We study a typical optimization model where the optimization variable is composed of multiple probability distributions. Though the model appears frequently in practice, such as for policy problems, it lacks specific analysis in the general setting.

Unlike single-objective optimization, which aggregates objectives into a scalar through weighted sums, MOPs focus on generating specific or diverse Pareto solutions and learning the entire Pareto set directly.

Motivated by this issue, we revisit this classical matrix recovery problem.

We can compress a rectifier network while exactly preserving its underlying functionality with respect to a given input domain if some of its neurons are stable.