AI 中文总结
研究异构推荐图中关系基数不同的问题，提出结合交叉熵和BPR的基数分解损失（CDL），通过实验验证CE-BPR冲突，表明CDL可提高属性嵌入可辨别性，揭示数据集行为受语义对齐和拓扑泄漏支配。
AI 中文摘要
在异构二分图上训练的图神经网络是推荐系统的常见基础。这些图中关系的基数各不相同，如用户-物品偏好是一对多，用户-属性特征是一对一。传统上对所有网络组件应用单一损失函数，通常是贝叶斯个性化排序（BPR）。虽BPR在推荐任务中效果好，但会使属性嵌入坍缩到近随机几何形状，污染用户节点嵌入，影响下游任务。本文提出基数分解损失（CDL），结合交叉熵（CE）和BPR，使模型能针对不同基数关系共同优化。通过实验表明两种损失在共享编码器参数空间中竞争，验证了CE-BPR冲突。在五个数据集上评估CDL，发现其能持续提高属性嵌入的可辨别性，且排序（NDCG）在属性携带有效偏好信号时改善，相关性弱时则冲突，用lambda参数权衡，发现数据集行为受语义对齐和拓扑泄漏两个图属性支配。
英文摘要
Graph Neural Networks trained on heterogenous bipartite graphs form a common basis in recommendation systems. These graphs often express relations that vary in cardinality, for example, user-item preferences are one-to-many and user-attribute features are one-to-one. Traditionally, a unique loss function is applied for all of the network components which is often Bayesian Personalized Ranking (BPR). While BPR works well for the recommendation task, we find that it causes attribute embeddings to collapse to near-random geometry -- a silent failure that leaves standard ranking metrics largely unaffected and therefore invisible to conventional evaluation. This in turn pollutes user node embeddings, which are shaped by both edge types simultaneously, hurting downstream tasks like personalization, segmentation, etc. Here we propose a Cardinality-Decomposed Loss (CDL) that combines both Cross Entropy (CE) and BPR to enable the model to collectively optimize for relations across cardinalities. We confirm this CE-BPR conflict by showing the two losses compete in the shared encoder's parameter space. We evaluate CDL on five datasets spanning two structural configurations -- one-to-one attributes on user nodes (MovieLens-1M, Last.fm-360K, PayPal Audience Factory, BookCrossing) and on item nodes (Yelp) -- and find that CDL consistently improves discriminability in attribute embeddings. We also show that ranking (NDCG) improves when attributes carry meaningful preference signal, but conflicts with it when the correlation is weak. We use a lambda parameter to navigate this trade-off, and a lambda-sweep reveals that dataset behavior is governed by two graph properties -- semantic alignment and topology leakage. Semantic alignment measures whether the attribute predicts preferences, while topology leakage measures whether the graph's connectivity already encodes it.
