Title: How Does Topology Bias Distort Message Passing in Graph Recommender? A Dirichlet Energy Perspective
Venue: NeurIPS 2025
Accepted: yes
Keywords: Simplicial Complex

Recommender System

Dirichlet Energy
Abstract: Graph-based recommender systems have achieved remarkable effectiveness by modeling high-order interactions between users and items. However, such approaches are significantly undermined by popularity bias, which distorts the interaction graph’s structure—referred to as topology bias. This leads to overrepresentation of popular items, thereby reinforcing biases and fairness issues through the user-system feedback loop. Despite attempts to study this effect, most prior work focuses on the embedding or gradient level bias, overlooking how topology bias fundamentally distorts the message passing process itself. We bridge this gap by providing an empirical and theoretical analysis from a Dirichlet energy perspective, revealing that graph message passing inherently amplifies topology bias and consistently benefits highly connected nodes. To address these limitations, we propose Test-time Simplicial Propagation (TSP), which extends message passing to higher-order simplicial complexes. By incorporating richer structures beyond pairwise connections, TSP mitigates harmful topology bias and substantially improves the representation and recommendation of long-tail items during inference. Extensive experiments across five real-world datasets demonstrate the superiority of our approach in mitigating topology bias and enhancing recommendation quality. The implementation code is available at https://github.com/sotaagi/TSP.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nGraph based recommender systems suffer from popularity bias. That is, the input graph (interaction graph between users and items) gets dominated by highly connected nodes which results in over-represenation of certain items. This results in reinforcing biases and fairness issues through the user-system feedback loop. This work analyses this topology bias through the lens of Dirichlet energy and show that message passing inherently minimises a global smoothing objective. Higher degree nodes accumulate larger embedding norms, a phenomenon called norm concentration. As a resolution, a test time simplicial propagation method is proposed which performs message passing over simplicial complexes with intra- and inter-simplex smoothing to avoid the dominance of certain nodes or substructures.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n\n1. The Dirichlet energy perspective to analyse graph based recommender systems is interesting.\n\n2. The formalization of norm concentration and how message passing favors highly connected nodes in recommender systems explaining over-representation of certain items is also fascinating.\n\n3. The paper is well-written and easy to follow.\n\n\n**Weaknessess**\n\n**Major weaknesses**\n\n1. I think the title of the paper should accurately reflect the contributions of the work. Currently, the title might prompt readers to think that the study is about topology bias in message passing GNNs covering more general form of GNNs such as GCNs, GATs, but the empirical analysis focuses specifically on **LightGCN-style architectures applied to graph based recommender systems**, which are simplified frameworks lacking feature transformations and non-linearities found in widely used GNNs. While I understand the creative liberty to have a catchy paper title, I think the title can be revised to better reflect the scope of the contributions.\n\n2. The idea that message passing (MP) is inherently minimizing Dirichlet energy is not a new insight. Extensive work studying over-smoothing in GNNs (see some of the references listed below [1], [2], [3]) have already established this fact. The way the work is currently presented doesn't adequately acknowledge this foundation or clearly articulate what's novel beyond existing theoretical understanding. It would make sense to properly position this work’s contributions in light of these related works.\n\n3. Although the norm concentration analysis is interesting, the idea that higher degree nodes receive larger message passing updates is obvious. For instance [4] also observes this phenomenon empirically (the current work also acknowledges this which is great). This leads again to my main issue which is properly discussing the contributions of the work in light of contemporary works. For instance works such as [9] and [10] treat this **degree bias/topology bias** more generally for GNNs and one can consider **norm concentration in LightGCN like architectures used specifically for recommender systems** as an application/special case of mitigating degree bias in GNNs ([4],[5],[6],[7],[8],[9],[10]).