On The Topological Expressive Power of Neural Networks

Giovanni Petri, António Leitão

Keywords: Neural Networks, Expressive Power, Decision Boundary, Classification

TL;DR: Characterizing neural networks' expressive power by topologically studying how many, how complex and how different are the decision boundaries it can express.

Abstract:

We propose a topological description of neural network expressive power.
We adopt the topology of the space of decision boundaries realized by a neural architecture as a measure of its intrinsic expressive power.
By sampling a large number of neural architectures with different sizes and design, we show how such measure of expressive power depends on the properties of the architectures, like depth, width and other related quantities.

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