Avoiding unsafe sets when training with Langevin Dynamics
How to guarantee neural network training avoids dangerous failure zones
When training a machine learning model with noisy gradient descent, the model can temporarily stray into dangerous regions before settling near its optimal solution. This paper proves that even in high-dimensional problems, the probability of landing in a designated failure zone becomes exponentially small — but only after an initial "burn-in" period whose length depends on the problem dimension, not just the steepness of the loss landscape.
Training procedures that wander through unsafe regions — even briefly — can cause real failures in deployed systems, from autonomous vehicles misclassifying obstacles to medical AI producing dangerous predictions. This work provides concrete mathematical guarantees about when and how badly a model can stray during training, letting practitioners either trust the process or redesign it to avoid specific high-risk zones altogether.