Physical Time as a Missing Dimension of Robot Policy Memory Dynamics

Physical Time as a Missing Dimension of Robot Policy Memory Dynamics. By Yushen Liang and eight others, from New York University Shanghai and the University of Electronic Science and Technology of China. Published on the fourteenth of October. No code repository is linked to it.

A robot policy with memory usually updates that memory once per observation. The memories evolve with the observation sequence, and in doing so they implicitly treat every update as the same amount of physical time. That assumption breaks in a specific way. Two identical observation histories can span different durations, and the right action can differ between them. A memory that only counts observations cannot tell those cases apart. The authors' framing is that physical time is a missing dimension of policy memory.

Temporal Flow Policy, or TFP, learns memory dynamics that retain past events and evolve the memory state over measured time intervals. The division of labour inside each transition is the core of it. The observations and the prior memory decide what the transition contains and on what time scales it operates. The elapsed time decides how far the state advances. Content comes from what was seen, and distance travelled comes from the clock.

TFP is not a policy on its own. It conditions diffusion and flow-matching policies through this memory state, and it is trained with those policies' native imitation objectives, the same ones those policies already use. The evaluation pairs it with Diffusion Policy and with pi zero point five, and compares memory designs under controlled conditions.

The first lesson from those comparisons is that successful timing depends on two things together: the measured intervals and the retained history. TFP achieves higher average success than recurrent memories and state-space memories that were given the same intervals. It also beats a variant that feeds the interval into a learned gate. So simply handing an existing memory the elapsed time is not what produces the gain.

Two probes look inside. Readouts from the memory recover the time since an event, and recover motion information after an occlusion. And when the supplied intervals are changed, actions are systematically delayed or advanced, which links the time input directly to behaviour. On real-robot tasks that require timing or memory, and on LIBERO evaluations, the authors report benefits in both physical and general manipulation.

The paper ends on a reframing. Robot memory, in this view, is not a store of observation history. It is a state that holds on to past events and moves forward with physical time, and the evidence offered for that view is behavioural: change the clock the policy is given, and the timing of its actions shifts with it.