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Theoretical Aspects of Neural Networks for Solving Combinatorial Optimization Problems

Christoph Hertrich (TU Berlin)


While artificial neural networks have significantly shaped modern society via breakthrough applications in various disciplines, there are many open questions concerning their theoretical understanding. This talk deals with feedforward neural networks with rectified linear units, which are widely used in practice. We view these networks as a model of computation and investigate its expressivity and complexity in the context of combinatorial optimization problems. The goal is to examine how many neurons and which network depth are required in order to solve different combinatorial optimization problems. After some introductory examples and surprising open problems in that context, we provide details on how a specific dynamic program for the knapsack problem can be realized on a neural network. This is joint work in progress with Martin Skutella.


Christoph Hertrich
TEL 512

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