Stochastic Proximal Gradient (SPG) methods have been widely used for solving optimization problems with a simple (possibly non-smooth) regularizer in machine learning and statistics.

One of the fundamental problems in learning neural networks is parameter recovery, where we assume the data are generated from a "teacher" network, and the task is to estimate the groundtruth parameters of the teacher network based on the generated data.

Usingalgebraic geometry,weestablish that UPCA is a well-defined algebraic problem in the sense that the only matrices of minimal rank that agree with the given data are row-permutations of the ground-truth matrix, arising as the unique solutions of a polynomial system of equations.

Pre-trained large language models (LLMs) based on Transformer have demonstrated striking in-context learning (ICL) abilities.

Fair machine learning.Generally, fair machine learning methods fall into three categories: preprocessing, in-processing, and post-processing [44, 7]. In this paper, we focus on in-processing methods thatmodify learning algorithms toremovediscrimination during thetraining process. All of those works are for indistribution fairness, and we investigate out-of-distribution fairness in this paper. Weuse LAFTR [42],anadversarial learning method that showsadvanced performance onfairness [47],tolearn a fair model in the source domain and adapt it to the target domain. We also test CFair[72] in our experiments.