In some studies (e.g., [C. Zhang et al. in Proceedings of the 5th International Conference on Learning Representations, OpenReview.net, 2017]) deep learning, it is observed that overparametrized neural networks achieve a small testing error even when training almost zero. Despite numerous works toward understanding this so-called double-descent phenomenon [M. Belkin al., Proc. Natl. Acad. Sci. ...

Abstract The quantization-based approaches not only are the effective methods for solving problems of approximate nearest neighbor search, but also effectively reduce storage space. However, many usually employ fixed nprobes to search process each query. This will lead extra query consumption. Additionally, we observed that as number points in cluster center product quantization increases, cost...

We obtain new asymptotic results about systems of N particles governed by Riesz interactions involving k-nearest neighbors each particle as $$N\rightarrow \infty $$ . These include a generalization to weighted potentials with external field. Such offer an appealing alternative other approaches for reducing the computational complexity N-body interaction. find first-order term large asymptotics ...