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.

翻译：近期针对集合函数的小批量一致性（MBC）研究指出，需按顺序处理并聚合划分集合的区块，同时确保所有划分得到相同输出。然而，现有MBC架构的约束条件导致模型表达能力受限。此外，当训练中需要全集合梯度时，先前工作未能解决大规模集合的处理问题。为解决上述问题，我们提出通用MBC（UMBC）集合函数类——该类函数可与任意非MBC组件协同使用，同时仍满足MBC特性，从而扩展了MBC场景中可使用的函数类范围。进一步地，我们提出一种高效的MBC训练算法，该算法能对全集合梯度进行无偏近似，且训练与测试阶段均能保持与集合规模无关的恒定内存开销。通过图像补全、文本分类、无监督聚类及高分辨率图像癌症检测等大量实验，验证了我们提出的可扩展集合编码框架的高效性与有效性。