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Approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby.
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Invertibility of neural network as operator on Wasserstein space
Here is a sufficient condition for non-injectivity under the assumption that $w=(\omega,\beta)$ and $\sigma(x;w)=\sigma(\omega\cdot x + \beta)$ i.e. an artificial neuron with activation $\sigma$, weig …