Self-organization of topographic bilinear networks for invariant recognition

We present a model for the emergence of ordered fiber projections that may serve as a basis for invariant recognition. After invariance transformations are self-organized, so-called control units competitively activate fiber projections for different transformation parameters. The model builds on a well-known ontogenetic mechanism, activity-based development of retinotopy, and it employs activity blobs of varying position and size to install different transformations. We provide a detailed analysis for the case of 1D input and output fields for schematic input patterns that shows how the model is able to develop specific mappings. We discuss results that show that the proposed learning scheme is stable for complex, biologically more realistic input patterns. Finally, we show that the model generalizes to 2D neuronal fields driven by simulated retinal waves.