Where are the neural architectures? The curse of structural flatness in neural network modelling

One of the many ocean swells in the history of computational approaches to mind and brain is the rise and fall of cognitive architectures. Although supplanted by neural networks as the dominant modelling modality, cognitive architectures possess many attributes sorely coveted by the computational modeller: large, architectural-level scales, unified explanations of disparate cognitive functions in single models, and rich, hierarchical-modular decompositional structure conducive to building and modifying large computational systems. In contrast, we find in the neural network literature a proliferation of small-scale, localised models of single tasks, isolated functions, or dissected brain areas. What would it take to unify all this local knowledge into an architectural neural model? The key property that ensures (de-)compositional structure is functional encapsulation – the preservation of component behaviour in disparate contexts. Here, by analysing the behaviour of attractor networks under composition, we demonstrate that neural networks lack functional encapsulation – a property we call ‘structural flatness’. The core conclusion drawn from the analysis is this: the notion of localised, encapsulated function, essential to the more ‘cartographic’ approaches to the brain, is conceptually consistent only when applied to single networks as wholes, and not to their parts. Following from this, if the brain possesses localised, encapsulated cognitive functions, then neural networks are not the proper formalism to realise this on a grand scale; if the brain does not possess encapsulated functionality, then a critical evaluation must be made of the conceptual utility of functional localisation within computational neuroscience, and how it shapes our empirical and theoretical efforts.