\n\n4. The resolution proposed to mitigate this topology bias is test-time simplicial complex propagation approach which although seems to work based on presented experimental validation, it is usually expensive to compute. Currently, the work compares with only few debiasing methods but what about works such as [5],[6],[7],[8],[9] and [10] which might provide a cheaper way to mitigate **degree bias in the general framework of GNNs** and not restricted to recommender systems? It would be interesting to check if such proposed methods already address the identified issue of topology bias. And why a more computationally expensive approach of lifting graphs to simplices is a better/preferred approach?\n\n\n**Minor weaknesses**\n\n1. L26-27 maybe explain in 1-2 lines what exactly is Matthew effect?\n\n2. The computational complexity for lifting the graphs into simplicial complex is missing.\n\n\n\n\n\n\n**References**\n\n1. A Note on Over-Smoothing for Graph Neural Networks. Cai et al, ICML 2020.\n\n2. PairNorm: Tackling Oversmoothing in GNNs. Zhao et al, ICLR 2020\n\n3. Not too little, not too much: a theoretical analysis of graph (over)smoothing. Keriven et al, 2022. \n\n4. Test-Time Embedding Normalization for Popularity Bias Mitigation. Kim et al, CIKM 2023.\n\n5. On Generalized Degree Fairness in Graph Neural Networks. Liu et al, AAAI 2023.\n\n6. GRAPHPATCHER: Mitigating Degree Bias for Graph Neural Networks via Test-time Augmentation. Ju et al, NeurIPS 2023.\n\n7. Tail-GNN: Tail-Node Graph Neural Networks. Liu et al, KDD, 2021.\n\n8. Investigating and Mitigating Degree-Related Biases in Graph Convolutional Networks. Tang et al. CIKM 2020.\n\n9. Theoretical and Empirical Insights into the Origins of Degree Bias in Graph Neural Networks. Subramonian et al, 2024.\n\n10. Degree-based stratification of nodes in Graph Neural Networks. Ali et al, ACML 2023.\n\nQUESTIONS:\nSee **weaknessess** above.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-23"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper provides, for the first time in the literature, a theoretical analysis of topology bias in message passing for graph-based recommender systems. Unlike similar previous analyses, mainly focusing on the node embeddings and gradients levels, the authors investigate this phenomenon under the lens of the Dirichlet energy. \n\nTo begin with, the paper theoretically demonstrates that performing the message passing is conceptually equivalent to setting a Dirichlet energy minimization problem. Secondly, they demonstrate how message passing leads to having a larger accumulation of embedding norms for high-degree nodes in the graph, and this phenomenon keeps amplifying the deeper we go in the message passing. \n\nOn such a basis, the authors propose a novel approach to tackle this issue, which interestingly runs in the inference step of the model's pipeline, thus it can be applied to any graph-based recommender systems during inference. The proposed pipeline creates a novel graph whose node connections are not necessarily based upon the topological structure of the original graph (which brings the bias information), but rather on the similarity of node embeddings conditioned on a hyperparameter $\\theta$. After that, the framework transitions to a simplicial complex (intra-simplex smoothing module) and a propagation function to propagate embeddings across simplicials (inter-simplex propagation module). Finally, a fusion strategy is adopted to combine all node representations from different orders of simplices. \n\nExtensive experimental results when applying the proposed solution during the inference process of three graph-based recommender models, against other debiasing baselines from the literature, largely demonstrate the efficacy of the proposed approach. This is true also across some recommendation datasets. Moreover, an ablation study on the main modules shows the goodness of the architectural choices made by the authors. Finally, an embedding distribution analysis empirically proves how the distribution is less concentrated in the case of the proposed solution, while a scalability study analyzes how the introduction of the methodology adds a very limited overhead on the simple inference of the original models.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n\n$\\bullet$ The paper has the merit to not providing yet another graph-based recommendation model, but rather to analyze a critical issue in the current literature, topological bias, and disentangle it from a different theoretical perspective than other analyses provided in the recent literature.