Autonomous agents operating in real-world scenarios frequently encounter uncertainty and make decisions based on incomplete information.

Recent studies show that even advanced attacks cannot break such defenses effectively, since the purification process induces an extremely deep computational graph which poses the potential problem of vanishing/exploding gradient, high memory cost, and unbounded randomness.

Cohen et al. (2021) empirically study the evolution of the largest eigenvalue of the loss Hessian, also known as sharpness, along the gradient descent (GD) trajectory and observe the Edge of Stability (EoS) phenomenon.

B.4 Existing theoretical intuition and empirical comparison to the proposed OCP block.

Finally, PDE-Refiner's connection to diffusion models enables an accurate and efficient assessment of the model's predictive uncertainty, allowing us to estimate when the surrogate becomes inaccurate.