Relative Transitions, Not Absolute Destinations: A Transfer-and-Ground Framework for Target-Trajectory-Free Human Mobility Generation

cs.LG Yidi Wang, Yunhe Zhang, Bangchao Deng, Dingqi Yang, Pengyang Wang · Oct 1, 2026
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What it does
Most trajectory generators require check-ins from the deployment city, which is unrealistic when only a public POI map is available. This work studies target-trajectory-free generation: synthesizing human mobility in a new city using only...
Why it matters
Its key insight is to replace absolute destination prediction with transferable relative transitions—semantic and geographic displacements between place contexts—and ground them onto the target POI graph via a behavior graph and an...
Main concern
The core factorization—separating transferable movement patterns from city-specific place identities—is conceptually strong and backed by a formal invariance argument. Nomad delivers clear distributional improvements across ten cities, yet...
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Plain-language introduction

Most trajectory generators require check-ins from the deployment city, which is unrealistic when only a public POI map is available. This work studies target-trajectory-free generation: synthesizing human mobility in a new city using only source trajectories and the target city's POI coordinates and categories. Its key insight is to replace absolute destination prediction with transferable relative transitions—semantic and geographic displacements between place contexts—and ground them onto the target POI graph via a behavior graph and an exploration–return walk. This factorization yields a theoretically principled and empirically evaluated method for zero-shot mobility synthesis.

Critical review
Verdict
Bottom line

The core factorization—separating transferable movement patterns from city-specific place identities—is conceptually strong and backed by a formal invariance argument. Nomad delivers clear distributional improvements across ten cities, yet the practical upside is tempered by modest downstream utility gains of only about 3% and a strict setting that assumes functional place correspondences hold across very different urban environments.

“Our core insight is to replace this city-bound output with context-conditioned relative transitions.”
Wang et al. · Section 1
“lowering the average error over the best baseline of each metric by about 15% in distributional fidelity and about 3% in downstream utility”
Wang et al. · Abstract
What holds up

The theoretical justification is clean: Theorem 2.7 proves that under translation alignment, embedding displacement $\boldsymbol{\delta}$ is the canonical transferable transition representation, which rigorously motivates the flow-matching prior over relative transitions. The multi-relational graph encoder with cross-city contrastive alignment and the extensive evaluation across fourteen city-to-city transfers provide strong empirical scaffolding for the approach.

“The displacement $\boldsymbol{\delta}(a,b)=\mathbf{h}_{b}-\mathbf{h}_{a}$ is transferable, and it is complete in that every transferable transition representation is a function of $\boldsymbol{\delta}$.”
Wang et al. · Theorem 2.7, Section 2.2
“The contrastive task then draws the same function from different cities into one region, so that the per-city embeddings become a single city-agnostic space.”
Wang et al. · Section 3.1
“the Flow Matching (FM) objective as $\mathcal{L}_{\scriptscriptstyle\text{FM}}(\theta)=\mathbb{E}_{t,p_{t}(x)}\|v_{t}(x)-u_{t}(x)\|^{2}$”
“GATv2 – a graph attention variant that has a universal approximator attention function, and is thus strictly more expressive than GAT”
Main concerns

The entire theoretical guarantee rests on Assumption 2.5, which assumes that functionally equivalent POIs across cities differ only by a constant translation in embedding space; the paper itself notes this guarantee is conditional and does not assert that real cities admit such a representation. The grounding step is mechanically brittle: each continuous transition is snapped to the nearest target POI via argmax cosine similarity (Equation 13), with no mechanism to reject poor matches when the target city lacks a semantically or geographically suitable POI. Furthermore, the downstream utility improvements are only about 3%, suggesting that substantial distributional gains do not strongly translate into better predictive models, and the reported 15% average gain is an unconventional per-metric aggregate that can mask high variance across individual transfers.

“There exists an offset $\mathbf{t}_{AB}\in\mathcal{H}$ such that $\mathbf{h}_{\varphi(p)}=\mathbf{h}_{p}+\mathbf{t}_{AB}$ for all $p\in\mathcal{P}_{A}$.”
Wang et al. · Assumption 2.5, Section 2.2
“Each sampled transition is snapped to the target POI whose own displacement from $i$ best matches it in both the semantic and the geographic channel”
Wang et al. · Section 3.3
Evidence and comparison

The paper provides direct visual evidence for its central mechanism: under matched contexts, NYC and TKY absolute destinations form separated clusters whereas relative transitions overlap almost entirely, supporting the claim that displacements carry less city-specific information. Ablation results in Table 2 show that excising flow-matching or the graph encoder degrades performance, confirming both components are necessary. However, the baseline comparisons are weakened by the zero-shot adaptation: neural baselines such as COLA and GTG are stripped of their target-adaptive components and evaluated with source statistics only, and the paper does not clarify whether these adaptations involved hyperparameter retuning for the zero-shot regime.

“For the absolute destinations, the two cities form clearly separated clusters, so they still reveals which city a movement belongs to. For the relative transitions, the two cities overlap almost entirely, demonstrating that it is nearly indistinguishable across cities.”
Wang et al. · Section 4.4.1, Figure 4
“COLA is a cross-city Mobility Transformer whose output vocabulary is extended to the target POIs, and GTG is a graph Transformer with domain adaptation capability. Here the statistics from source cities are as its input to adapt our zero-shot setting.”
Wang et al. · Section 4.1.1
Reproducibility

Critical implementation details are deferred to appendices not shown in the main text: the algorithmic procedures, computational analysis, and running time comparisons are relegated to Appendix D, and preprocessing pipelines, code, and data links are absent. Hyperparameters such as the flow integration steps $N$ and behavior graph sample count $K$ are only briefly analyzed in Figure 5, while dataset splits, optimization settings, and random seeds remain unspecified, presenting a significant barrier to independent reproduction.

“Please refer to Appendix D for detailed procedures of the proposed algorithm, corresponding computational analysis and running time comparison.”
Wang et al. · Section 3.3
“As shown in Figure 5, distributional fidelity is significantly affected by $N$ and $K$.”
Wang et al. · Section 4.4.2
Abstract

Individual mobility trajectories support urban analysis and location-based services, yet most trajectory generators require observations from their deployment city. This assumption excludes precisely the cities where trajectories are unavailable even though points of interest (POIs) and their attributes can be obtained from public maps. We study target-trajectory-free generation: learning from POIs and trajectories in source cities while utilizing only POI coordinates and categories in a target city, with no target trajectory or trajectory-derived statistic available for training, model selection, or generation. Existing trajectory generators typically predict absolute destinations, entangling reusable movement behavior with city-specific POI identities and spatial layouts. Our core insight is to replace this city-bound output with context-conditioned relative transitions. We propose Nomad, a transfer-and-ground framework that separates learning how people move from determining where those movements are realized. Specifically, a history-conditioned flow-matching model learns from source trajectories a transition prior over semantic displacement between POI contexts, geographic displacement, and elapsed time; at inference, a behavior graph and an exploration--return walk ground sampled transitions onto the target POI map. This factorization enables a direct test of representation level transferability without assuming invariance of the full mobility distribution. Extensive experiments across ten cities and 14 transfers show that Nomad outperforms adaptation baselines in trajectory fidelity and downstream utility, lowering the average error over the best baseline of each metric by about 15% in distributional fidelity and about 3% in downstream utility.

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