We propose a deep amortized clustering (DAC), a neural architecture which learns to cluster datasets efficiently using a few forward passes. DAC implicitly learns what makes a cluster, how to group data points into clusters, and how to count the number of clusters in datasets. DAC is meta-learned using labelled datasets for training, a process distinct from traditional clustering algorithms which usually require hand-specified prior knowledge about cluster shapes/structures. We empirically show, on both synthetic and image data, that DAC can efficiently and accurately cluster new datasets coming from the same distribution used to generate training datasets.
[Overview]
In this paper, the authors proposed a new clustering method called deep amortized clustering (DAC). Inspired by Lee et al 2019, the authors exploited a transformer to gather the contextual information across different dataset points and then predict the cluster label for each data point. The main difference from Lee et al is that the proposed DAC sequentially estimate the cluster labels for the data points and thus more flexible to estimate the number of clusters in the whole dataset. Based on the proposed DAC method, the authors evaluated the performance on both unsupervised clustering and supervised clustering tasks. it turns out the proposed method has achieved better or comparable performance to previous work on various datasets while hold less computational cost. 
[Pros]
1. In this paper, the authors extended the clustering method in Lee et al to a new method called Deep Amortized Clustering (DAC) for data clustering. In this new method, the number of clusters can be unknown at the beginning and the model itself will sequentially cluster the data points into different groups until are data points have been assigned to some clusters. This is an interesting method in that it does not need to specify the number of clusters at the beginning, and thus become more flexible.
2. To achieve the DAC, the authors proposed two losses, one is Minimum Loss Filtering (MLF) and one is Anchor Filtering to cope with either multi-gaussian-distributed data points or even harder datasets. Meanwhile, the authors also proposed to estimate the density P(x; \theta) in the case that the distribution is not knowing in prior.
3. The authors evaluated the proposed method on both synthetic dataset and realistic dataset. On the synthetic dataset, the proposed method is compared with VBDPM and ACT-ST, two methods that can cope with dataset with unknown number of clusters. On the realistic datasets, the authors evaluated on the EMNIST which is of non-MoG distribution. Besides, the authors further evaluated the method on MiniImageNet features and Omniglot dataset, and showcased comparable performance to previous methods but much shorter running  time.
[Cons]
1. Overall, the paper is poorly written and organized. First, the notations in the method section are hard to follow. There are a number of notations which are all capital characters, either representing a function or a method. Second, the whole training process and inference process of the proposed method is not clear to me. How the model is trained on the training set, what are the learnable parameters in the proposed model and what are the settings for the hyper-parameters, etc. Third, it is hard to get the takeaway messages from the experiment sections. The experimental settings for each subsection are not very clearly explained, and the analysis on the experimental results are also vague.
2. In the method, the authors proposed Minimum Loss Filtering (MLF) for clustering with the loss function in Eq(5). During training, the authors use some training data with ground-truth labels to optimize the loss function. However, it is not clear which parameters will be learned in the optimization. Also, after the training, what the exact inference procedure should be is also not clear to me. Overall, it is really hard to me to follow this section on the filtering process. The authors should definitely describe the process more clearly.
3. The experimental results shown in the paper are hard to interpret. First, the setting for each experiment is not clear to me. In Figure 3, it is hard to understand the figures clearly. In table 2 and table 3, some of the clustering methods are deterministic, such as K-means, Spectral clustering, DEC. However, some other clustering methods are learning to clustering methods, such as KCL and MCL. Putting all of the numbers in the same table is confusing and make it hard to compare. I would suggest the authors make a clear distinction between different methods: 1) deep clustering methods which directly cluster on top of the test set; 2) learning to clustering method which learn some parameters on training set and then generalize to test set; 3) amortized clustering, which also learn some parameters on training and then test on the test set with just one forward pass. Splitting the testing results into three group will be helpful to the readers to understand the paper and the proposed method.
4. Another missed part in the model is the ablation study. How sensitive the model is to different training set, e.g., different training dataset size, different number of training clusters, and different hyper-parameters, etc. Without these information, it is hard to know how well robust the proposed DAC method can generalize.
 
5. Finally, the proposed method was built upon Lee at al 2019, to extend the previous method to a sequential clustering problem. I think a title "deep amortized clustering" is a bit misleading and exaggerated on the proposed method.
[Summary]
In this paper, the authors proposed a new method called Deep Amortized Clustering (DAC) for amortized clustering. Unlike the previous work Lee et al, the proposed DAC sequentially filter the data points from the whole set and construct the clusters gradually. This is a meaningful method in that it can be applied to those data without explicit number of clusters. However, the presentation of the method and experiments make it hard to follow, and thus hard to capture the contributions of the proposed method, and also its capacity. As also mentioned above, I would highly suggest the authors revise the paper so that it can present better the method and the experimental section.