Localist networks represent information in a very simple and straightforward way. However, localist modelling of complex behaviours ultimately entails the use of intricate “hand-designed” connectionist structures. It is, in fact, mainly these two aspects of localist network models that I believe have turned many researchers off them (perhaps wrongly so).

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.

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.

Localist networks are symbolic models, because their nodes refer to extra-mental objects and events. Hence, localist networks can be combined with symbolic computations to form hybrid models. Such models are already familiar and they are likely to represent the dominant type of cognitive model in the next few decades.

The distinction made by Page between localist and distributed representations seems confounded by the distinction between competitive and associative learning. His manifesto can also be read as a plea for competitive learning. The power of competitive models can even be extended further, by simulating similarity effects in forced-choice perceptual identification (Ratcliff & McKoon 1997) that have defied explanation by most memory models.

A dynamic threshold, which controls the nature and course of learning, is a pivotal concept in Page's general localist framework. This commentary addresses various issues surrounding biologically plausible implementations for such thresholds. Relevant previous research is noted and the particular difficulties relating to the creation of so-called instance representations are highlighted. It is stressed that these issues also apply to distributed models.

Page's proposal to stipulate representations in which individual units correspond to meaningful entities is too unconstrained to support effective theorizing. An approach combining general computational principles with domain-specific assumptions, in which learning is used to discover representations that are effective in solving tasks, provides more insight into why cognitive and neural systems are organized the way they are.

The standard dogmatism ignores the fact that neural coding is extremely flexible, and the degree of “coarseness” versus “locality” of representation in real brains can be different under different task conditions. The real question that should be asked is: What is the operating point of neural coding under natural behavioural conditions? Several sources of evidence suggest that under natural conditions some degree of distribution of coding pervades the nervous system.

Page has performed an important service by dispelling several myths and misconceptions concerning the localist approach. The localist position and computational model presented in the target article, however, are overly restrictive and do not address the representation of complex conceptual items such as events, situations, actions, and plans. Working toward the representation of such items leads to a more sophisticated and articulated view of the localist approach.

The Page target article is interesting because of apparent coverage of many psychological phenomena with simple, unified neural techniques. However, prototype phenomena cannot be covered because the strongest response would be to the first-learned stimulus in each category rather than to a prototype stimulus or most frequently presented stimuli. Alternative methods using distributed coding can also achieve portability of network knowledge.

Page's manifesto makes a case for localist representations in neural networks, one of the advantages being ease of interpretation. However, even localist networks can be hard to interpret, especially when at some hidden layer of the network distributed representations are employed, as is often the case. Hidden Markov models can be used to provide useful interpretable representations.

Page's “localist” code, a population code with occasional, maximally firing elements, does not seem to us usefully or testably different from sparse population coding. Some of the evidence adduced by Page for his proposal is not actually evidence for it, and coding by maximal firing is challenged by lower firing observed in neuronal responses to natural stimuli.

The commentators have raised some interesting issues but none question the viability of a localist approach to connectionist modelling. Once localist models are properly defined they can be seen to exhibit many properties relevant to the modelling of both psychological and brain function. They can be used to implement exemplar models, prototype models and models of sequence memory and they form a foundation upon which symbolic models can be constructed. Localist models are insensitive to interference and have learning rules that are biologically plausible. They have more explanatory value than their distributed counterparts and they relate transparently to a number of classic mathematical models of behaviour.

Neural organization: Structure, function, and dynamics shows how theory and experiment can supplement each other in an integrated, evolving account of the brain's structure, function, and dynamics. (1) Structure: Studies of brain function and dynamics build on and contribute to an understanding of many brain regions, the neural circuits that constitute them, and their spatial relations. We emphasize Szentágothai's modular architectonics principle, but also stress the importance of the microcomplexes of cerebellar circuitry and the lamellae of hippocampus. (2) Function: Control of eye movements, reaching and grasping, cognitive maps, and the roles of vision receive a functional decomposition in terms of schemas. Hypotheses as to how each schema is implemented through the interaction of specific brain regions provide the basis for modeling the overall function by neural networks constrained by neural data. Synthetic PET integrates modeling of primate circuitry with data from human brain imaging. (3) Dynamics: Dynamic system theory analyzes spatiotemporal neural phenomena, such as oscillatory and chaotic activity in both single neurons and (often synchronized) neural networks, the self-organizing development and plasticity of ordered neural structures, and learning and memory phenomena associated with synaptic modification. Rhythm generation involves multiple levels of analysis, from intrinsic cellular processes to loops involving multiple brain regions. A variety of rhythms are related to memory functions. The Précis presents a multifaceted case study of the hippocampus. We conclude with the claim that language and other cognitive processes can be fruitfully studied within the framework of neural organization that the authors have charted with John Szentágothai.

Neural organization attempts to thwart, at least in part, modern neuroscientists' tendency to focus reductionistically on ever smaller microsystems. But although emphasizing higher levels of systems organization, the authors end up enforcing reductionisms of their own, principally the reduction of their domain to the study of invariable normal functioning, without explicit modeling of the deviations that constitute disease states or aging. This reductionism seriously weakens the authors' claims about the truth of their quantitative models.

We praise Arbib et al.'s Neural organization for its support of the integration of different levels of analysis, while noting that it does not always achieve what it advocates. We extend this approach into an area of neuropsychological activity in need of the structure offered by Organization at the intersection of the conflated fields of executive function and frontal lobe function.

Arbib et al. describe mathematical and computational models in neuroscience as well as neuroanatomy and neurophysiology of several important brain structures. This is a useful guide to mathematical and computational modelling of the structure and function of nervous system. The book highlights the need to develop a theory of brain functioning, and it offers some useful approaches and concepts.

Neuroanatomy and neurophysiology are insufficient to specify function. Modeling is essential to elucidate function, but psychophysics is also required. An example is the cognitive and sensorimotor branches of the visual system: anatomy shows direct cross talk between the branches. Psychophysics in normal humans shows links from cognitive to sensorimotor, but the reverse link is excluded by visual illusions affecting the cognitive system but not the sensorimotor system.

Neural organization raises, in an especially clear way, a major problem confronting contemporary cognitive science. The problem (the “big issue” of my title) is: What is the relation between the strategies used to solve basic problems of perception and action and those used to solve more abstract or “cognitive” problems? Is there a smooth, incremental route from what Arbib et al. call “instinctual schemas” to higher-level kinds of cognitive prowess? I argue that, despite some suggestive comments, Arbib et al. do not resolve this issue.

Neural organization achieves its stated goal to “show how theory and experiment can supplement each other in an integrated, evolving account of structure, function, and dynamics” (p. ix), showing in a variety of contexts – from olfactory processing to spatial navigation, motor learning and more – how function may be realized in the neural tissue, with explanatory and predictive neural network models providing a cornerstone in this approach.