Many tasks in video analysis and understanding boil down to the need for frame-based feature learning, aiming to encapsulate the relevant visual content so as to enable simpler and easier subsequent processing. While supervised strategies for this learning task can be envisioned, self and weakly-supervised alternatives are preferred due to the difficulties in getting labeled data. This paper introduces LRProp -- a novel weakly-supervised representation learning approach, with an emphasis on the application of temporal alignment between pairs of videos of the same action category. The proposed approach uses a transformer encoder for extracting frame-level features, and employs the DTW algorithm within the training iterations in order to identify the alignment path between video pairs. Through a process referred to as ``pair-wise position propagation'', the probability distributions of these correspondences per location are matched with the similarity of the frame-level features via KL-divergence minimization. The proposed algorithm uses also a regularized SoftDTW loss for better tuning the learned features. Our novel representation learning paradigm consistently outperforms the state of the art on temporal alignment tasks, establishing a new performance bar over several downstream video analysis applications.