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FRInGe: Distribution-Space Integrated Gradients with Fisher–Rao Geometry

NeurIPS 2026 · Probabilistic and scientific modeling › Variational and generative sampling · approach: Gradient estimation for discrete variables · 0 citations (OpenAlex)

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Proposes FRInGe, an Integrated Gradients variant that defines the reference as a maximum-entropy predictive distribution and the path as a Fisher–Rao geodesic, lifted to input space via pullback Fisher geometry with KL and Euclidean trust regions.

Problem

Integrated Gradients explanations are brittle: they depend on heuristic input-space baselines, straight-line paths, discretization error, and saturation.

Approach

Defines both the IG reference and the interpolation schedule in predictive distribution space (uniform reference, Fisher–Rao geodesic), realizes the schedule as an input-space trajectory via a damped natural-gradient step under the pullback Fisher metric, and stabilizes it with KL and Euclidean trust regions before integrating input gradients.

Key results

• FRInGe attains the best MAS-Insertion on all six architectures (e.g., RN18 0.597 vs IG 0.443 on MAS-Ins).
• MAS-Deletion ranks first on three architectures; SmoothGrad is better on blur-based deletion AUC (RN18 0.122 vs FRInGe 0.130).
• Runtime is 4.7x to 22.3x slower than IG on sequential execution (e.g., ResNet-18 55.12 s vs 2.90 s on 64 images).

Surprising findings

• Activating the Euclidean trust-region cap increases endpoint KL and worsens waypoint tracking, so the method does not reach the maximum-entropy target exactly.
• Max Sensitivity results are mixed relative to IG, so local robustness is not uniformly improved.

Limitations

• Computational overhead is substantially higher than standard IG due to inner CG solves per waypoint.
• Completeness holds only with respect to the realized endpoint, not a fixed input baseline; endpoint may not reach the maximum-entropy target.
• Gains are concentrated on MAS metrics; perturbation AUC and local robustness are mixed.

Experimental setup

Datasets: ImageNet

Benchmarks: ImageNet validation subset (1,000 images)

Metrics: MAS-Insertion MAS-Deletion Insertion AUC Deletion AUC Infidelity Max Sensitivity Sparseness completeness residual

Baselines: Integrated Gradients IG^2 SmoothGrad GuidedIG Adversarial IG GGIG GeoIG

Builds on: Integrated Gradients Expected Gradients Guided Integrated Gradients Geodesic Integrated Gradients SmoothGrad

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