Book Reviews

Gary Marcus has thrown down the gauntlet to connectionists. It may not be as challenging as that thrown down by Fodor and Pylyshyn (1988), but it raises many questions nonetheless. In this book, Marcus argues that commonly used connectionist models such as multilayer perceptrons (MLPs) and simple recurrent networks (SRNs) are inadequate for representing many aspects of Human cognition. In addition, he also exposes deficiencies in models using temporal synchrony or tensor-based representations. For experienced connectionist modellers, the rst two chapters could be skipped, as chapter one provides a general overview of the book and chapter two describes how MLPs and SRNs function. However, for an individual new to this eld of research, chapter two would provide a good grounding in connectionist modelling techniques. The first challenges to commonly used connectionist models appear in chapter three, which explores the ability of MLPs and SRNs to express relationships between variables (as used in algebraic rules). The deciencies discussed include MLPs having great difficulty in extrapolating relations such as the identity relation (where an MLP is successfully trained to autoassociate even numbers but then fails dramatically when tested on odd numbers) and modelling of linguistic phenomena (the past tense). The discussion of this latter task is comprehensive, with Marcus arguing that only connectionist models that perform this task by implementing (though not explicitly) rule and memory models perform well on this task, whilst connectionist models not implementing such operations over variables do poorly. Here Marcus provides an alternative to standard connectionist representational schemes by outlining the concept of ‘registers’ (used to store bindings between variables and instances). He suggests several ways that registers could be constructed in neural tissue, such as by using cell assemblies (Hebb 1949) and autaptic (self-excitatory) cells (Trehub 1991, Calvin 1996). Registers also provide for the kinds of memory where learning can take place with exposure to only a single trial. Marcus then goes on to show the inadequacies of other connectionist techniques such as temporal synchrony when representing variable binding. It is argued that the main limitation of temporal synchrony models comes from their being able to keep distinct only a small number of phases (typically less than ten), whereas Marcus suggests that Humans can potentially represent millions of bindings. Chapter four discusses structured representations, and again highlights the problems that MLPs and SRNs have in dealing with these. As well as the problems encountered when attempting to represent structured representations in MLPs and SRNs, Marcus also exposes a limitation of temporal synchrony when used to represent complex structure. He argues that the problem with using temporal synchrony to model recursion is that this technique allows only one level of binding. Although acknowledging that Hummel and Holyoak (1997) have dealt with this restriction by constructing an additional binding mechanism (conjunctive nodes), Marcus questions Connection Science, Vol. 14, No. 1, 2002, 85–91