Title: Pushing the limits of self-supervised learning: Can we outperform supervised learning without labels?. Abstract: Despite recent progress made by self-supervised methods in representation learning with residual networks, they still underperform supervised learning on the ImageNet classification benchmark, limiting their applicability in performance critical settings. Building  on  prior  theoretical  insights  from  RELIC  [Mitrovic et  al.,  2021],  we  include  additional  inductive  biases  into  self-supervised  learning. We propose a new self-supervised representation learning method, RELICv2,which  combines  an  explicit  invariance  loss  with  a  contrastive  objective  over  avaried set of appropriately constructed data views to avoid learning spurious cor-relations and obtain more informative representations. RELICv2 achieves 77.1% top-1 classification accuracy on ImageNet using linear evaluation with a ResNet50 architecture and 80.6% with larger ResNet models, outperforming previous state-of-the-art self-supervised approaches by a wide margin. Most notably, RELICv2 is the first unsupervised representation learning method to consistently outperform the supervised baseline in a like-for-like comparison over a range of ResNet architectures. Finally, we show that despite using ResNet encoders, RELICv2 is comparable to state-of-the-art self-supervised vision transformers.