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Martin Skutella

2 accepted papers

2021

Provably Good Solutions to the Knapsack Problem via Neural Networks of Bounded Size

AAAI 2021technical

The development of a satisfying and rigorous mathematical understanding of the performance of neural networks is a major challenge in artificial intelligence. Against this background, we study the expressive power of neural networks through the example of the classical NP-hard Knapsack Problem. Our…

2021

Towards Lower Bounds on the Depth of ReLU Neural Networks

NeurIPS 2021poster

We contribute to a better understanding of the class of functions that is represented by a neural network with ReLU activations and a given architecture. Using techniques from mixed-integer optimization, polyhedral theory, and tropical geometry, we provide a mathematical counterbalance to the univer…