Softmax Loss (SL) is widely applied in recommender systems (RS) and has demonstrated effectiveness. This work analyzes SL from a pairwise perspective, revealing two significant limitations: 1) the relationship between SL and conventional ranking metrics like DCG is not sufficiently tight; 2) SL is highly sensitive to false negative instances. Our analysis indicates that these limitations are primarily due to the use of the exponential function. To address these issues, this work extends SL to a new family of loss functions, termed Pairwise Softmax Loss (PSL), which replaces the exponential function in SL with other appropriate activation functions. While the revision is minimal, we highlight three merits of PSL: 1) it serves as a tighter surrogate for DCG with suitable activation functions; 2) it better balances data contributions; and 3) it acts as a specific BPR loss enhanced by Distributionally Robust Optimization (DRO). We further validate the effectiveness and robustness of PSL through empirical experiments. The code is available at https://github.com/Tiny-Snow/IR-Benchmark.

翻译：Softmax损失函数（SL）在推荐系统（RS）中应用广泛且已被证明有效。本文从成对视角对SL进行分析，揭示了其两个显著局限性：1）SL与传统排序指标（如DCG）的关联不够紧密；2）SL对假负例样本高度敏感。分析表明，这些局限性主要源于指数函数的使用。为解决这些问题，本文将SL扩展为一个新的损失函数族——成对Softmax损失函数（PSL），其使用其他合适的激活函数替代SL中的指数函数。尽管修改幅度极小，我们重点阐述了PSL的三个优势：1）通过选用合适的激活函数，PSL可作为DCG更紧密的替代目标；2）能更好地平衡数据贡献度；3）可作为经分布鲁棒优化（DRO）增强的特定BPR损失函数。我们通过实证实验进一步验证了PSL的有效性与鲁棒性。代码发布于https://github.com/Tiny-Snow/IR-Benchmark。