Adversarial robustness, which mainly contains sensitivity-based robustness
and spatial robustness, plays an integral part in the robust generalization. In
this paper, we endeavor to design strategies to achieve universal adversarial
robustness. To hit this target, we firstly investigate the less-studied spatial
robustness and then integrate existing spatial robustness methods by
incorporating both local and global spatial vulnerability into one spatial
attack and adversarial training. Based on this exploration, we further present
a comprehensive relationship between natural accuracy, sensitivity-based and
different spatial robustness, supported by the strong evidence from the
perspective of robust representation. More importantly, in order to balance
these mutual impacts of different robustness into one unified framework, we
incorporate \textit{Pareto criterion} into the adversarial robustness analysis,
yielding a novel strategy called \textit{Pareto Adversarial Training} towards
universal robustness. The resulting Pareto front, the set of optimal solutions,
provides the set of optimal balance among natural accuracy and different
adversarial robustness, shedding light on solutions towards universal
robustness in the future. To the best of our knowledge, we are the first to
consider the universal adversarial robustness via multi-objective optimization