Domains in neural networks with restricted-range interactions

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Abstract
A class of neural networks is analyzed in which the interaction range grows sublinearly with the network diameter. This avoids wiring problems and leads to rapid formation of (pure or mixed) domains, which later coarsen and develop smooth domain walls that may be driven and finally pinned by weak, noisy data. Notably, the mixture states are destroyed by rapidly growing pure droplets, while the pinned pure domains can reconstruct exponentially many composite patterns, built from patches of ‘‘learned’’ basic textures or symbols.