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The Geometry of Random Neural Networks

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If you have a question about this talk, please contact Po-Ling Loh .

We study the geometric properties of random neural networks by investigating the boundary volumes of their excursion sets for different activation functions, as the depth increases. More specifically, we show that, for activations which are not very regular (e.g., the Heaviside step function), the boundary volumes exhibit fractal behavior, with their Hausdorff dimension monotonically increasing with the depth. On the other hand, for activations which are more regular (e.g., ReLU, logistic and tanh), as the depth increases, the expected boundary volumes can either converge to zero, remain constant or diverge exponentially, depending on a single spectral parameter which can be easily computed. Our theoretical results are confirmed in some numerical experiments based on Monte Carlo simulations.

Based on joint works with Simmaco Di Lillo, Michele Salvi and Stefano Vigogna.

This talk is part of the Statistics series.

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Average on Saturdays: 7579.85802469 kWh Zoom via link https://eng-cam.zoom.us/j/84914529444?pwd=Uml3OEM2c1BtbFhqaU1CcXN3akYwQT09 Hardy Building 101 (first floor), Downing Site, Cambridge

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