From Contraction to Chaos: Compounding Error Resistant World Models for Robots

Learned world models are usually rolled out autoregressively: each prediction is fed back as input, so small one-step errors compound over the horizon. How fast they compound is determined by the system’s sensitivity to initial conditions, one of the three mathematical properties of chaos. Under a tracking controller, deviations are corrected, and errors stay bounded; in a chaotic system, they grow exponentially. Auto-regressive (AR) models, such as the temporal convolutional networks widely used in mobile robotics, learn a simple one-step map but pay the full cost of compounding. One-shot Multi-step (MS) models never feed back their own errors, which theory predicts should pay off over long horizons. However, they cannot reuse what they learn for one step when predicting the next, so they need more data to learn the multi-step map. Neither class dominates across the sensitivity spectrum. We propose Multi-Step Temporal Mixture Probabilistic (MTM-Pro), a hybrid world model trained offline on logged trajectories with two coupled objectives: an MS objective that fuses overlapping multi-step forecasts through a learned temporal mixture, and an AR objective that rolls the model out on its own predictions. We evaluate on five datasets chosen to span the sensitivity spectrum: closed-loop quadcopter tracking on nominal trajectories, on aggressive trajectories, and at the edge of the control envelope; open-loop driving of an off-road uncrewed ground vehicle (UGV); and the chaotic Lorenz system. AR baselines degrade as sensitivity increases, while MS baselines become competitive only on the most sensitive system. MTM-Pro matches the best baseline on the least sensitive datasets and reduces 5-second drift by more than three orders of magnitude on Lorenz, making it the only model reliable across the whole spectrum. Our code and links to all datasets are publicly available at https://anonymous.4open.science/r/MTM-Pro.