# Tangentially Aligned Integrated Gradients for User-Friendly Explanations

arXiv: https://arxiv.org/abs/2503.08240 · HTML: https://mlsanity.com/paper/2503.08240/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 33 references that are in the map.
- First posted on arXiv 11 Mar 2025.

## Builds on (most cited first, 22 of 22)

- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [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)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [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)
- [Captum: A unified and generic model interpretability library for PyTorch](https://mlsanity.com/paper/2009.07896/) (2020)
- [The (Un)reliability of saliency methods](https://mlsanity.com/paper/1711.00867/) (2017)
- [Challenges in Representation Learning: A report on three machine learning contests](https://mlsanity.com/paper/1307.0414/) (2013)
- [Not Just a Black Box: Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1605.01713/) (2016)
- [Opportunities and Challenges in Explainable Artificial Intelligence (XAI): A Survey](https://mlsanity.com/paper/2006.11371/) (2020)
- [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)
- [The Unreasonable Effectiveness of Deep Learning in Artificial Intelligence](https://mlsanity.com/paper/2002.04806/) (2020)
- [Statistical exploration of the Manifold Hypothesis](https://mlsanity.com/paper/2208.11665/) (2022)
- [Manifold Integrated Gradients: Riemannian Geometry for Feature Attribution](https://mlsanity.com/paper/2405.09800/) (2024)
- [The Manifold Hypothesis for Gradient-Based Explanations](https://mlsanity.com/paper/2206.07387/) (2022)
- [Do Perceptually Aligned Gradients Imply Adversarial Robustness?](https://mlsanity.com/paper/2207.11378/) (2022)
- [A Note about: Local Explanation Methods for Deep Neural Networks lack Sensitivity to Parameter Values](https://mlsanity.com/paper/1806.04205/) (2018)
- [Probabilistic Lipschitzness and the Stable Rank for Comparing Explanation Models](https://mlsanity.com/paper/2402.18863/) (2024)

## Built on by (most cited first, 3 of 3)

- [SMA: Who Said That? Auditing Membership Leakage in Semi-Black-box RAG Controlling](https://mlsanity.com/paper/2508.09105/) (2025)
- [Path-Weighted Integrated Gradients for Interpretable Dementia Classification](https://mlsanity.com/paper/2509.17491/) (2025)
- [Graph-based Integrated Gradients for Explaining Graph Neural Networks](https://mlsanity.com/paper/2509.07648/) (2025)

## Abstract (arXiv)

Integrated gradients is prevalent within machine learning to address the black-box problem of neural networks. The explanations given by integrated gradients depend on a choice of base-point. The choice of base-point is not a priori obvious and can lead to drastically different explanations. There is a longstanding hypothesis that data lies on a low dimensional Riemannian manifold. The quality of explanations on a manifold can be measured by the extent to which an explanation for a point lies in its tangent space. In this work, we propose that the base-point should be chosen such that it maximises the tangential alignment of the explanation. We formalise the notion of tangential alignment and provide theoretical conditions under which a base-point choice will provide explanations lying in the tangent space. We demonstrate how to approximate the optimal base-point on several well-known image classification datasets. Furthermore, we compare the optimal base-point choice with common base-points and three gradient explainability models.