Title: Graph-Theoretic Insights into Bayesian Personalized Ranking for Recommendation
Venue: NeurIPS 2025
Accepted: yes
Keywords: Graph self-supervised learning

Bayesian Personalized Ranking

latent hyperbolic geometry

loss function

Network geometry
Abstract: Graph self-supervised learning (GSL) is essential for processing graph-structured data, reducing the need for manual labeling. Traditionally, this paradigm has extensively utilized Bayesian Personalized Ranking (BPR) as its primary loss function. Despite its widespread application, the theoretical analysis of its node relations evaluation have remained largely unexplored. This paper employs recent advancements in latent hyperbolic geometry to deepen our understanding of node relationships from a graph-theoretical perspective. We analyze BPR’s limitations, particularly its reliance on local connectivity through 2-hop paths, which overlooks global connectivity and the broader topological structure. To address these shortcomings, we purpose a novel loss function, BPR+, designed to encompass even-hop paths and better capture global connectivity and topological nuances. This approach facilitates a more detailed measurement of user-item relationships and improves the granularity of relationship assessments. We validate BPR+ through extensive empirical testing across five real-world datasets and demonstrate its efficacy in refining graph self-supervised learning frameworks. Additionally, we explore the application of BPR+ in drug repositioning, highlighting its potential to support pharmaceutical research and development. Our findings not only illuminate the success factors of previous methodologies but also offer new theoretical insights into this learning paradigm.


Peer reviews:
comments: SUMMARY:
This paper analyzes the limitations of BPR loss in graph self-supervised learning (GSL) from a graph-theoretic perspective. The author argues that BPR relies solely on 2-hop paths for node-relation evaluation, ignoring global topology. They propose BPR+, a novel loss function incorporating even-hop paths via TopoLa distance (derived from latent hyperbolic geometry) to capture global connectivity.

STRENGTHS AND WEAKNESSES:
Strengths

1. This paper is solid, and most of the theories are accompanied by corresponding theoretical analyses.

2. This paper conduct complete experimental verification to demonstrate the rationality of its analyses and methods, and the proposed BPR+ has shown promising performance improvements.

Weaknesses

1. The inclusion and meaning of the abstract node need to be more clearly presented, since this is the reason why the calculation method of the original BPR loss can be understood as a 2-hop path. This is also one of the core issues addressed in this paper.

2. Although the paper provides reasonable insights, the novelty of the proposed BPR+ has limitations.

3. There is a lack of comparison with related work. More relevant work would help readers understand the background and the contributions of this paper.

QUESTIONS:
See the Weaknesses

LIMITATIONS:
Yes
TITLE: Official Review
CLARITY: 2
IMPACT: 2
ORIGINALITY: 3
DATE: 2025-06-25

