Paper:
A weakly supervised learning based clustering framework is proposed in this paper. As the core of this framework, we introduce a novel multiple instance learning task based on a bag level label called unique class count (ucc), which is the number of unique classes among all instances inside the bag. In this task, no annotations on individual instances inside the bag are needed during training of the models. We mathematically prove that with a perfect ucc classifier, perfect clustering of individual instances inside the bags is possible even when no annotations on individual instances are given during training. We have constructed a neural network based ucc classifier and experimentally shown that the clustering performance of our framework with our weakly supervised ucc classifier is comparable to that of fully supervised learning models where labels for all instances are known. Furthermore, we have tested the applicability of our framework to a real world task of semantic segmentation of breast cancer metastases in histological lymph node sections and shown that the performance of our weakly supervised framework is comparable to the performance of a fully supervised Unet model.

Review:
This paper proposes a new type of weakly supervised clustering / multiple instance learning (MIL) problem in which bags of instances (data points) are labeled with a "unique class count (UCC)*, rather than any bag-level or instance-level labels.  For example, a histopathology slide (the bag), consisting of many individual pixels to be labeled (the instances) could be labeled at the bag level only with UCC = 1 (for only healthy or only metastatic) or UCC = 2 (for mixed / border case).  The paper then proposes an approach for clustering instances based on the following two-step approach: (1) a UCC model is trained to predict the UCC given an input bag, and (2) the features of this learned UCC model are used in an unsupervised clustering algorithm to the get the instance-level clusters / labels.  The paper also provides a theoretical argument for why this approach is feasible.
Overall this paper proposes a (1) novel and creative approach that is well validated both (2) theoretically and (3) empirically, and relevant to a real-world problem, and thus I believe should be accepted.  In slightly more detail:
- (1) MIL where we are given bag-level labels only is a well-studied problem that occurs in many real world settings, such as the histopathology one used in this paper.  However to this reader's knowledge, this is a new variant that is both creative and motivated by an actual real-world study, which is exciting and alone warrants presentation at the conference in my opinion.
- (2) The theoretical treatment is high-level, but still serves a clear purpose of establishing feasibility of the proposed method- this modest and appropriate purpose serves the paper well.
- (3) The empirical results are thorough---e.g. the use of the two loss components for the UCC model are appropriately ablated, there are a range of baseline approaches compared to, multiple evaluation points are provided (i.e. both UCC prediction and final clustering metrics), and a real world use case is presented--and the results are impressive.
Some comments to improve the paper:
- The connection of the proposed UCC approach to the motivating histopath example should be explicitly stated upfront to help the reader understand how this method could be used and how it makes sense!
- It seems that the KDE element of the UCC model was chosen in part to enable the theoretical analysis?  If so, this should be clearly stated to help the reader understand the design rationale.
- Either way, it seems that a different approach than the KDE layer could have been taken- this should be added to the ablation experiments