web infrastructure teams

Abstract: Multivariate time series forecasting plays a critical role in Web and cyber-physical systems, where large-scale services and IoT infrastructures generate complex temporal data. Transformer-based models have achieved strong empirical performance in this domain, yet the principles governing the expressive capacity of their learned representations remain insufficiently understood. Moreover, many existing models rely on simplified decoding strategies, including channel-independent modeling and direct projection heads, which limit their ability to capture complex multivariate dynamics. To address these challenges, we propose RankFormer, a novel encoder-decoder architecture for multivariate time series forecasting. We establish a rank-based analysis framework to investigate how tokenization, embedding, and attention designs affect the representation capacity of time series Transformers. Our analysis reveals that patchification increases the potential representation capacity by aggregating multiple temporal observations into each token, while subsequent encoding operations determine how much of this capacity is realized. Guided by these insights, we develop a rank-enhancing encoder with Hourglass Attention to improve rank stability during information interaction. Furthermore, we introduce the Interactive Progressive Decoder (IPD), which improves future trajectory modeling through global-guided cross-channel interaction and progressive refinement. Extensive experiments on real-world long-term forecasting benchmarks demonstrate that RankFormer achieves competitive performance against state-of-the-art methods. Code repository: https://github.com/TangPeiwang/Rankformer.

Abstract: Score monotonicity and rank monotonicity are properties describing the behavior of a centrality measure when an arc is added to a network: the former requires that the score of the target of the arc should increase, the latter that its importance with respect to the remaining nodes should not deteriorate. While in directed networks almost all classical centrality measures satisfy both properties, in undirected networks they fail for most measures: adding an edge can reduce the score or the rank of one of its endpoints. Semi-monotonicity is a recently introduced weaker property for undirected networks, requiring that at least one of the two endpoints of the new edge enjoys monotonicity, and it is known to hold for closeness, harmonic centrality, distance-decay centralities and betweenness. In this paper we study semi-monotonicity for three classical spectral centrality measures: eigenvector centrality, Katz's index, and PageRank. We prove that all of them are strictly rank semi-monotone on connected undirected graphs, and that all of them are also score semi-monotone, (the only exception being eigenvector centrality when scores are normalized by projecting the constant vector on the dominant eigenspace, for which we provide a counterexample). In particular, adding an edge can never decrease the PageRank of both its endpoints, which answers a question left open in previous work.