<ul><li>Negative distance kernels are widely used in maximum mean discrepancies (MMDs) and have shown favorable numerical results in various applications.</li><li>However, due to its non-smoothness in x=y, classical theoretical results do not hold true.</li><li>A new Lipschitz differentiable kernel is proposed that maintains the favorable properties of the negative distance kernel.</li><li>The new kernel performs similarly well as the negative distance kernel in gradient descent methods, but now with theoretical guarantees.</li></ul>

Smoothed Distance Kernels for MMDs and Applications in Wasserstein Gradient Flows

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