Title: Blockwise self-supervised learning with Barlow Twins. Abstract: Current state-of-the-art deep networks are all powered by backpropagation. In this paper, we explore alternatives to full backpropagation in the form of blockwise learning rules, leveraging the latest developments in self-supervised learning. Notably, we show that a blockwise pretraining procedure consisting of training independently the 4 main blocks of layers of a ResNet-50 with Barlow Twins loss function at each block performs almost as well as end-to-end backpropagation on ImageNet: a linear probe trained on top of our blockwise pretrained model obtains a top-1 classification accuracy of 70.48\%, only 1.1\% below the accuracy of an end-to-end pretrained network (71.57\% accuracy). We perform extensive experiments to understand the impact of different components within our method and explore a variety of adaptations of self-supervised learning to the blockwise paradigm, building an exhaustive understanding of the critical avenues for scaling local learning rules to large networks, with implications ranging from hardware design to neuroscience.