#selfdirectedproject

Jenny Grant

Connectionist models provide a new paradigm for understanding how information might be represented in the brain. A seductive but naive idea is that single neurons (or tiny neural bundles) might be devoted to the representation of each thing the brain needs to record. For example, we may imagine that there is a grandmother neuron that fires when we think about our grandmother. However, such local representation is not likely. There is good evidence that our grandmother thought involves complex patterns of activity distributed across relatively large parts of cortex.

It is interesting to note that distributed, rather than local representations on the hidden units are the natural products of connectionist training methods. The activation patterns that appear on the hidden units while NETtalk processes text serve as an example. Analysis reveals that the net learned to represent such categories as consonants and vowels, not by creating one unit active for consonants and another for vowels, but rather in developing two different characteristic patterns of activity across all the hidden units.

Given the expectations formed from our experience with local representation on the printed page, distributed representation seems both novel and difficult to understand. But the technique exhibits important advantages. For example, distributed representations, (unlike symbols stored in separate fixed memory locations) remain relatively well preserved when parts of the model are destroyed or overloaded. More importantly, since representations are coded in patterns rather than firings of individual units, relationships between representations are coded in the similarities and differences between these patterns. So the internal properties of the representation carry information on what it is about (Clark 1993, 19). In contrast, local representation is conventional. No intrinsic properties of the representation (a unit's firing) determine its relationships to the other symbols. This self-reporting feature of distributed representations promises to resolve a philosophical conundrum about meaning. In a symbolic representational scheme, all representations are composed out of symbolic atoms (like words in a language). Meanings of complex symbol strings may be defined by the way they are built up out of their constituents, but what fixes the meanings of the atoms?

Connectionist representational schemes provide an end run around the puzzle by simply dispensing with atoms. Every distributed representation is a pattern of activity across all the units, so there is no principled way to distinguish between simple and complex representations. To be sure, representations are composed out of the activities of the individual units. But none of these ‘atoms’ codes for any symbol. The representations are sub-symbolic in the sense that analysis into their components leaves the symbolic level behind.

The sub-symbolic nature of distributed representation provides a novel way to conceive of information processing in the brain. If we model the activity of each neuron with a number, then the activity of the whole brain can be given by a giant vector (or list) of numbers, one for each neuron. Both the brain's input from sensory systems and its output to individual muscle neurons can also be treated as vectors of the same kind. So the brain amounts to a vector processor, and the problem of psychology is transformed into questions about which operations on vectors account for the different aspects of human cognition.

Sub-symbolic representation has interesting implications for the classical hypothesis that the brain must contain symbolic representations that are similar to sentences of a language. This idea, often referred to as the language of thought (or LOT) thesis may be challenged by the nature of connectionist representations. It is not easy to say exactly what the LOT thesis amounts to, but van Gelder (1990) offers an influential and widely accepted benchmark for determining when the brain should be said to contain sentence-like representations. It is that when a representation is tokened one thereby tokens the constituents of that representation. For example, if I write ‘John loves Mary’ I have thereby written the sentence's constituents: ‘John’ ‘loves’ and ‘Mary’. Distributed representations for complex expressions like ‘John loves Mary’ can be constructed that do not contain any explicit representation of their parts (Smolensky 1991). The information about the constituents can be extracted from the representations, but neural network models do not need to explicitly extract this information themselves in order to process it correctly (Chalmers 1990). This suggests that neural network models serve as counterexamples to the idea that the language of thought is a prerequisite for human cognition. However, the matter is still a topic of lively debate (Fodor 1997).

The novelty of distributed and superimposed connectionist information storage naturally causes one to wonder about the viability of classical notions of symbolic computation in describing the brain. Ramsey (1997) argues that though we may attribute symbolic representations to neural nets, those attributions do not figure in legitimate explanations of the model's behavior. This claim is important because the classical account of cognitive processing, (and folk intuitions) presume that representations play an explanatory role in understanding the mind. It has been widely thought that cognitive science requires, by its very nature, explanations that appeal to representations (Von Eckardt 2003). If Ramsey is right, the point may cut in two different ways. Some may use it to argue for a new and non-classical understanding of the mind, while others would use it to argue that connectionism is inadequate since it cannot explain what it must. However, Haybron (2000) argues against Ramsey that there is ample room for representations with explanatory role in radical connectionist architectures. Roth (2005) makes the interesting point that contrary to first impressions, it may also make perfect sense to explain a net's behavior by reference to a computer program, even if there is no way to discriminate a sequence of steps of the computation through time.

The debate concerning the presence of classical representations and a language of thought has been clouded by lack of clarity in defining what should count as the representational “vehicles” in distributed neural models. Shea (2007) makes the point that the individuation of distributed representations should be defined by the way activation patterns on the hidden units cluster together. It is the relationships between clustering regions in the space of possible activation patterns that carry representational content, not the activations themselves, nor the collection of units responsible for the activation. On this understanding, prospects are improved for locating representational content in neural nets that can be compared in nets of different architectures, that is causally involved in processing, and which overcomes some objections to holistic accounts of meaning.

In a series of papers Horgan and Tienson (1989, 1990) have championed a view called representations without rules. According to this view classicists are right to think that human brains (and good connectionist models of them) contain explanatorily robust representations; but they are wrong to think that those representations enter in to hard and fast rules like the steps of a computer program. The idea that connectionist systems may follow graded or approximate regularities (“soft laws” as Horgan and Tienson call them) is intuitive and appealing. However, Aizawa (1994) argues that given an arbitrary neural net with a representation level description, it is always possible to outfit it with hard and fast representation-level rules. Guarini (2001) responds that if we pay attention to notions of rule following that are useful to cognitive modeling, Aizawa's constructions will seem beside the point.

One of the attractions of distributed representations in connectionist models is that they suggest a solution to the problem of determining the meanings of brain states. The idea is that the similarities and differences between activation patterns along different dimensions of neural activity record semantical information. In this way, the similarity properties of neural activations provide intrinsic properties that fix meaning. However, Fodor and Lepore (1992, Ch. 6) challenge similarity based accounts on two fronts. The first problem is that human brains presumably vary significantly in the number of and connections between their neurons. Although it is straightforward to define similarity measures on two nets that contain the same number of units, it is harder to see how this can be done when the basic architectures of two nets differ. The second problem Fodor and Lepore cite is that even if similarity measures for meanings can be successfully crafted, they are inadequate to the task of meeting the desiderata which a theory of meaning must satisfy.

Churchland (1998) shows that the first of these two objections can be met. Citing the work of Laakso and Cottrell (2000) he explains how similarity measures between activation patterns in nets with radically different structures can be defined. Not only that, Laakso and Cottrell show that nets of different structures trained on the same task develop activation patterns which are strongly similar according to the measures they recommend. This offers hope that empirically well defined measures of similarity of concepts and thoughts across different individuals might be forged.

On the other hand, the development of a traditional theory of meaning based on similarity faces severe obstacles (Fodor and Lepore 1999), for such a theory would be required to assign sentences truth conditions based on an analysis of the meaning of their parts, and it is not clear that similarity alone is up to such tasks as fixing denotation in the way a standard theory demands. However, most connectionists who promote similarity based accounts of meaning reject many of the presupposition of standard theories. They hope to craft a working alternative which either rejects or modifies those presuppositions while still being faithful to the data on human linguistic abilities.

Development

Experimenting ways to arrange the paper cuts I have made as I don’t like them on their own.

Development

Experimenting ways to arrange the paper cuts I have made as I don’t like them on their own.

Development

Experimenting ways to arrange the paper cuts I have made as I don’t like them on their own.