  Epistemic uncertainty quantification (UQ) identifies where models lack
knowledge. Traditional UQ methods, often based on Bayesian neural networks, are
not suitable for pre-trained non-Bayesian models. Our study addresses
quantifying epistemic uncertainty for any pre-trained model, which does not
need the original training data or model modifications and can ensure broad
applicability regardless of network architectures or training techniques.
Specifically, we propose a gradient-based approach to assess epistemic
uncertainty, analyzing the gradients of outputs relative to model parameters,
and thereby indicating necessary model adjustments to accurately represent the
inputs. We first explore theoretical guarantees of gradient-based methods for
epistemic UQ, questioning the view that this uncertainty is only calculable
through differences between multiple models. We further improve gradient-driven
UQ by using class-specific weights for integrating gradients and emphasizing
distinct contributions from neural network layers. Additionally, we enhance UQ
accuracy by combining gradient and perturbation methods to refine the
gradients. We evaluate our approach on out-of-distribution detection,
uncertainty calibration, and active learning, demonstrating its superiority
over current state-of-the-art UQ methods for pre-trained models.
