Barrier Function Conformal Safety Clearance Certification with CVaR for Driving Trajectory Selection

What the math gives to ML

The paper provides two transferable mechanisms for neural trajectory systems: a differentiable separating-axis barrier margin that lower-bounds exact oriented-box clearance, and split conformal calibration that converts an imperfect predicted margin into a statistically valid lower safety certificate. The barrier can be used as a training loss or inference-time rejection criterion for trajectory generators, scorers, world models, and reinforcement-learning policies. The conformal procedure can calibrate the margin of the actually selected neural trajectory without requiring the predictor itself to be statistically correct. Both mechanisms produce falsifiable signatures: the geometric barrier should conservatively track exact collision clearance, while held-out coverage should approach or exceed the target level under exchangeable episodes.