Online research in philosophy

We contend that if efficiency and reliability are important factors in neural information processing then distributed, not localist, representations are “evolution's best bet.” We note that distributed codes are the most efficient method for representing information, and that this efficiency minimizes metabolic costs, providing adaptive advantage to an organism.

Page argues convincingly for several important properties of localist representations in connectionist models of cognition. I argue that another important property of localist representations is that they serve as the starting point for connectionist representations of symbolic (relational) structures because they express meaningful properties independent of one another and their relations.

Page has done connectionist researchers a valuable service in this target article. He points out that connectionist models using localized representations often work as well or better than models using distributed representations. I point out that models using distributed representations are difficult to understand and often lack parsimony and plausibility. In conclusion, I give an example – the case of the missing fundamental in music – that can easily be explained by a model using localist representations but can be explained only with great difficulty and implausibility by a model using distributed representations.

In order to benefit from the advantages of localist coding, neural models that feature winner-take-all representations at the top level of a network hierarchy must still solve the computational problems inherent in distributed representations at the lower levels.

Two categorization arguments pose particular problems for localist connectionist models. The internal representations of localist networks do not reflect the variability within categories in the environment, whereas networks with distributed internal representations do reflect this essential feature of categories. We provide a real biological example of perceptual categorization in the monkey that seems to require population coding (i.e., distributed internal representations).

Bifurcation analysis of a real-time implementation of an ART network, which is functionally similar to the generalized localist model discussed in Page's manifesto shows that it yields a phase transition from local to distributed representation owing to continuous variation of the range of inhibitory connections. Hence there appears to be a qualitative dichotomy between local and distributed representations at the level of connectionistic networks conceived of as instances of nonlinear dynamical systems.

A number of examples are given of how localist models may incorporate distributed representations, without the types of nonlocal interactions that often render distributed models implausible. The need to analyze the information that is encoded by these representations is also emphasized as a metatheoretical constraint on model plausibility.

We focus on two components of Page's argument in favour of localist representations in connectionist networks: First, we take issue with the claim that localist representations can give rise to generalisation and show that whenever generalisation occurs, distributed representations are involved. Second, we counter the alleged shortcomings of distributed representations and show that their properties are preferable to those of localist approaches.

In the Localist Manifesto, Page enumerated several computational advantages that localist representations have over distributed representations, but the most important difference between such networks concerns their theoretical clarity. Distributed representations are normally closed to theoretical interpretation and, for that reason, contribute little to psychology, whereas the meaning of the information processing in networks using localist representations can be transparent.

Over the last decade, fully distributed models have become dominant in connectionist psychological modelling, whereas the virtues of localist models have been underestimated. This target article illustrates some of the benefits of localist modelling. Localist models are characterized by the presence of localist representations rather than the absence of distributed representations. A generalized localist model is proposed that exhibits many of the properties of fully distributed models. It can be applied to a number of problems that are difficult for fully distributed models, and its applicability can be extended through comparisons with a number of classic mathematical models of behaviour. There are reasons why localist models have been underused, though these often misconstrue the localist position. In particular, many conclusions about connectionist representation, based on neuroscientific observation, can be called into question. There are still some problems inherent in the application of fully distributed systems and some inadequacies in proposed solutions to these problems. In the domain of psychological modelling, localist modelling is to be preferred. Key Words: choice; competition; connectionist modelling; consolidation; distributed; localist; neural networks; reaction-time.