Laplacian Eigenspaces, Horocycles and Neuron Models on Hyperbolic Spaces

no code implementations • 1 Jan 2021 • Ming-Xi Wang

We use hyperbolic Poisson kernel to construct the horocycle neuron model on hyperbolic spaces, which is a spectral generalization of the classical neuron model.

Approximation capabilities of neural networks on unbounded domains

no code implementations • 21 Oct 2019 • Ming-Xi Wang, Yang Qu

In this paper, we prove that a shallow neural network with a monotone sigmoid, ReLU, ELU, Softplus, or LeakyReLU activation function can arbitrarily well approximate any L^p(p>=2) integrable functions defined on R*[0, 1]^n.

The option pricing model based on time values: an application of the universal approximation theory on unbounded domains

no code implementations • 2 Oct 2019 • Yang Qu, Ming-Xi Wang

We propose a time value related decision function to treat a classical option pricing problem raised by Hutchinson-Lo-Poggio.