come from. Invariably they are simply programmed in, but this is not sufficient for a truly intelligent system acting in an open ended environment (i.e. where it will encounter unexpected things and situations). This question has come to be known as the symbol grounding (or, symbol anchoring where the symbols refer to objects) problem. Discussion of this issue largely stemmed from Harnad’s paper The Symbol Grounding Problem (Harnad 1990). While both symbolic and non-symbolic systems have their applications, if we are to construct intelligent systems that are to function in open ended world (i.e. where all the objects that it will deal with, and symbols to represent these objects, are not predefined), it will be necessary for the system to ground its symbols in experience. There may be some controversy on this but it is the author’s aim to assume this position and attempt to solve issues of symbol grounding, rather than entering into philosophical debate. We demonstrate methods by which symbols may emerge from nonsymbolic data. Here we propose a modified feed-forward network which performs this task. Symbol grounding, the mapping of perception into a symbolic representation, takes the following two forms. In the first, the intelligent system is presented with non-symbolic examples of a concept and it proceeds to create a symbolic description of the concept. This is language creation: starting with input that may be non-symbolic, such as our raw experience of the world, the system creates a new set of symbols to describe this input. In the second form, the intelligent system is presented with both the non-symbolic examples, and a symbolic description (a representation of the concept in some language which is more extensive than a single name) for the example, and it proceeds to learn the meaning of the symbols in the context of the examples. This is a form of language learning. In this paper we present our results for both of these forms of symbol grounding. Why do humans use symbols? Communication with other people is one obvious use. Are there strictly internal uses of symbols? Symbols allow us to make generalizations that would otherwise be impossible. A simple backpropagation network can generalize between things that are close within its input space. Without symbolic representations we would probably be limited in a similar way. One area in which symbol grounding is particularly important is robotics (Jung & Zelinsky 2000). This area is not well developed, yet is essential if robots are to function in a flexible way, as opposed to simply performing a repetitive task(Adams 2001). The experiment described here creates a symbolic description of handwritten digits, in propositional logic. It is not claimed that the description thus obtained is useful in itself. In addition, the symbolic representation is in the form of propositional logic which has limited expressive power. However, it is a first step in constructing similar networks which create descriptions in the far more expressive language of predicate logic. These networks are described in section . This research implements two types of symbol grounding. In one, a system is presented with non-symbolic input along with a symbolic description of that input. The normal feed-forward network that is used for classification is an example of this type of grounding, where the symbolic descriptions are very simple (i.e. the system merely indicates ’yes’ or ’no’ as to whether the input is an example of some concept). Alternatively, the network might be presented with more complex symbolic descriptions (such as a formula of propositional or predicate logic) and the network would have the task of learning the meanings of the individual symbols. The second type of symbol grounding has the system performing classification tasks, but in the process of learning to classify the examples it also generates a symbolic description of the classes. The first of these types of grounding is a limited form of language creation (where the syntax is predefined as that of propositional logic, but the meaning of the symbols themselves is defined by the system) while the second is language learning. The experiments here combine these two types of grounding. Specialized feed-forward networks are presented examples of a subset of the training classes. A symbolic description (in propositional logic) is derived. Then examples of a new class are added to the original set of examples. The original network is applied to this augmented set of examples, computing the values of the propositional variables for this new set. These propositional values are added to the inputs of this training set. Another specialized network is then applied to this augmented data set in such a way that it can make use of the known propositional values (the existing language) and derive necessary new propositional variables, in order to solve the new classification problem. This process is repeated until all of the available classes have been added. a b c d logical formula 0 0 0 0 false 0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 -1 0 1 0 -1 0 1 1 -1 0 1 1 -2 1 0 0 0 true 1 0 0 -1 1 0 -1 0 1 -1 0 0 1 0 -1 1 1 -1 0 1 1 -1 -1 1 1 -1 -1 2 Table 1: Algebraic Representation of Logical Formulas Representing Logical Formulas Algebraically In this section we discuss how logical connectives can be represented as differentiable functions. For example, if there are two propositional variables, and (which will be represented as the outputs of particular neurons, where an output of 1 would mean true and an output of 0 would mean false), a formula of propositional logic may be represented algebraically as

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@inproceedings{HorvitzNeuralSG, title={Neural Symbol Grounding}, author={Richard Horvitz and Raj Bhatnagar} }