The cerebral cortex of mammals comprises a series of topographic maps, forming sensory and motor areas such as those in the visual, auditory, and somatosensory systems. Understanding the rules that govern the development of these maps and how this topographic organization relates to information processing is critical for the understanding of cortical processing and whole brain function. Previous computational models have shown that topographic maps can develop through a process of self-organization, if spatially localized patches of cortical neurons are activated by particular stimuli. This thesis presents a series of computational models, based on this principle of self-organization, that focus on the development of the map of orientation preference in primary visual cortex (V1). This map is the prototypical example of topographic map development in the brain, and is the most widely studied, however the same self-organizing principles can also apply to maps of many other visual features and maps in many other sensory areas. Experimental evidence indicates that orientation preference maps in V1 develop in a stable way, with the initial layout determined before eye opening. This constraint is at odds with previous self-organizing models, which have used biologically unfounded ad-hoc methods to obtain robust and reliable development. Such mechanisms inherently lead to instability, by causing massive reorganization over time. The first model presented in this thesis (ALISSOM) shows how ad-hoc methods can be replaced with biologically realistic homeostatic mechanisms that lead to development that is both robust and stable. This model shows for the first time how orientation maps can remain stable despite the massive circuit reconstruction and change in visual inputs occurring during development. This model also highlights the requirements for homeostasis in the developing visual circuit. A second model shows how this development can occur using circuitry that is consistent with the known wiring in V1, unlike previous models. This new model, LESI, contains Long-range Excitatory and Short-range Inhibitory connections between model neurons. Instead of direct long-range inhibition, it uses di-synaptic inhibition to ensure that when visual stimuli are at high contrast, long-range excitatory connections have an overall inhibitory influence. The results match previous models in the special case of the high-contrast inputs that drive development most strongly, but show how the behavior relates to the underlying circuitry, and also make it possible to explore effects at a wide range of contrasts. The final part of this thesis explores the differences between rodents and higher mammals that lead to the lack of topographic organization in rodent species. A lack of organization for orientation also implies local disorder in retinotopy, and analysis of retinotopy data from two-photon calcium imaging in mouse (provided by Tom Mrsic- Flogel, University College London) confirms this hypothesis. A self-organizing model is used to investigate how this disorder can arise via variation in either feed-forward connections to V1 or lateral connections within V1, and how the effects of disorder may vary between species. These results suggest that species with and without topographic maps implement similar visual algorithms differing only in the values of some key parameters, rather than having fundamental differences in architecture. Together, these results help us understand how and why neurons develop preferences for visual features such as orientation, and how maps of these neurons are formed. The resulting models represent a synthesis of a large body of experimental evidence about V1 anatomy and function, and offer a platform for developing a more complete explanation of cortical function in future work.

This thesis investigates a set of non-classical visual receptive field properties observed in the primate brain. Two main phenomena were explored. The first phenomenon was neurons with head-centered visual receptive fields, in which a neuron responds maximally to a visual stimulus in the same head-centered location across all eye positions. The second phenomenon was perisaccadic receptive field dynamics, which involves a range of experimentally observed response behaviours of an eye-centered neuron associated with the advent of a saccade that relocates the neuron's receptive field. For each of these two phenomena, a hypothesis was proposed for how a neural circuit with a suitable initial architecture and synaptic learning rules could, when subjected to visually-guided training, develop the receptive field properties in question. Corresponding neural network models were first trained as hypothesized, and subsequently tested in conditions similar to experimental tasks used to interrogate the physiology of the relevant primate neural circuits. The behaviour of the models was compared to neurophysiological observations as a metric for their explanatory power. In both cases the neural network models were in broad agreement with experimental observations, and the operation of these models was studied to shed light on the neural processing behind these neural phenomena in the brain.