arXiv subjects

Lilian Marey

Publications and source records attributed to Lilian Marey.

7 recordsLinked to original sources

arXiv2026

Edge-Girth as a Structural Edge Feature for Graph Neural Networks

Graph neural networks (GNN) based on message passing are provably no more powerful than the one-dimensional Weisfeiler--Leman colour-refinement test (1-WL): two graphs it cannot tell apart receive identical representations, however deep or wide the network. A common remedy augments node or edge features with precomputed structural descriptors, most often counts of a fixed small subgraph such as triangles or longer cycles, but such counts require committing in advance to the size of the substructure counted, a choice usually made blind to the data. We study a descriptor that avoids this choice. The edge-girth of an edge is the length of a shortest cycle through it, and its multiplicity is the number of such shortest cycles; together they form a per-edge invariant that reports cycles of arbitrary length, computable exactly by a single breadth-first search per edge. Injected into a gated message-passing architecture, EGAGNN, it reaches a test MAE a factor three below the closest gated comparator on the ZINC-12k regression benchmark at 104k parameters; against bounded cycle-counting descriptors under the same architecture, it matches only a dictionary counting cycles up to length eight, using twice as many channels, while a dictionary capped at length four performs no better than no structural information at all. On graph discrimination we prove a matching limitation: on graphs where every edge sees the same number of shortest cycles of the same length, the descriptor becomes constant and any model built on it collapses back to the 1-WL bound. This holds without exception across all 400 pairs of the BREC benchmark: not one of the 90 such pairs is distinguished.

cs.LG↗

arXiv2026

On the Realizability of Edge-Girth Sequences

The edge-girth of an edge $e$ in a simple connected graph is the length of a shortest cycle containing $e$, with $g_e = \infty$ if no such cycle exists. The edge-girth sequence of a graph is the nondecreasing sequence of edge-girth values over all its edges. We prove that a sequence $S$ is realizable as the edge-girth sequence of a simple connected graph if and only if it satisfies a recursive criterion: writing $S = S_0 \uplus (g^{(m)})$ where $g$ is the maximum edge-girth value of $S$ with multiplicity $m$ and $S_0$ is the prefix subsequence, $S$ is realizable if and only if $S_0$ is realizable and the multiplicity $m$ lies in a set entirely determined by $g$ and the maximum diameter $d^*_{S_0}$ achievable by graphs realizing $S_0$. We further determine $d^*_S$ for any realizable sequence: for constant sequences $(g^{(m)})$, we obtain a closed-form formula when $g$ is even and a recursive formula when $g$ is odd. For general sequences, we provide a recursive algorithm computing $d^*_S$ together with explicit constructions of diameter-achieving graphs.

math.CO↗

arXiv2026

Structural Bias Beyond Homophily: A Study of Fairness in Link Prediction

Graph link prediction (LP) plays a critical role in socially impactful applications such as job recommendation and friendship formation, making fairness a critical concern in this task. While many fairness-aware methods manipulate graph structures to mitigate prediction disparities, the topological biases inherent to social graphs remain poorly understood and are consistently conflated with homophily alone. In this work, we study the relationship between structural biases and fairness outcomes in LP. To this end, we formalize a taxonomy of topological bias measures and introduce a graph generation method producing a diverse corpus of synthetic graphs with controlled structural properties. Using this corpus, we show empirically that fairness outcomes are strongly correlated with graph topology, and that current fairness-aware methods remain sensitive to structural biases beyond homophily. These findings highlight the need for structurally grounded evaluations in fair graph learning.

cs.LG↗

arXiv2026

k-hop Fairness: Addressing Disparities in Graph Link Prediction Beyond First-Order Neighborhoods

Link prediction (LP) plays a central role in graph-based applications, particularly in social recommendation. However, real-world graphs often reflect structural biases, most notably homophily, the tendency of nodes with similar attributes to connect. While this property can improve predictive performance, it also risks reinforcing existing social disparities. In response, fairness-aware LP methods have emerged, often seeking to mitigate these effects by promoting inter-group connections, that is, links between nodes with differing sensitive attributes (e.g., gender), following the principle of dyadic fairness. However, dyadic fairness overlooks potential disparities within the sensitive groups themselves. To overcome this issue, we propose $k$-hop fairness, a structural notion of fairness for LP, that assesses disparities conditioned on the distance between nodes in the graph. We formalize this notion through predictive fairness and structural bias metrics, and propose pre- and post-processing mitigation strategies. Experiments across standard LP benchmarks reveal: (1) a strong tendency of models to reproduce structural biases at different $k$-hops; (2) interdependence between structural biases at different hops when rewiring graphs; and (3) that our post-processing method achieves favorable $k$-hop performance-fairness trade-offs compared to existing fair LP baselines.

cs.LG↗

arXiv2025

Modeling Musical Genre Trajectories through Pathlet Learning

The increasing availability of user data on music streaming platforms opens up new possibilities for analyzing music consumption. However, understanding the evolution of user preferences remains a complex challenge, particularly as their musical tastes change over time. This paper uses the dictionary learning paradigm to model user trajectories across different musical genres. We define a new framework that captures recurring patterns in genre trajectories, called pathlets, enabling the creation of comprehensible trajectory embeddings. We show that pathlet learning reveals relevant listening patterns that can be analyzed both qualitatively and quantitatively. This work improves our understanding of users' interactions with music and opens up avenues of research into user behavior and fostering diversity in recommender systems. A dataset of 2000 user histories tagged by genre over 17 months, supplied by Deezer (a leading music streaming company), is also released with the code.

cs.IR↗

arXiv2024

Do Recommender Systems Promote Local Music? A Reproducibility Study Using Music Streaming Data

This paper examines the influence of recommender systems on local music representation, discussing prior findings from an empirical study on the LFM-2b public dataset. This prior study argued that different recommender systems exhibit algorithmic biases shifting music consumption either towards or against local content. However, LFM-2b users do not reflect the diverse audience of music streaming services. To assess the robustness of this study's conclusions, we conduct a comparative analysis using proprietary listening data from a global music streaming service, which we publicly release alongside this paper. We observe significant differences in local music consumption patterns between our dataset and LFM-2b, suggesting that caution should be exercised when drawing conclusions on local music based solely on LFM-2b. Moreover, we show that the algorithmic biases exhibited in the original work vary in our dataset, and that several unexplored model parameters can significantly influence these biases and affect the study's conclusion on both datasets. Finally, we discuss the complexity of accurately labeling local music, emphasizing the risk of misleading conclusions due to unreliable, biased, or incomplete labels. To encourage further research and ensure reproducibility, we have publicly shared our dataset and code.

cs.IR↗

arXiv2024

Modeling Activity-Driven Music Listening with PACE

While the topic of listening context is widely studied in the literature of music recommender systems, the integration of regular user behavior is often omitted. In this paper, we propose PACE (PAttern-based user Consumption Embedding), a framework for building user embeddings that takes advantage of periodic listening behaviors. PACE leverages users' multichannel time-series consumption patterns to build understandable user vectors. We believe the embeddings learned with PACE unveil much about the repetitive nature of user listening dynamics. By applying this framework on long-term user histories, we evaluate the embeddings through a predictive task of activities performed while listening to music. The validation task's interest is two-fold, while it shows the relevance of our approach, it also offers an insightful way of understanding users' musical consumption habits.

cs.IR↗