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper re-interprets the common BPR loss function in recommendation under the lens of hyperbolic geometry to work on its current limitations and improve them. \n\nConcretely, the authors start by observing that the calculation of the predicted user-item interaction score, namely can be also re-interpreted as the $(u, i)$ entry of the Gram matrix of the node embeddings. This allows to go from the original user-item graph topology to another network involving user and item nodes, along with some dummy nodes representing the embedding latent elements. Thus, calculating $\\hat{y}_{ui}$ eventually implies assessing the number of 2-hops connecting any user and item in the graph through the dummy embedding node. While the number of 2-hops connections is positively correlated to the energy distance between nodes in the hyperbolic space, the authors claim only using 2-hops distances is not sufficient. \n\nThus, they propose an improved version of the BPR loss, dubbed BPR+, where the computation of $\\hat{y}_{ui}$ is replaced with the calculation of the topological distance between the two nodes, computed at even-numbered hops (i.e., 2-4-6-... hops). This improved loss has the advantage of incorporating more global information and capturing the topological structure between users and items in the system. \n\nFinally, as the computation of the topological distances is computationally expensive (because it involves a matrix power repeated multiple times), the authors propose to work on the decomposed representation of node embeddings through SVD. \n\nExtensive experiments on five recommendation datasets, when testing the BPR+ loss on five baselines, demonstrate the improved recommendation performance with respect to the shallow models. Further analyses considering the relation between the topological similarity and the loss, and the union of neighbors and loss, provide another important perspective on the proposed loss. Moreover, an efficiency study shows how the integration of the SVD decomposition can greatly improve the training time of the model. Finally, the authors efficiently apply the same proposed methodology to another similar domain and task, namely, drug repositioning, demonstrating how BPR+ can outperform other baselines on this task.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n\n$\\bullet$ The paper has the merit to question the goodness of one of the most established loss methodologies in the literature, namely, BPR, in the realm of graph self-supervised learning. Thus, it can hold great significance in the current literature on the topic. \n\n$\\bullet$ The proposed methodology seems adequately sound, being supported by theoretical proofs for each introduced theorem (as also evidenced in the Supplementary Material part).  \n\n$\\bullet$ It is nice to see how the proposed approach can be applied to any graph-based recommender system without necessarily modifying its structure and methodology underneath.  \n\n$\\bullet$ The experimental section is quite clear and shows the efficacy of the model under different perspectives. \n\n$\\bullet$ Remarkably, the authors apply the proposed approach for another task and domain, namely, drug repositioning, demonstrating how the approach can go further the scenario of personalized item recommendation.\n\n**Weaknesses**\n\n$\\bullet$ To the best of my understanding, the code is not released at review time, thus not ensuring the complete reproducibility of the work. While the authors acknowledge the usage of the framework SSLRec, I think it would have been beneficial for them to provide the code for their implemented work.  \n\n$\\bullet$ To the best of my understanding, it is not clear to which power the matrix computation (equations 10 and 11) is actually performed. The authors should have better clarified this aspect.  \n\n$\\bullet$ I am wondering which would be the implications of applying the proposed strategy to monopartite graphs (instead of bipartite graphs as in the paper's case).  \n\n$\\bullet$ Moreover, I am also wondering how the computational complexity of the model would change if, in the BPR schema, we sample more than 1 negative item per each positive item. The literature has shown how this could potentially improve results, and I think that analyzing this aspect would be beneficial to improve the quality of the work.\n\nQUESTIONS:\nMy questions are mainly referred to the last three weaknesses I raised.\n\nQ1) To which power the computations in equations 10-11 are computed?\n\nQ2) Can the proposed approach be potentially applied to monopartite graphs (i.e., graphs with nodes from one single partition, such as citation networks)? And, in case, which would it be the implication of that? Could it be beneficial also to them?\n\nQ3) The literature has shown how computing more than 1 negative for each positive item in the BPR loss can be beneficial to improve the performance [\\*]. How this would impact on your loss function? Would this increase the computational complexity?\n\n**References**\n\n[\\*] Steffen Rendle, Walid Krichene, Li Zhang, and John R. Anderson. 2020. Neural Collaborative Filtering vs. Matrix Factorization Revisited. In RecSys. ACM, 240–248.\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper focuses on the field of graph self-supervised learning, analyzing the widely used but rarely examined BPR (Bayesian Personalized Ranking) loss function. It identifies and verifies its weaknesses in capturing global connectivity and topological similarity from multiple perspectives. Building on the perspective of latent hyperbolic geometry, the authors propose a more effective distance metric called TopoLa and its corresponding loss function BPR+. The improvements brought by BPR+ are validated on five public datasets, enhancing the performance of LightGCN and other contrastive learning models. Furthermore, in the field of drug repositioning, the proposed model achieves significant improvements over existing approaches.\nThe main contributions of this paper are as follows:\n1.\tRevealing the limitations of traditional BPR loss.\n2.\tAnalyzing the effectiveness of common graph convolution operations under the latent hyperbolic framework.\n3.\tProposing a novel loss function, BPR+, which enhances model performance.\n4.\tOptimizing the computational complexity of BPR+.\n5.\tConducting extensive experiments to demonstrate the superiority of proposed method, establishing a new framework for drug repositioning.\n\nSTRENGTHS AND WEAKNESSES:\nFirst of all, regarding the quality of proposed TopoLa technique, its derived methods BPR+ and TopoDR demonstrate statistically significant superior performance over existing models in experiments, confirming the effectiveness of the approach. Furthermore, this work provides comprehensive theoretical foundations for the technique's validity from the perspective of latent hyperbolic geometry, including mathematical proofs and physical property analysis, making it a thorough and well-substantiated research contribution.\nSecondly, regarding the clarity, this paper begins with a systematic analysis of BPR's limitations, employs latent hyperbolic geometry as a robust analytical framework, and subsequently develops novel methods with computational complexity optimizations. The work culminates in comprehensive experimental validation of the proposed approach's effectiveness. The logical progression is complete and well-structured, with particularly clear presentation. Furthermore, the inclusion of source code and datasets in the appendix enhances reproducibility, enabling verification of the reported results.\nThen, regarding the significance of this work, the proposed novel metric represents a breakthrough in traditional loss functions through cross-domain knowledge integration by the research team. Notably, it exhibits considerable model-agnostic characteristics, enabling broad applicability across various graph-structured algorithms. These features suggest substantial potential for future utilization and development in the field, but it still potentially possesses a bit of complexity issue which will be addressed in the Question part.\nFinally, the proposed even-hop paths based method in this paper can be regarded as an extension of traditional BPR loss that incorporates insights from latent hyperbolic geometry. By condensing multi-level topological structure information into multi-hop path representations, this approach achieves more accurate capture of topological similarity and global connectivity. Thus, the underlying originality and reasoning is well-justified.\n\nQUESTIONS:\nFirstly, the paper acknowledges the over-smoothing phenomenon in higher layers of LightGCN while proposing the new method involving multi-layer aggregation. I would appreciate clarification on whether the TopoLa-based approach is susceptible to over-smoothing, or if specific design optimizations have been implemented to prevent this issue.\nThen, the proposed methodology demonstrates that the addition/removal of a single node can influence representation learning across the entire graph. This characteristic raises concerns about its adaptability to real-world scenarios with dynamic user/item pools. I would like to understand the authors' analysis and potential improvements regarding this aspect.\nThird, beyond time complexity, space complexity represents another critical consideration for graph algorithms, as storing intermediate node states often requires substantial memory resources. Has the new method been evaluated in terms of its space complexity requirements?\nThese three points constitute my primary questions after careful reading. Satisfactory explanations to these concerns could lead to an 'Accept' rating.\n\nLIMITATIONS:\nYes, the authors have addressed the limitations in their paper, and I have provided further suggestions in the previous part.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}