Incorruptible Neural Networks: Training Models that can Generalize to Large Internal Perturbations

Flat regions of the neural network loss landscape have long been hypothesized to correlate with better generalization properties. A closely related but distinct problem is training models that are robust to internal perturbations to their weights, which may be an important need for future low-power hardware platforms. In this paper, we explore the usage of two methods, sharpness-aware minimization (SAM) and random-weight perturbation (RWP), to find minima robust to a variety of random corruptions to weights. We consider the problem from two angles: generalization (how do we reduce the noise-robust generalization gap) and optimization (how do we maximize performance from optimizers when subject to strong perturbations). First, we establish, both theoretically and empirically, that an over-regularized RWP training objective is optimal for noise-robust generalization. For small-magnitude noise, we find that SAM's adversarial objective further improves performance over any RWP configuration, but performs poorly for large-magnitude noise. We link the cause of this to a vanishing-gradient effect, caused by unevenness in the loss landscape, affecting both SAM and RWP. Lastly, we demonstrate that dynamically adjusting the perturbation strength to match the evolution of the loss landscape improves optimizing for these perturbed objectives.