<ul><li>We present the Fourier Sliced-Wasserstein (FSW) embedding - a novel method to embed multisets and measures over R^d into Euclidean space.</li><li>The FSW embedding approximately preserves the sliced Wasserstein distance on distributions, resulting in meaningful representations that capture the input structure.</li><li>Unlike other methods, the FSW embedding is bi-Lipschitz on multisets and injective on measures, offering significant advantages over sum- or max-pooling techniques.</li><li>Numerical experiments confirm the superiority of FSW embedding in practical learning tasks, achieving state-of-the-art performance in learning Wasserstein distance and improved robustness in PointNet with reduced parameters.</li></ul>

Fourier Sliced-Wasserstein Embedding for Multisets and Measures

Discover more