  Loss functions steer the optimization direction of recommendation models and
are critical to model performance, but have received relatively little
attention in recent recommendation research. Among various losses, we find
Softmax loss (SL) stands out for not only achieving remarkable accuracy but
also better robustness and fairness. Nevertheless, the current literature lacks
a comprehensive explanation for the efficacy of SL. Toward addressing this
research gap, we conduct theoretical analyses on SL and uncover three insights:
1) Optimizing SL is equivalent to performing Distributionally Robust
Optimization (DRO) on the negative data, thereby learning against perturbations
on the negative distribution and yielding robustness to noisy negatives. 2)
Comparing with other loss functions, SL implicitly penalizes the prediction
variance, resulting in a smaller gap between predicted values and and thus
producing fairer results. Building on these insights, we further propose a
novel loss function Bilateral SoftMax Loss (BSL) that extends the advantage of
SL to both positive and negative sides. BSL augments SL by applying the same
Log-Expectation-Exp structure to positive examples as is used for negatives,
making the model robust to the noisy positives as well. Remarkably, BSL is
simple and easy-to-implement -- requiring just one additional line of code
compared to SL. Experiments on four real-world datasets and three
representative backbones demonstrate the effectiveness of our proposal. The
code is available at https://github.com/junkangwu/BSL
