The dissertation begins with review of the modular structure of the neocortex and ideas about its overall functioning. We show how a clearer picture of the architecture and an emphasis on developmental models can simultaneously resolve certain theoretical questions and lead to further progress. The next part describes two models based closely on cortical anatomy and compared with physiological studies. The first contained 51 cell populations in 6 layers, with connectivity derived through application of constraint satisfaction to anatomical data. The second model simplified this to a 3-layer structure with fewer celltypes while preserving its important features. Both models replicated results of slice experiments and suggested that laminar activity differences seen there arise from the restriction of most axonal and dendritic arbors to their layers of origin. This structure, with relatively weak inter-layer interactions, challenges traditional conceptions of strong vertical modularity ("columns") within cortical areas, yet it is based rigorously on neurobiological data.
The third part develops methods of calculating influences between principal cell populations to simplify the second model further to three fields of interacting graded-response units. This network is comparable to -- though more complex than -- architectures such as the Kohonen map. The fourth part describes this architecture's performance under a Hebbian learning algorithm subject to two sets of inputs, mimicking the situation where cortical areas receive feedforward and feedback inputs to different layers. The multi-layer architecture allows input connections to develop with greater independence than in the one-layer case and alleviates a difficulty with the latter in which inputs with differing widths or connection densities can destructively interfere.
What is known is that both the aspects of the sensory-motor milieu that each area represents and characteristics of the interactions between them develop on the basis of experience starting from a more skeletal genetic template. Intriguingly, individual differences arise both at the structural and functional levels (though these have barely been related to each other). One is immediately led to speculate on possible ways that more detailed knowledge of this process could be related to the world of everyday life. Do the abilities of the artist or the musician have their basis in, say, relatively enhanced interactions between sets of areas, or alterations to their representational formats? Can one develop the potential to acquire entire classes of skills through training designed to affect these variables? Are there inherent tradeoffs all must make in the acquisition of expertise because of neural representational interference?
A second, more basic set of questions revolves around the issue of the representation of concepts. Modern research within cognitive semantics has attempted to discover the atomic components, as it were, of abstract thought. It concludes that, plausibly, the root substrate consists of basic sensory and motor experience patterns, which are then combined dynamically over a range of timescales to yield the ideas which inhabit our conscious awareness. We should like to characterize both the components and the dynamics further, so as to relate them to our capacities for learning given the specifics of the cortical framework sketched above. Is it reasonable to use as minimal components patterns of activity across single areas, or would something smaller or larger do better? This choice then determines the nature of the possible dynamics at the conceptual level, given constraints from the neural level.
Insight into these issues is the holy grail towards which this thesis work is directed -- but, as was the case from the perspectives of most of the Round Table knights, it will remain distant and imaginary. But this legend also tells us that more than half the battle is not to forget the goal, and accordingly our efforts are directed more towards unraveling generalities than specifics of cortical function. Details of particular behaviors or potential computations are brought in only when needed to flesh out an otherwise tenuous mental framework.
We begin with the observation that the first step in understanding any system's operation is to determine its most salient component parts. Researchers have long considered a cortex a collection of areas each composed of cells distributed into several layers, but the degree and nature of the interaction between these components is poorly characterized. Most analyses and models have therefore ignored the component structure and concentrated on what might occur in a single layer, and the few that have not have made significant assumptions or simplifications, limiting the insight they provided. Our first goal is therefore to clarify the basic structure of the system, so that models and analyses beyond the single-layer level may have a place to begin.
An initial review of the general structure of the neocortex as it varies across different areas within several species helps us find our place, and the perspective allows us to identify overall themes and parameters of cortical organization that will shape our approach. An initial comparison of three evolutionary stages from reptiles to `primitive' mammalian organization to `progressive' mammals suggests two conclusions. First, sensory processing in networks of cortical areas is largely a parallel, distributed phenomenon rather than a serial one at this level. Second, there are two channels of information flow involving different circuits within areas. One transfers input from the periphery to deeper within the system, the other carries `state information' from there back out. Further comparisons reveal that, although the broad outlines of these `feedforward' and `feedback' circuits vary little across modern mammals, there are certain systematic variations at an intermediate scale both across areas and between species, some of which can be related to possible computational function at an informal level.
