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In recent years, a variety of contrastive learning based unsupervised visual representation learning methods have been designed and achieved great success in many visual tasks. Generally, these methods can be roughly classified into four categories: (1) standard contrastive methods with an InfoNCE like loss, such as MoCo and SimCLR; (2) non-contrastive methods with only positive pairs, such as BYOL and SimSiam; (3) whitening regularization based methods, such as W-MSE and VICReg; and (4) consistency regularization based methods, such as CO2. In this study, we present a new unified contrastive learning representation framework (named UniCLR) suitable for all the above four kinds of methods from a novel perspective of basic affinity matrix. Moreover, three variants, i.e., SimAffinity, SimWhitening and SimTrace, are presented based on UniCLR. In addition, a simple symmetric loss, as a new consistency regularization term, is proposed based on this framework. By symmetrizing the affinity matrix, we can effectively accelerate the convergence of the training process. Extensive experiments have been conducted to show that (1) the proposed UniCLR framework can achieve superior results on par with and even be better than the state of the art, (2) the proposed symmetric loss can significantly accelerate the convergence of models, and (3) SimTrace can avoid the mode collapse problem by maximizing the trace of a whitened affinity matrix without relying on asymmetry designs or stop-gradients.