MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Locality of global stochastic interaction in directed acyclic networks

Nihat Ay


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.

infomax principle, stochastic interaction, directed acyclic networks, information geometry, random fields

Related publications

2002 Repository Open Access
Nihat Ay

Locality of global stochastic interaction in directed acyclic networks

In: Neural computation, 14 (2002) 12, pp. 2959-2980