The Kinematic Similarity Principle: A Shared Kinematic Distribution across Mobility Domains Enables Zero-Shot Trajectory Prediction

Existing trajectory predictors are specialized to a single mobility domain, such as pedestrians, vehicles, vessels, or aircraft. Zero-shot transfer has so far been studied within one domain, where the target is a new city, dataset, or task, while the mobility domain remains fixed. When the mobility domain is held out, existing predictors do not consistently outperform simple constant-velocity extrapolation. This is because they learn the scale and context of the domain they are trained on rather than the structure of motion that transcends domains. We show that such a shared motion structure indeed exists in the form of a shared kinematic distribution of short-horizon motion. Once such motion is expressed at the scale of its domain, domains share a distribution of future displacement given past kinematics. We call this regularity the *kinematic similarity principle*. A predictor that targets this shared motion can therefore be trained on data from some domains and applied to a held-out domain. We propose KineTraj, a predictor that exploits this principle. It includes (i) a scale-invariant kinematic encoder that expresses windows at the characteristic scale of its domain; (ii) a domain-agnostic backbone that takes only the resulting normalized representation as input, employing no domain labels or absolute scales; and (iii) a so-called KineMix decoder that combines closed-form motion regimes through a learned gate and residual to rescale predictions to the scale of a domain. On a leave-one-domain-out benchmark encompassing six datasets spanning five mobility domains, KineTraj, with 0.59M parameters, reduces best-of-20 ADE by 18% and FDE by 22% relative to the strongest domain-specific predictor trained under the same protocol, and it matches or exceeds trajectory and time-series foundation models applied zero-shot. Code is available at https://anonymous.4open.science/r/kinetraj_code-0D48.