Recent work on mini-batch consistency (MBC) for set functions has brought attention to the need for sequentially processing and aggregating chunks of a partitioned set while guaranteeing the same output for all partitions. However, existing constraints on MBC architectures lead to models with limited expressive power. Additionally, prior work has not addressed how to deal with large sets during training when the full set gradient is required. To address these issues, we propose a Universally MBC (UMBC) class of set functions which can be used in conjunction with arbitrary non-MBC components while still satisfying MBC, enabling a wider range of function classes to be used in MBC settings. Furthermore, we propose an efficient MBC training algorithm which gives an unbiased approximation of the full set gradient and has a constant memory overhead for any set size for both train- and test-time. We conduct extensive experiments including image completion, text classification, unsupervised clustering, and cancer detection on high-resolution images to verify the efficiency and efficacy of our scalable set encoding framework. Our code is available at github.com/jeffwillette/umbc

翻译：近期关于集合函数的小批量一致性（MBC）研究，强调了在保证所有分区输出相同的前提下，对划分后的集合进行顺序处理与聚合的必要性。然而，现有MBC架构的约束条件导致模型表达能力受限。此外，当需要全集梯度时，先前工作尚未解决大集合训练问题。针对上述问题，我们提出通用MBC（UMBC）集合函数类——该类函数可在满足MBC条件的同时与非MBC组件任意组合，从而拓展可应用于MBC场景的函数类别范围。进一步地，我们提出一种高效的MBC训练算法，该算法可提供全集梯度的无偏近似，且对于任意规模集合在训练与测试阶段均保持恒定内存开销。通过在图像补全、文本分类、无监督聚类及高分辨率图像癌症检测等任务上的广泛实验，验证了我们可扩展集合编码框架的效率与有效性。我们的代码已开源至github.com/jeffwillette/umbc。