Neural Polytopes
This initiates research in generative discrete geometry for surface approximation using machine learning, which is foundational but incremental as it builds on known neural network properties.
The paper discovered that simple ReLU neural networks generate polytopes approximating a unit sphere, with the polytope types controlled by network architecture, and extended this to neural polytopes for various activations, exhibiting geometric duality.
We find that simple neural networks with ReLU activation generate polytopes as an approximation of a unit sphere in various dimensions. The species of polytopes are regulated by the network architecture, such as the number of units and layers. For a variety of activation functions, generalization of polytopes is obtained, which we call neural polytopes. They are a smooth analogue of polytopes, exhibiting geometric duality. This finding initiates research of generative discrete geometry to approximate surfaces by machine learning.