Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Tuesday, May 05, 2015, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Hafsteinn Einarsson

A learning rule for local homeostatic plasticity

In this talk I will present a simple STDP inspired learning rule which achieves local homeostatic plasticity, i.e. it adapts the weight of its synapses w.r.t. the input. I will present this rule in the context of a hetero-associative learning task which goes as far back as a paper by Willshaw in Nature in 1969.

For a vertex set V let U and U' be collections of subsets of V. A hetero-associative memory storage can be thought of as a mapping from U to U'. For a complete bipartite graph with partite sets V and V' and all edges with weight 0 initially one can learn to associate a subset X in V with a subset X' in V' by simply making all of the edges between them have weight 1. This is Willshaw's rule and he studied this process in the special case when the subsets in V were random subsets of a fixed size and respectively so for V'. Now if X is set to be active (and all other vertices in V and V' inactive) X' can be restored by activating all vertices in V' which have in-degree |X| via weight 1 edges from X. Willshaw showed that for |V|=|V'|=n and subsets of size log(n) one could asymptotically insert 0.48(n/log(n))^2 associations this way until they stop having the property that a.a.s. there are only finitely many false positives.

Even though the result might sound impressive there are small number effects which make it less impressive in practice and for parameter ranges which apply in the brain (e.g. then the graph is not complete any more but in fact sparse). This has inspired a line of research which goal is to improve on Willshaw's result in a more bioplausible setting.

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