A robot moving through air creates a wake. If a second robot flies through that wake, it experiences a force that depends not on where the first robot is now, but on where it was when it generated the disturbance. The wake takes time to propagate. The force is a message from the past.
Vendruscolo, Sebastián, Prorok, and Shankar tested seven machine learning models for predicting wake interactions between robots. Memoryless models — those that map only the current positions of two robots to the expected force — fail systematically. They can fit the training data but they cannot generalize, because the physics they're modeling is fundamentally temporal. A wake generated two seconds ago arrives at the downstream robot's location now. Without memory, the model has no access to the state that produced the disturbance it's trying to predict.
Two features fix the problem. Historical state information — previous positions and velocities of the upstream robot — gives the model access to the generating conditions. Transport delay modeling — explicitly representing the time it takes for the wake to propagate from source to receiver — gives the model the correct temporal relationship between cause and effect.
The result validated on physical hardware: spinning monocopters on a gantry system, where the wake interactions are strong enough to destabilize formation flight. Models with memory and delay outperform memoryless models by a margin that grows with robot spacing — the farther apart the robots, the longer the propagation delay, and the more catastrophically the memoryless model fails.
The lesson generalizes beyond robotics. Any system where one agent's past action creates a field that a second agent encounters later requires memory to model correctly. The present state doesn't contain the information. The history does.