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Learning objectives of recommender models remain largely unexplored. Most methods routinely adopt either pointwise (e.g., binary cross-entropy) or pairwise (e.g., BPR) loss to train the model parameters, while rarely pay attention to softmax loss due to the high computational cost. Sampled softmax 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 studies use sampled softmax loss as the learning objective to train the recommender. Worse still, none of them explore its properties and answer "Does sampled softmax loss suit for item recommendation?" and "What are the conceptual advantages of sampled softmax loss, as compared with the prevalent losses?", to the best of our knowledge.In this work, we aim to better understand sampled softmax loss for item recommendation. Specifically, we first theoretically reveal three model-agnostic advantages: (1) mitigating popularity bias, which is beneficial to long-tail recommendation; (2) mining hard negative samples, which offers informative gradients to optimize model parameters; and (3) maximizing the ranking metric, which facilitates top-𝐾 performance. Moreover, we probe the model-specific characteristics on the top of various recommenders. Experimental results suggest that sampled softmax loss is more friendly to historyand graph-based recommenders (e.g., SVD++ [21] and LightGCN [13]), but performs poorly for ID-based models (e.g., MF [22]). We ascribe this to its shortcoming in learning representation magnitude, making the combination with the models that are also incapable of adjusting representation magnitude learn poor representations. In contrast, the history-and graph-based models, which naturally adjust representation magnitude according to node degree, are able to compensate for the shortcoming of sampled softmax loss. We will release our implementations upon acceptance.

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With the greater emphasis on privacy and security in our society, the problem of graph unlearning -revoking the influence of specific data on the trained GNN model, is drawing increasing attention. However, ranging from machine unlearning to recently emerged graph unlearning methods, existing efforts either resort to retraining paradigm, or perform approximate erasure that fails to consider the inter-dependency between connected neighbors or imposes constraints on GNN structure, therefore hard to achieve satisfying performance-complexity trade-offs.In this work, we explore the influence function tailored for graph unlearning, so as to improve the unlearning efficacy and efficiency for graph unlearning. We first present a unified problem formulation of diverse graph unlearning tasks w.r.t. node, edge, and feature. Then, we recognize the crux to the inability of traditional influence function for graph unlearning, and devise Graph Influence Function (GIF), a model-agnostic unlearning method that can efficiently and accurately estimate parameter changes in response to a 𝜖-mass perturbation in deleted data. The idea is to supplement the objective of the traditional influence function with an additional loss term of the influenced neighbors due to the structural dependency. Further deductions on the closed-form solution of parameter changes provide a better understanding of the unlearning mechanism. We conduct extensive experiments on four representative GNN models and three benchmark datasets to justify the superiority of GIF for diverse graph unlearning tasks in terms of unlearning efficacy, model utility, and unlearning efficiency. Our implementations are available at https://github.com/wujcan/GIF-torch/.