\n\n$\\bullet$ The paper is well-written and easy to follow.\n\n$\\bullet$ The methodology is quite clear and sound, as it is supported quite nicely by the background section. All theorems seem adequately sound and are rigorously proven in the Supplementary Material section.\n\n$\\bullet$ The proposed approach, which tackles the outlined issues, is nicely applied at inference time, thus not hurting the training of the models in any ways. The inference is also very limitedly hurt.\n\n$\\bullet$ Experimental settings are extensive with many evaluated dimensions. The code is released at review time, thus ensuring the complete reproducibility of the code and results presented in the paper.\n\n**Weaknesses**\n\n$\\bullet$ The authors might have considered to include a further baseline (RP3Beta [\\*]) which comes from a less-recent literature but works quite well on the user-item graph through random-walk and it is especially designed to not penalize less popular items. I think including this baseline as a standalone model to be compared against the other would provide a very nice complementary evaluation to the paper.\n\n$\\bullet$ In relation to the above, I think the authors might also consider to measure other recommendation measures which are usually adopted to assess the diversity in the recommendation lists [\\*\\*] and the presence of items from the long-tail [\\*\\*\\*].\n\n**References**\n\n[\\*] Christoffel et al., Blockbusters and Wallflowers: Accurate, Diverse, and Scalable Recommendations with Random Walks. RecSys 2015.\n\n[\\*\\*] S. Vargas, P. Castells, Rank and relevance in novelty and diversity metrics for recommender systems, in: RecSys, ACM, 2011, pp. 109–116. \n\n[\\*\\*\\*] Himan Abdollahpouri, Robin Burke, and Bamshad Mobasher. 2017. Controlling Popularity Bias in Learning-to-Rank Recommendation. In RecSys. ACM, 42–46.\n\nQUESTIONS:\nMy main questions are related to the two weaknesses I outlined above.\n\nQ1) Could the authors provide additional results when running the model RP3beta on the tested datasets?\n\nQ2) How are the recommendation performance when considering additional standard bias and fairness metrics in the literature, such as the expected free discovery (EFD) and the average percentage of long-tail items (APLT)?\n\nQ3) Do the authors have any intuition on how their theoretical analysis and subsequent methodology could be differently applied to the user side and the item side? In principle, the two sides are different and show different properties, also in the topological bias (i.e., low-high activeness on the platform for the user vs. popular/niche products for the items).\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper studied graph-based recommender methods. The authors started by analyzing the common popularity bias issue in the graph-based methods, from a Dirichlet energy perspective. Combined with the theoretical analysis, the authors proposed TSP, a training framework for existing graph-based recommender methods to alleviate the effect of popularity bias. The proposed TSP contains multiple steps, such as the semantic graph reconstruction, which leverages a pretrained model to add in predicted edges, similar to graph structure learning, and a few following steps as detailed in Sec. 4.2.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1. Popularity bias is a very important problem in collaborative filtering, which may even be enlarged in graph-based methods due to message passing. I'm glad to see papers trying to solve this critical issue.\n2. This paper is well supported by theoretical analysis.\n\nWeakness:\n1. Graph-based (or message passing-based) recommender methods are often criticized by their limitations on efficiency when it comes to larger graphs [1]. While the authors has shown that the proposed TSP added limited overhead to lightGCN, considering that TSP has steps such as calculating the graph laplacian, I'm concerned on the efficiency of the proposed method.\n2. Additional experiments on larger scale datasets would be appreciated.\n\n[1] UltraGCN: Ultra Simplification of Graph Convolutional Networks for Recommendation, CIKM 2021\n\nQUESTIONS:\n1. The term \"semantic graph\" is quite confusing. IIUC, the graph-based collaborative filtering methods doesn't use any semantic features, but instead learn ID embeddings for each nodes. The way TSP reconstructs the semantic graph is very similar to existing literature in graph structure learning and graph data augmentation, which were not discussed in this work. Hence I wonder why the reconstructed graph is named \"semantic graph\" when it's more of a \"augmented graph\"?\n\nLIMITATIONS:\nsee weakness", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-03"}