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Convergence of SGD for Training Neural Networks with Sliced Wasserstein Losses
Optimal Transport has sparked vivid interest in recent years, in particular thanks to the Wasserstein distance, which provides a geometrically sensible and intuitive way of comparing probability measures.
Properties of Discrete Sliced Wasserstein Losses
We investigate the regularity and optimisation properties of this energy, as well as its Monte-Carlo approximation $\mathcal{E}_p$ (estimating the expectation in SW using only $p$ samples) and show convergence results on the critical points of $\mathcal{E}_p$ to those of $\mathcal{E}$, as well as an almost-sure uniform convergence and a uniform Central Limit result on the process $\mathcal{E}_p(Y)$.
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