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Locality of global stochastic interaction in directed acyclic networks. (English) Zbl 1079.68582
Summary: 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.

MSC:
68T05 Learning and adaptive systems in artificial intelligence
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[1] DOI: 10.1162/089976698300017746 · doi:10.1162/089976698300017746
[2] DOI: 10.1109/18.930911 · Zbl 0997.94009 · doi:10.1109/18.930911
[3] DOI: 10.1037/h0054663 · doi:10.1037/h0054663
[4] DOI: 10.1214/aop/1020107773 · Zbl 1010.62007 · doi:10.1214/aop/1020107773
[5] DOI: 10.1162/neco.1989.1.3.295 · doi:10.1162/neco.1989.1.3.295
[6] DOI: 10.1088/0954-898X/12/3/301 · doi:10.1088/0954-898X/12/3/301
[7] DOI: 10.1162/neco.1995.7.6.1129 · Zbl 05479838 · doi:10.1162/neco.1995.7.6.1129
[8] DOI: 10.1113/jphysiol.1962.sp006837 · doi:10.1113/jphysiol.1962.sp006837
[9] DOI: 10.1113/jphysiol.1968.sp008455 · doi:10.1113/jphysiol.1968.sp008455
[10] DOI: 10.1214/aoms/1177729694 · Zbl 0042.38403 · doi:10.1214/aoms/1177729694
[11] Laughlin S., Z. Naturforsch. 36 pp 910– (1981)
[12] DOI: 10.1073/pnas.83.19.7508 · doi:10.1073/pnas.83.19.7508
[13] DOI: 10.1109/2.36 · Zbl 05087941 · doi:10.1109/2.36
[14] DOI: 10.1162/neco.1997.9.8.1661 · doi:10.1162/neco.1997.9.8.1661
[15] DOI: 10.1162/089976698300016972 · doi:10.1162/089976698300016972
[16] DOI: 10.1073/pnas.91.11.5033 · doi:10.1073/pnas.91.11.5033
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