The learning objective plays a fundamental role to build a recommender system. Most methods routinely adopt either pointwise or pairwise loss to train the model parameters, while rarely pay attention to softmax loss due to its computational complexity when scaling up to large datasets or intractability for streaming data. The sampled softmax (SSM) loss emerges as an efficient substitute for softmax loss. Its special case, InfoNCE loss, has been widely used in self-supervised learning and exhibited remarkable performance for contrastive learning. Nonetheless, limited recommendation work uses the SSM loss as the learning objective. Worse still, none of them explores its properties thoroughly and answers ``Does SSM loss suit for item recommendation?'' and ``What are the conceptual advantages of SSM loss, as compared with the prevalent losses?'', to the best of our knowledge. In this work, we aim to offer a better understanding of SSM for item recommendation. Specifically, we first theoretically reveal three model-agnostic advantages: (1) mitigating popularity bias; (2) mining hard negative samples; and (3) maximizing the ranking metric. However, based on our empirical studies, we recognize that the default choice of cosine similarity function in SSM limits its ability in learning the magnitudes of representation vectors. As such, the combinations of SSM with the models that also fall short in adjusting magnitudes may result in poor representations. One step further, we provide mathematical proof that message passing schemes in graph convolution networks can adjust representation magnitude according to node degree, which naturally compensates for the shortcoming of SSM. Extensive experiments on four benchmark datasets justify our analyses, demonstrating the superiority of SSM for item recommendation. Our implementations are available in both TensorFlow and PyTorch.

翻译：学习目标在构建推荐系统中起着基础性作用。大多数方法通常采用逐点损失或成对损失来训练模型参数，而很少关注Softmax损失，因为当扩展到大型数据集或处理流式数据时，其计算复杂度较高甚至难以实施。采样Softmax（SSM）损失作为Softmax损失的一种高效替代方案应运而生。其特例——InfoNCE损失，在自监督学习中已被广泛使用，并在对比学习中展现出卓越性能。然而，据我们所知，有限的推荐工作将SSM损失作为学习目标。更糟糕的是，尚无研究深入探索其特性并回答“SSM损失是否适合物品推荐？”以及“与主流损失相比，SSM损失在概念上有哪些优势？”在本工作中，我们旨在提供对SSM在物品推荐中更深入的理解。具体而言，我们首先从理论上揭示了三个模型无关的优势：（1）缓解流行度偏差；（2）挖掘难负样本；（3）最大化排名指标。然而，基于我们的实证研究，我们认识到SSM中余弦相似度函数的默认选择限制了其学习表示向量幅度的能力。因此，SSM与同样在调整幅度方面存在不足的模型结合可能导致较差的表示。进一步地，我们提供了数学证明，表明图卷积网络中的消息传递机制可以根据节点度调整表示幅度，这自然弥补了SSM的缺点。在四个基准数据集上的大量实验验证了我们的分析，证明了SSM在物品推荐中的优越性。我们的实现在TensorFlow和PyTorch中均可获得。