Locality of global stochastic interaction in directed acyclic networks
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Submission date: 03. Sep. 2001 (revised version: March 2002)
published in: Neural computation, 14 (2002) 12, p. 2959-2980
DOI number (of the published article): 10.1162/089976602760805368
Keywords and phrases: infomax principle, stochastic interaction, directed acyclic networks, information geometry, random fields
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The hypothesis of invariant maximization of interaction (IMI) is formulated within the setting of random fields. According to this hypothesis, learning processes maximize the stochastic interaction of the neurons subject to constraints. We consider the extrinsic constraint in terms of a fixed input distribution on the periphery of the network. Our main intrinsic constraint is given by a directed acyclic network structure. First mathematical results about the strong relation of the local information flow and the global interaction are stated in order to investigate the possibility of controlling IMI optimization in a completely local way. Furthermore, we discuss some relations of this approach to the optimization according to Linsker's Infomax principle.