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The question of how to probe contextual word representations for linguistic structure in a way that is both principled and useful has seen significant attention recently in the NLP literature. In our contribution to this discussion, we argue for a probe metric that reflects the fundamental trade-off between probe complexity and performance: the Pareto hypervolume. To measure complexity, we present a number of parametric and non-parametric metrics. Our experiments using Pareto hypervolume as anarXiv:2010.02180v2 fatcat:d6w36kqm5zbndafg7jupirk26u