In recent research, contrastive learning has proven to be a highly effective method for representation learning and is widely used for dense retrieval. However, we identify that relying solely on contrastive learning can lead to suboptimal retrieval performance. On the other hand, despite many retrieval datasets supporting various learning objectives beyond contrastive learning, combining them efficiently in multi-task learning scenarios can be challenging. In this paper, we introduce M3, an advanced recursive Multi-hop dense sentence retrieval system built upon a novel Multi-task Mixed-objective approach for dense text representation learning, addressing the aforementioned challenges. Our approach yields state-of-the-art performance on a large-scale open-domain fact verification benchmark dataset, FEVER. Code and data are available at: https://github.com/TonyBY/M3
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