# Manifold Integrated Gradients: Riemannian Geometry for Feature Attribution

arXiv: https://arxiv.org/abs/2405.09800 · HTML: https://mlsanity.com/paper/2405.09800/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 60 references that are in the map.
- First posted on arXiv 16 May 2024.

## Builds on (most cited first, 30 of 33)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [Striving for Simplicity: The All Convolutional Net](https://mlsanity.com/paper/1412.6806/) (2014)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [Interpretable Explanations of Black Boxes by Meaningful Perturbation](https://mlsanity.com/paper/1704.03296/) (2017)
- [Interpretation of Neural Networks is Fragile](https://mlsanity.com/paper/1710.10547/) (2017)
- [Fooling LIME and SHAP: Adversarial Attacks on Post hoc Explanation Methods](https://mlsanity.com/paper/1911.02508/) (2019)
- [Generative Visual Manipulation on the Natural Image Manifold](https://mlsanity.com/paper/1609.03552/) (2016)
- [Explanations can be manipulated and geometry is to blame](https://mlsanity.com/paper/1906.07983/) (2019)
- [Hyperspherical Variational Auto-Encoders](https://mlsanity.com/paper/1804.00891/) (2018)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [Continuous Hierarchical Representations with Poincar'e Variational Auto-Encoders](https://mlsanity.com/paper/1901.06033/) (2019)
- [Fooling Neural Network Interpretations via Adversarial Model Manipulation](https://mlsanity.com/paper/1902.02041/) (2019)
- [Guided Integrated Gradients: An Adaptive Path Method for Removing Noise](https://mlsanity.com/paper/2106.09788/) (2021)
- [Mixed-curvature Variational Autoencoders](https://mlsanity.com/paper/1911.08411/) (2019)
- [The Riemannian Geometry of Deep Generative Models](https://mlsanity.com/paper/1711.08014/) (2017)
- [A Rigorous Study of Integrated Gradients Method and Extensions to Internal Neuron Attributions](https://mlsanity.com/paper/2202.11912/) (2022)
- [Attribution in Scale and Space](https://mlsanity.com/paper/2004.03383/) (2020)
- [Fast and Robust Shortest Paths on Manifolds Learned from Data](https://mlsanity.com/paper/1901.07229/) (2019)
- [Detecting Out-of-distribution Samples via Variational Auto-encoder with Reliable Uncertainty Estimation](https://mlsanity.com/paper/2007.08128/) (2020)
- [Investigating Saturation Effects in Integrated Gradients](https://mlsanity.com/paper/2010.12697/) (2020)
- [Which Models have Perceptually-Aligned Gradients? An Explanation via Off-Manifold Robustness](https://mlsanity.com/paper/2305.19101/) (2023)
- [Fooling Partial Dependence via Data Poisoning](https://mlsanity.com/paper/2105.12837/) (2021)
- [The Manifold Hypothesis for Gradient-Based Explanations](https://mlsanity.com/paper/2206.07387/) (2022)
- [IDGI: A Framework to Eliminate Explanation Noise from Integrated Gradients](https://mlsanity.com/paper/2303.14242/) (2023)

## Built on by (most cited first, 21 of 21)

- [Using the Path of Least Resistance to Explain Deep Networks](https://mlsanity.com/paper/2502.12108/) (2025)
- [Tangentially Aligned Integrated Gradients for User-Friendly Explanations](https://mlsanity.com/paper/2503.08240/) (2025)
- [SMA: Who Said That? Auditing Membership Leakage in Semi-Black-box RAG Controlling](https://mlsanity.com/paper/2508.09105/) (2025)
- [AdaptGrad: Adaptive Sampling to Reduce Noise](https://mlsanity.com/paper/2410.07711/) (2024)
- [Riemannian Integrated Gradients: A Geometric View of Explainable AI](https://mlsanity.com/paper/2503.00892/) (2025)
- [Measuring the (Un)Faithfulness of Concept-Based Explanations](https://mlsanity.com/paper/2504.10833/) (2025)
- [Counterfactual Explanations on Robust Perceptual Geodesics](https://mlsanity.com/paper/2601.18678/) (2026)
- [Auditing Sybil: Explaining Deep Lung Cancer Risk Prediction Through Generative Interventional Attributions](https://mlsanity.com/paper/2602.02560/) (2026)
- [Manifold-Aligned Guided Integrated Gradients for Reliable Feature Attribution](https://mlsanity.com/paper/2605.02167/) (2026)
- [Spectral Integrated Gradients for Coarse-to-Fine Feature Attribution](https://mlsanity.com/paper/2605.19607/) (2026)
- [Fast Fourier Correlation is a Highly Efficient and Accurate Feature Attribution Algorithm from the Perspective of Control Theory and Game Theory](https://mlsanity.com/paper/2504.02016/) (2025)
- [Path-Weighted Integrated Gradients for Interpretable Dementia Classification](https://mlsanity.com/paper/2509.17491/) (2025)
- [Diffusion Integrated Gradients: Controllable Path Generation for Flexible Feature Attribution](https://mlsanity.com/paper/2606.22314/) (2026)
- [Comprehensive and Reliable Feature Attribution for Diverse Modalities and Models via Frequency-Domain Insights](https://mlsanity.com/paper/2411.18343/) (2024)
- [On the notion of missingness for path attribution explainability methods in medical settings: Guiding the selection of medically meaningful baselines](https://mlsanity.com/paper/2508.14482/) (2025)
- [Graph-based Integrated Gradients for Explaining Graph Neural Networks](https://mlsanity.com/paper/2509.07648/) (2025)
- [From Baselines to Transport Geodesics: Axiomatic Attribution via Optimal Generative Flows](https://mlsanity.com/paper/2603.05093/) (2026)
- [FRInGe: Distribution-Space Integrated Gradients with Fisher--Rao Geometry](https://mlsanity.com/paper/2605.06404/) (2026)
- [COGENT: Counterfactual Gaussian Explanations for Volumetric Medical Images](https://mlsanity.com/paper/2608.11422/) (2026)
- [Pushing the (Decision) Boundaries: Dynamically Calibrating Differentially Private Noise to Explainability in Federated Learning](https://mlsanity.com/paper/2609.03851/) (2026)
- [Explaining Hyperbolic Neural Networks via Geometry-Aware Relevance Propagation](https://mlsanity.com/paper/2609.35128/) (2026)

## Abstract (arXiv)

In this paper, we dive into the reliability concerns of Integrated Gradients (IG), a prevalent feature attribution method for black-box deep learning models. We particularly address two predominant challenges associated with IG: the generation of noisy feature visualizations for vision models and the vulnerability to adversarial attributional attacks. Our approach involves an adaptation of path-based feature attribution, aligning the path of attribution more closely to the intrinsic geometry of the data manifold. Our experiments utilise deep generative models applied to several real-world image datasets. They demonstrate that IG along the geodesics conforms to the curved geometry of the Riemannian data manifold, generating more perceptually intuitive explanations and, subsequently, substantially increasing robustness to targeted attributional attacks.