Bottom-up trajectory generators lose the long tail: ScaleTraj picks a movement scale before it picks a destination cell

Once individual-level trajectory generators are aggregated into a population, they systematically deviate from the real displacement distribution, a phenomenon framed as the Population-Level Displacement Gap and observed across Markov, EPR, recurrent, Transformer, variational autoencoder and generative adversarial paradigms. Top-down models reproduce aggregate power-law statistics but struggle to guarantee realistic individual trajectories, while bottom-up generators synthesize individual traces yet often fail to preserve key population-level regularities after aggregation; the phenomenon had previously been reported only for specific leading models. On GeoLife and Tencent Beijing all seven controlled baselines deviate from the test distribution, in two opposite modes: most inflate the fitted cutoff and over-produce long trips, while the LLM-based generator CoPB, examined as an external qualitative case, has a released synthetic dataset with a markedly shorter tail, a different failure mode.

The Scale Fidelity Profile localizes displacement error to specific spatial scales and shows that population-level displacement mismatches co-occur with misallocation of trips across scales. Earlier evaluations relied mainly on aggregate metrics such as displacement distribution, radius of gyration and visitation frequency, which show that the distribution deviates but not where in the displacement range the deviation concentrates. After partitioning displacements into neighborhood, city, urban and region bands by a Gaussian mixture fit on training log-displacements, most data-driven baselines over-produce region-scale trips and under-produce neighborhood-scale trips, with the Scale Fidelity Profile on GeoLife ranging from 0.038 for STAR to 0.406 for TrajGPT; on Tencent Beijing TrajGPT and TrajSynVAE have similar exponent deviations (0.280 versus 0.296) but Scale Fidelity Profiles of 0.228 versus 0.080.

ScaleTraj treats movement scale as an explicit routing variable, predicting the scale first and then the destination cell conditioned on it, so each scale band receives dedicated model capacity. Conventional autoregressive generators run a single softmax over the full cell vocabulary, leaving scale structure implicit and allocating capacity by token frequency, so sparse region-scale trips receive a weak learning signal. On Tencent Beijing the Scale Fidelity Profile is 0.003, the exponent deviation 0.021 and the cutoff 24 km; on GeoLife they are 0.003, 0.026 and 131 km, better than the compared baselines on all three diagnostics on both datasets, while the eight individual-level JSD metrics remain competitive.

The evaluation covers two real datasets, GeoLife and Tencent Beijing, and compares two model-driven and five data-driven generators, with the synthetic data released by the LLM-based generator CoPB used as a qualitative external case without retraining; generation runs in a known-user setting that replays trained user codes so synthetic and real populations share the same anchors.

Absolute Scale Fidelity Profile values depend on implementation choices such as the smoothing constant and logarithm base, so the metric is best read as a relative ranking across methods under a fixed protocol; the truncated power law and the Scale Fidelity Profile are diagnostics of distributional fidelity, not complete definitions of mobility realism. Results come from a single generation run per configuration and variance across repeated runs is not reported; learned user latent codes also restrict evaluation to known users, and generalization to unseen users remains future work.