The field of machine learning and geometric optimization is witnessing significant developments in explainability and computational efficiency. Researchers are focusing on designing novel methods to provide insights into complex models and datasets, enhancing trust and interpretability. Notably, there is a growing interest in explaining dataset shifts and transport phenomena, with approaches leveraging Explainable AI to attribute distances to various data components. Furthermore, the development of streaming algorithms for computing distances and matching problems is improving the scalability of these methods.

In terms of computational efficiency, significant progress is being made in speeding up algorithms for calculating distances, such as the Chamfer distance and the Hausdorff distance, with new algorithms achieving near-linear time complexity. Additionally, the development of dynamic algorithms for bi-chromatic matching is enabling efficient monitoring of distributional drift in real-time.

Some noteworthy papers in this regard include:

• Wasserstein Distances Made Explainable, which proposes a novel solution for attributing Wasserstein distances to various data components.
• Streaming Sliced Optimal Transport, which introduces a method for computing sliced Wasserstein distances from sample streams, achieving low memory complexity while providing theoretical guarantees on the approximation error.
• Even Faster Algorithm for the Chamfer Distance, which improves the running time of the Chamfer distance algorithm to near-linear time complexity.
• Fully Dynamic Euclidean Bi-Chromatic Matching in Sublinear Update Time, which presents the first fully dynamic algorithm for Euclidean bi-chromatic matching with sub-linear update time, enabling effective monitoring of distributional drift in real-time.