想象中的轨迹展开是运动学的，而非动力学的：长时域世界模型失败的诊断

摘要

世界模型中的长时域失败通常被归因于误差累积，这是一种笼统的框架，无法区分具体哪种误差在累积。我们提出一种基于运动学与动力学相对关系的重述：世界模型倾向于基于运动学而非动力学进行想象。我们将此操作化为想象的“运动学一致性误差”（iKCE），这是一种逐时间步的诊断指标，用于衡量推演结果偏离封闭形式的运动学零假设的程度，并辅以扰动协议，检验物理条件跨越临界区域时iKCE是否响应。我们在已公开的、在DMC walker-walk任务上训练的DreamerV3检查点上实例化了该诊断。结果显示，模型生成的iKCE比匹配的真实物理推演的iKCE高出约两个数量级。在跨越步态崩溃边界的摩擦系数扫描实验中，即使训练策略的奖励在同一区间内崩塌，模型iKCE在统计上保持平稳，呈现出运动学而非动力学的特征。该诊断能够区分运动学与动力学想象，其有效时域超过具体系统的步态周期。

English

Long-horizon failure in world models is conventionally attributed to compounding error, a generic framing that does not distinguish what kind of error compounds. We propose a kinematic-vs-dynamic reframing: world models tend to imagine kinematically rather than dynamically. We operationalize this as the imagined Kinematic-Consistency Error, a per-step diagnostic that measures how far a rollout departs from a closed-form kinematic null, paired with a perturbation protocol that tests whether iKCE responds when physical conditions cross a regime boundary. We instantiate the diagnostic on a released DreamerV3 checkpoint trained on DMC walker-walk, where imagined iKCE runs roughly two orders of magnitude above that of matched real-physics rollouts. Across a friction sweep that crosses the gait-collapse boundary, the model's iKCE stays statistically flat even as the trained policy's reward collapses through the same range, providing the kinematic-not-dynamic signature. The diagnostic distinguishes kinematic from dynamic imagination at horizons longer than the embodiment's gait period.