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           A pairwise loss like DPO can only enlarge the relative probability gap between the winner and loser. <a href="https://arxiv.org/abs/2402.13228" target="_blank">Pal et al., 2024</a> observed that DPO only drives the loser's likelihood to be small, but the winner's likelihood barely changes.
           We observe the same phenomenon and in contrast, SPPO can boost the probability density of the winner.