Christoph Hertrich LSE

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Christoph Hertrich (LSE) • 19 April 2023 • Understanding Neural Network Expressivity via Polyhedral Geometry • Neural networks with rectified linear unit (ReLU) activations are one of the standard models in modern machine learning. Despite their practical importance, fundamental theoretical questions concerning ReLU networks remain open until today. For instance, what is the precise set of (piecewise linear) functions exactly representable by ReLU networks with a given depth? Even the special case asking for the number of layers to compute a function as simple as max{0, x1, x2, x3, x4} has not been solved yet. In this talk we will explore the relevant background to understand this question and report about recent progress using tropical and polyhedral geometry as well as a computer-aided approach based on mixed-integer programming. This is based on joint works with Amitabh Basu, Marco Di Summa, and Martin Skutella (NeurIPS 2021), as well as Christian Haase and Georg Loho (ICLR 2023). • Slides for this talk are available at: • https://kasprzyk.work/seminars/pdf/He... • Visit the Online Machine Learning Seminar webpage at: • https://kasprzyk.work/seminars/ml.html

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