Low-dimensional embeddings, from classical spectral embeddings to modern neural-net-inspired methods, are a cornerstone in the modeling and analysis of complex networks. Recent work by Seshadhri et al. (PNAS 2020) suggests that such embeddings cannot capture local structure arising in complex networks.

We show the utility of our method by applying it to gradient descent with shuffling and mini-batch gradient descent, reaffirming key results from existing literature under a unified framework.

In this paper, we first propose a flexible framework for safe screening based on the Fenchel-Rockafellar duality and then deriveastrong safe screening rule for norm-regularized least squares using the proposed framework.