Median Temporal Ensembling: Training-Free Robust Aggregation for Action-Chunked Visuomotor Policies

Action-chunked visuomotor policies predict overlapping trajectories, so every executed action is covered by several predictions. Temporal ensembling smooths execution by combining these predictions with an exponentially weighted mean. One corrupted prediction can move the aggregate without bound: its breakdown point is 0. We use adversarial corruption to stress this deployed aggregator and to compare two kinds of guarantee. A metric guarantee bounds the response to a perturbation of a given size. A combinatorial guarantee instead bounds the damage when at most q of the M candidates covering a timestep are corrupted, whatever their size. Encoder adversarial fine-tuning recovers 44% of the loss under the published patch attack, but only 7.3% after the attacker's step size is increased. By contrast, the coordinate-wise median of the same candidate set keeps its recovered fraction flat as attack optimisation increases. Median temporal ensembling costs one line and requires no retraining. Across 25 (configuration, corruption-level) combinations it is never worse than the mean and is significantly better in 15. It also transfers to a second policy class, and it recovers performance under a failure with no attacker in the loop at all: camera frames that arrive blank. Its effect on clean data is configuration-dependent, from -0.04 to +0.07. We also give the boundary: corruption that shifts every covering prediction by the same amount is invisible to this whole family of statistics, and no equivariant aggregator can remove it.