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 A. Steger, D. Steurer and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Thursday, March 17, 2022, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Simon Weber

Training Fully-Connected Neural Networks is ER-Complete

We consider the algorithmic problem of finding the optimal weights to a two-layer ReLU fully-connected neural network, to fit a given set of data points. We show that the problem is ∃R-complete. Our results hold even if the following restrictions are all added simultaneously. •There are exactly two output neurons. •There are exactly two input neurons. •The data has only a constant number of different labels. •The number of middle neurons is linear in the number of data points. •The data needs to be fitted exactly. This shows that even the simplest possible neural networks are difficult to train. This is joint work with Daniel Bertschinger, Christoph Hertrich (London), Paul Jungeblut (Karlsruhe), and Tillmann Miltzow (Utrecht).

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