Title: Exploring Non-Contrastive Representation Learning for Deep Clustering. Abstract: Existing deep clustering methods rely on contrastive learning for representation learning, which require negative examples to form an embedding space where all instances are well-separated. However, the negative examples inevitably give rise to the class collision issue, compromising the representation learning for clustering. In this paper, we explore the non-contrastive representation learning for deep clustering, termed NCC, which is based on BYOL, a representative method without negative examples.  First, we propose a positive sampling strategy to align one augmented view of instance with the neighbors of another view so that we can avoid the class collision issue caused by the negative examples and hence improve the within-cluster compactness. Second, we propose a novel prototypical contrastive loss, ProtoCL, which can encourage prototypical alignment between two augmented views and prototypical uniformity, hence maximizing the inter-cluster distance.  Moreover, we formulate NCC in an Expectation-Maximization (EM) framework, in which E-step utilizes spherical k-means to estimate the pseudo-labels of instances and distribution of prototypes from the target network and M-step leverages the proposed losses to optimize the online network. As a result, NCC is able to form an embedding space where all clusters are well-separated and within-cluster examples are compact. Experimental results on several clustering benchmark datasets as well as ImageNet-1K demonstrate that the proposed NCC outperforms the state-of-the-art methods by a significant margin.