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Mag-Mamba: Modeling Coupled spatiotemporal Asymmetry for POI Recommendation

Zhuoxuan Li, Tangwei Ye, Jieyuan Pei, Haina Liang, Zhongyuan Lai, Zihan Liu, Yiming Wu, Qi Zhang, Liang Hu

TL;DR

This work proposes Mag-Mamba, a framework whose core insight lies in modeling spatiotemporal asymmetry as phase-driven rotational dynamics in the complex domain, and introduces a Complex-valued Mamba module that generalizes traditional scalar state decay into joint decay-rotation dynamics, explicitly modulated by both time intervals and magnetic geographic priors.

Abstract

Next Point-of-Interest (POI) recommendation is a critical task in location-based services, yet it faces the fundamental challenge of coupled spatiotemporal asymmetry inherent in urban mobility. Specifically, transition intents between locations exhibit high asymmetry and are dynamically conditioned on time. Existing methods, typically built on graph or sequence backbones, rely on symmetric operators or real-valued aggregations, struggling to unify the modeling of time-varying global directionality. To address this limitation, we propose Mag-Mamba, a framework whose core insight lies in modeling spatiotemporal asymmetry as phase-driven rotational dynamics in the complex domain. Based on this, we first devise a Time-conditioned Magnetic Phase Encoder that constructs a time-conditioned Magnetic Laplacian on the geographic adjacency graph, utilizing edge phase differences to characterize the globally evolving spatial directionality. Subsequently, we introduce a Complex-valued Mamba module that generalizes traditional scalar state decay into joint decay-rotation dynamics, explicitly modulated by both time intervals and magnetic geographic priors. Extensive experiments on three real-world datasets demonstrate that Mag-Mamba achieves significant performance improvements over state-of-the-art baselines.

Mag-Mamba: Modeling Coupled spatiotemporal Asymmetry for POI Recommendation

TL;DR

This work proposes Mag-Mamba, a framework whose core insight lies in modeling spatiotemporal asymmetry as phase-driven rotational dynamics in the complex domain, and introduces a Complex-valued Mamba module that generalizes traditional scalar state decay into joint decay-rotation dynamics, explicitly modulated by both time intervals and magnetic geographic priors.

Abstract

Next Point-of-Interest (POI) recommendation is a critical task in location-based services, yet it faces the fundamental challenge of coupled spatiotemporal asymmetry inherent in urban mobility. Specifically, transition intents between locations exhibit high asymmetry and are dynamically conditioned on time. Existing methods, typically built on graph or sequence backbones, rely on symmetric operators or real-valued aggregations, struggling to unify the modeling of time-varying global directionality. To address this limitation, we propose Mag-Mamba, a framework whose core insight lies in modeling spatiotemporal asymmetry as phase-driven rotational dynamics in the complex domain. Based on this, we first devise a Time-conditioned Magnetic Phase Encoder that constructs a time-conditioned Magnetic Laplacian on the geographic adjacency graph, utilizing edge phase differences to characterize the globally evolving spatial directionality. Subsequently, we introduce a Complex-valued Mamba module that generalizes traditional scalar state decay into joint decay-rotation dynamics, explicitly modulated by both time intervals and magnetic geographic priors. Extensive experiments on three real-world datasets demonstrate that Mag-Mamba achieves significant performance improvements over state-of-the-art baselines.
Paper Structure (41 sections, 7 theorems, 52 equations, 7 figures, 3 tables)

This paper contains 41 sections, 7 theorems, 52 equations, 7 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Next POI Recommendation
  4. Directed Graph Modeling
  5. Complex-Valued Rotations
  6. Preliminaries
  7. Problem Definition
  8. Spatiotemporal Asymmetry
  9. The Proposed Model
  10. Overview
  11. Magnetic Phase Encoder
  12. Geographic graph construction.
  13. From transition counts to antisymmetric edge signals.
  14. Low-rank spatiotemporal basis factorization.
  15. Antisymmetric direction fields and Hermitian complex adjacency.
  16. ...and 26 more sections

Key Result

Lemma 1

For each basis $r$, the matrix $A^{(r)}$ defined in eq:app_A_construct is antisymmetric: $(A^{(r)})^\top=-A^{(r)}$. Consequently, $\Phi^{(r)}_{ji}=-\Phi^{(r)}_{ij}$ and the complex adjacency $H^{(r)}$ defined in eq:app_phi_H_def is Hermitian: $(H^{(r)})^\ast = H^{(r)}$, i.e., $H^{(r)}_{ji}=\overline

Figures (7)

  • Figure 1: Illustration of the Coupled Spatiotemporal Asymmetry in urban mobility.
  • Figure 2: Overview of the proposed Mag-Mamba framework, consisting of a Magnetic Phase Encoder, a context feature embedding module, and a Mag-Mamba layer.
  • Figure 3: Sensitivity analysis of the magnetic phase dimension (Left) and the low-rank temporal bases (Right) on the TKY dataset.
  • Figure 4: Sensitivity analysis of the magnetic charge parameter $q$ (Left) and the Mamba layers (Right) on the TKY dataset.
  • Figure 5: Performance comparison (MRR) between Strongly Symmetric and Strongly Asymmetric subgroups on the TKY dataset.
  • ...and 2 more figures

Theorems & Definitions (9)

  • Lemma 1: Antisymmetry $\Rightarrow$ Hermitian adjacency
  • Lemma 2: Hermitian PSD of the magnetic Laplacian
  • Corollary 1: Real spectrum and orthonormal eigenbasis
  • Proposition 1: Scale and global-phase invariance of phase differences
  • Remark 1: Degenerate eigenspaces
  • Lemma 3: Offline cost is one-time precomputation
  • Lemma 4: Online linearity of Mag-Mamba inference
  • Proposition 2: Phase injection as topological forcing on instantaneous frequency
  • Remark 2: Interpretation