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

arXiv: https://arxiv.org/abs/2605.06404 · HTML: https://mlsanity.com/paper/2605.06404/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 17 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 13 of 13)

- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Explanations can be manipulated and geometry is to blame](https://mlsanity.com/paper/1906.07983/) (2019)
- [Guided Integrated Gradients: An Adaptive Path Method for Removing Noise](https://mlsanity.com/paper/2106.09788/) (2021)
- [Attribution in Scale and Space](https://mlsanity.com/paper/2004.03383/) (2020)
- [Manifold Integrated Gradients: Riemannian Geometry for Feature Attribution](https://mlsanity.com/paper/2405.09800/) (2024)
- [IG2: Integrated Gradient on Iterative Gradient Path for Feature Attribution](https://mlsanity.com/paper/2406.10852/) (2024)
- [Improving Integrated Gradient-based Transferable Adversarial Examples by Refining the Integration Path](https://mlsanity.com/paper/2412.18844/) (2024)
- [Integrated Decision Gradients: Compute Your Attributions Where the Model Makes Its Decision](https://mlsanity.com/paper/2305.20052/) (2023)
- [Using the Path of Least Resistance to Explain Deep Networks](https://mlsanity.com/paper/2502.12108/) (2025)
- [Maximum Entropy Baseline for Integrated Gradients](https://mlsanity.com/paper/2204.05948/) (2022)
- [A New Baseline Assumption of Integated Gradients Based on Shaply value](https://mlsanity.com/paper/2310.04821/) (2023)
- [Constructing sensible baselines for Integrated Gradients](https://mlsanity.com/paper/2412.13864/) (2024)

## Abstract (arXiv)

Gradient-based attribution methods are model-faithful and scalable, but Integrated Gradients (IG) can be brittle because explanations depend on heuristic baselines, straight-line paths, discretization, and saturation. We propose Fisher--Rao Integrated Gradients (FRInGe), which defines both the reference and interpolation schedule in predictive distribution space. FRInGe replaces input baselines with a maximum-entropy predictive reference and follows a Fisher-Rao geodesic on the probability simplex. The corresponding input-space trajectory is realized through the pullback Fisher metric and stabilized by KL and Euclidean trust regions; attributions are obtained by integrating input gradients along this trajectory. Across six ImageNet architectures, FRInGe most clearly improves calibration-oriented attribution metrics, especially MAS scores, while remaining competitive on perturbation AUC and infidelity.