In the next chapter, we develop conceptual tools for sharpening these ideas by reviewing the major comprehensive theories -- incomplete as they are -- of cortical function that have been advanced. These fall into three classes, differing mainly on the proposed role for feedback connections: one suggests they mediate attentional focus, one that they provide for dynamic reconstruction and prediction of unavailable stimulus features, and one that they increase efficiency in the learning process by implementing analysis/synthesis loops. Although all three are consistent with the (limited) available physiological evidence, they make different predictions as to the relative effects of feedback input on processing within areas and also on the existence of within-area functional segregation. Attentional modulation requires that feedback connections act in a multiplicative, gain-control-like fashion but does not necessarily require their weight structure be that detailed -- approximate coverage of a stimulus location (in feature space) may often suffice. It does suggest, however, that areas may actually send different information in the feedforward and feedback directions, a trait shared by the analysis/synthesis hypothesis. Both the latter and the reconstruction hypotheses, however require the feedback connection matrices have approximately the same resolution of detail as the feedforward ones -- but they differ in that, in the analysis/synthesis hypothesis, the feedforward and feedback signals must be subtracted from one another to further computation, whereas for dynamic reconstruction a purely cooperative interaction is optimal.
The predictions of these theories can be tested through comparison with the actual functional circuit architecture within cortical areas, which can reveal the interactions between the feedforward and feedback inputs to different layers. With this aim in mind, we return to the subject of anatomical structure in the next part of the dissertation. The current picture of within-area circuitry is murky owing to its complexity together with the qualitative nature of much of the available data, and we clarify it by building a sequence of three models reducing out dispensible detail. The first was constructed using single-compartment spiking cells by applying constraint satisfaction directly to celltype distribution and connectivity data primarily from rat primary sensory cortex. We compared its behavior with experiments in slice preparations, verifying that the derived architecture functions realistically. An observed partial decoupling in laminar activities observed experimentally is shown to have its basis in vertical restriction of pyramidal axonal arbors, challenging the predominant view of the cortex as strongly vertically-integrated. It also supports both the attentional modulation and analysis/synthesis theories, since feedforward and feedback signals are sent separately from different layers. The second model also employs spiking cells and is simplified from the first to a structure involving only 3 layers but preserving all major architectural features. It, too, replicates the physiological results, but its simpler structure involves fewer parameters and is more amenable to further study of computational properties.
For analysis and comparison to other computational neural network architectures, however, it is useful to simplify one step further, eliminating inhibitory cell populations and replacing spiking cells with continuous-response units. In the next part of the dissertation we develop and compare three methods for doing this. The results are largely similar, even though one method involves taking `physiological' measurements from simulations while the others rely only on the `anatomical' connection data. This means that constructing network architectures corresponding to different areas in different species can be done relatively easily.
At this point we can test a second aspect of the theoretical predictions outlined earlier. The connections within the last model are consistent in terms of sign with the predictions of both the attention and reconstruction hypotheses, and the question remains as to whether the weight matrices observed in reality are plausibly detailed enough to support reconstruction. We address this by studying the development of input connections to our model under a Hebbian rule -- if the details of cortical connections are determined by experience, a reasonable developmental model should be able to produce them given appropriate input. We compare Hebbian development in both single- and multiple-layer networks where the input fibers connect via arbors with widely differing widths and densities -- as they do for typical feedforward and feedback connections in the real cortex. Both unstructured and structured correlation matrices are considered -- the unstructured ones are differences-of-Gaussians similar to those used in previous models for orientation selectivity and ocular dominance, while the structured ones are based on simulated receptive fields potentially involved in solving a problem in early vision -- the computation of structure from motion.
We found that the laminated architecture permits the development of receptive fields based on intracortically-mediated interactions between inputs to different layers, even when their arbors are of different widths and/or densities. This remains true when interactions between layers are much weaker than those between them, as in the 3-layer spiking model and actually characteristic of many areas and species. In contrast, input arbors must be closely balanced in strength and width for similar receptive fields to emerge in a one-layer configuration; otherwise normalization either eliminates one of the two or leads to a trivial center-surround structure with the narrower arbor occupying the center. When all layers in the 3-layer model receive both inputs, weak interactions between them suffice to align the receptive field maps. Finally, when structured input correlations based on simulated V1 and MT receptive field responses were used, we were unsuccessful in obtaining receptive fields appropriate for contour-from-motion reconstruction (perhaps implemented neurally in area V2), but the results with 3-layer network were more promising since they avoided problems associated with the (anatomically-determined) different widths and densities of the input arbors.
Thus, the laminated architecture of the neocortex with input terminations in different layers is amenable to the development of structured weight matrices, supporting the reconstruction hypothesis, but emergence may not be robust under all circumstances. More generally, our results suggest that single-layer abstractions of cortical areas are insufficient for modeling large scale integrative processing, but the methods we developed lay a foundation for proceeding beyond these while retaining a firm connection to anatomical structure.