Mirror Symmetric Topographic Maps Can Arise from Activity-Dependent Synaptic Changes

Plasticity-induced symmetry relationships between adjacent self-organizing topographic maps

In many species, adjacent topographic maps in sensory neocortex are found to be oriented as roughly mirror-image copies of one another. Here we use a computational model to show for the first time that, in principle, adjacent cortical topographic maps that are mirror-image symmetric along two dimensions can arise from activity-dependent changes if the distribution radius of afferents sufficiently exceeds that of horizontal intracortical interactions. We also find that infrequently, other types of intermap symmetry and previously unexpected map relationships (such as interlocking rotation, in which two adjacent maps become intertwined) can occur. These results support the hypothesis that activity-dependent synaptic changes play a more important role in forming the orientations of adjacent cortical maps than is currently recognized.

A model for learning topographically organized parts-based representations of objects in visual cortex: topographic nonnegative matrix factorization

Object representation in the inferior temporal cortex (IT), an area of visual cortex critical for object recognition in the primate, exhibits two prominent properties: (1) objects are represented by the combined activity of columnar clusters of neurons, with each cluster representing component features or parts of objects, and (2) closely related features are continuously represented along the tangential direction of individual columnar clusters. Here we propose a learning model that reflects these properties of parts-based representation and topographic organization in a unified framework. This model is based on a nonnegative matrix factorization (NMF) basis decomposition method. NMF alone provides a parts-based representation where nonnegative inputs are approximated by additive combinations of nonnegative basis functions. Our proposed model of topographic NMF (TNMF) incorporates neighborhood connections between NMF basis functions arranged on a topographic map and attains the topographic property without losing the parts-based property of the NMF. The TNMF represents an input by multiple activity peaks to describe diverse information, whereas conventional topographic models, such as the self-organizing map (SOM), represent an input by a single activity peak in a topographic map. We demonstrate the parts-based and topographic properties of the TNMF by constructing a hierarchical model for object recognition where the TNMF is at the top tier for learning high-level object features. The TNMF showed better generalization performance over NMF for a data set of continuous view change of an image and more robustly preserving the continuity of the view change in its object representation. Comparison of the outputs of our model with actual neural responses recorded in the IT indicates that the TNMF reconstructs the neuronal responses better than the SOM, giving plausibility to the parts-based learning of the model.

Self-organizing neural projections

The Self-Organizing Map (SOM) algorithm was developed for the creation of abstract-feature maps. It has been accepted widely as a data-mining tool, and the principle underlying it may also explain how the feature maps of the brain are formed. However, it is not correct to use this algorithm for a model of pointwise neural projections such as the somatotopic maps or the maps of the visual field, first of all, because the SOM does not transfer signal patterns: the winner-take-all function at its output only defines a singular response. Neither can the original SOM produce superimposed responses to superimposed stimulus patterns. This presentation introduces a new self-organizing system model related to the SOM that has a linear transfer function for patterns and combinations of patterns all the time. Starting from a randomly interconnected pair of neural layers, and using random mixtures of patterns for training, it creates a pointwise-ordered projection from the input layer to the output layer. If the input layer consists of feature detectors, the output layer forms a feature map of the inputs.