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Results tagged with fa.functional-analysis
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user 12939
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
1
vote
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 …
- 459
14
votes
2
answers
888
views
Do distance functionals separate probability measures?
Let $(\Omega,d)$ be a compact metric space and $\mathcal P(\Omega)$ its space of Borel probability measures. Let $D=\{ d_p\mid p\in\Omega\}$ where $d_p(x)=d(p,x)$ be the set of all "distance functiona …
- 459
1
vote
How does a statistical divergence change under a Lipschitz push-forward map?
For the 1-Wasserstein metric $W_1$ on the Borel probability measures $\mathcal P(X)$ of a compact metric space $(X,d)$, recall the Kantorovich-Rubinstein formula:
$$
W_1(\mu,\nu) = \sup_{f\in\text{Lip …
- 459