Uncertainty Estimation of Deep Neural Networks under Weight Perturbations

When deployed on unreliable hardware, deep neural networks (DNNs) encounter weight perturbations that affect model outputs, increasing uncertainty and posing significant risks to the application of deep learning in safety-critical domains. Current uncertainty estimation approaches generally ignore the influence of weight perturbations. Lacking explicit theoretical modeling and quantification of this effect, these methods remain inadequate for noisy DNNs. To address these limitations, we develop a hardware-noise-aware mean-variance propagation framework for DNNs under weight perturbations. The deployed weights are modeled as trained weights corrupted by hardware noises, and closed-form recursive updates are derived to prop agate the output mean and variance based on assumed density filtering. Moreover, an uncertainty-aware training is proposed to reduce the model output uncertainty by integrating the derived propagated variance into the loss function. Extensive experiments demonstrate that our method exhibits superior performance in uncertainty estimation compared with the state-of-the-art methods, particularly in high-noise environments, while also improving model robustness.