Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, October 27, 2015, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Felix Weissenberger

On a One-Shot Model for Sequence Learning

Motivated by a system to store and retrieve sequences in a neural network, we study the following problem. Given a graph and a subset of its vertices A0 we define a sequence of subsets A0,…,Al recursively: Ai+1 is the set of vertices with at least k neighbours into the set Ai. Our goal is to find a sparse random graph which contains a long sequence such that the Ai's have roughly the same specified size and do not overlap too much. For the right p, Gnp contains such a sequence of logarithmic length. We show that starting with a slightly larger p and deleting a small fraction of the edges (constrained by the motivating system) yields a sequence of polynomial length. This is joint work with H. Einarsson, J. Lengler, F. Meier, and A. Steger

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