This paper considers completions of COMs (complexes oriented matroids) to ample partial cubes of the same VC-dimension. We show that these exist for OMs (oriented matroids) and CUOMs (complexes of uniform oriented matroids). This implies that OMs and CUOMs satisfy the sample compression conjecture -- one of the central open questions of learning theory. We conjecture that every COM can be completed to an ample partial cube without increasing the VC-dimension.

翻译：本文考虑了Coms(复杂型机器人)的完成量,以充分部分立方体为同一VC分层。我们发现,OMs(定向型机器人)和CUOMs(统一型机器人复合体)都存在,这意味着OMs和CUOMs满足了样本压缩假设 -- -- 学习理论的核心问题之一。我们推测,每个COMs都可以完全部分立方体,而不会增加VC分层。