Correct and Weight: A Simple Yet Effective Loss for Implicit Feedback Recommendation

TL;DR

Implicit-feedback recommender systems suffer from pervasive false negatives in unobserved interactions. The paper introduces the Corrected and Weighted (CW) loss, which combines Positive-Unlabeled (PU) style correction of the negative distribution with confidence-aware weighting to emphasize positives and confident negatives while down-weighting uncertain ones. The authors derive a PU-based decontamination of the negative signal, introduce a tunable weighting that favors reliable pairs, and propose a final CW objective that upper-bounds the ranking metric $- ext{logDCG}$, yielding improved top-$K$ rankings across MF, LightGCN, and XSimGCL on four large, sparse datasets. The approach is simple and plug-and-play, requiring no changes to sampling or heavy computational overhead, making it applicable to a wide range of existing recommendation models. Empirical results and ablations demonstrate that CW consistently improves over state-of-the-art losses, reduces false-negative bias, and is robust to prior assumptions and sampling variations.

Abstract

Learning from implicit feedback has become the standard paradigm for modern recommender systems. However, this setting is fraught with the persistent challenge of false negatives, where unobserved user-item interactions are not necessarily indicative of negative preference. To address this issue, this paper introduces a novel and principled loss function, named Corrected and Weighted (CW) loss, that systematically corrects for the impact of false negatives within the training objective. Our approach integrates two key techniques. First, inspired by Positive-Unlabeled learning, we debias the negative sampling process by re-calibrating the assumed negative distribution. By theoretically approximating the true negative distribution (p-) using the observable general data distribution (p) and the positive interaction distribution (p^+), our method provides a more accurate estimate of the likelihood that a sampled unlabeled item is truly negative. Second, we introduce a dynamic re-weighting mechanism that modulates the importance of each negative instance based on the model's current prediction. This scheme encourages the model to enforce a larger ranking margin between positive items and confidently predicted (i.e., easy) negative items, while simultaneously down-weighting the penalty on uncertain negatives that have a higher probability of being false negatives. A key advantage of our approach is its elegance and efficiency; it requires no complex modifications to the data sampling process or significant computational overhead, making it readily applicable to a wide array of existing recommendation models. Extensive experiments conducted on four large-scale, sparse benchmark datasets demonstrate the superiority of our proposed loss. The results show that our method consistently and significantly outperforms a suite of state-of-the-art loss functions across multiple ranking-oriented metrics.

Figures (6)

• Figure 1: Illustration of the false negative problem inherent in implicit feedback recommendation. A negative item $j$ is typically sampled from the general distribution of unlabeled items for a user $u$, denoted as $p_u$. This distribution, however, is a mixture of true negatives (from the underlying distribution $p_u^-$) and false negatives. The goal of our work is to decontaminate this training signal by formally approximating the true negative distribution $p_u^-$ using the observable distributions $p_u$ and $p_u^-$.
• Figure 2: The ranking objective of our proposed method. The model is trained to anchor the ranked list by pushing true positives to the top and confident negatives to the bottom. Consequently, uncertain items, which include potential false negatives, are implicitly positioned in the middle ranks.
• Figure 3: The loss curve with respect to $r_{ui}$ and $r_{uj}$. The region labeled FN denotes the area where false negatives are likely to occur. The red "?" region represents uncertain instances whose labels or confidence are ambiguous. The + region corresponds to the confident zone where the recommender system has been effectively optimized.
• Figure 4: NDCG@20 performance of the proposed loss under varying values of $\tau^+$ using LightGCN as the recommendation model. The term pop. denotes that $\tau^+$ is computed based on item popularity.
• Figure 5: Comparison of the proposed method with different numbers of positive samples across four datasets. The results are based on LightGCN model.