Fisher-Rao Sensitivity for Out-of-Distribution Detection in Deep Neural Networks

Deep neural networks often remain overconfident on Out-of-Distribution (OoD) inputs. We revisit this problem through Riemannian information geometry. We model the network's predictions as a statistical manifold and find that OoD inputs exhibit higher local Fisher-Rao sensitivity. By quantifying this sensitivity with the trace of the Fisher Information Matrix (FIM), we derive a unifying geometric connection between two common OoD signals: feature magnitude and output uncertainty. Analyzing the limitations of this multiplicative form, we extend our analysis using a product manifold construction. This provides a theoretical framework for the robust additive scores used in state-of-the-art (SOTA) detectors and motivates our final, competitive method.