# Riemann Sum Optimization for Accurate Integrated Gradients Computation

arXiv: https://arxiv.org/abs/2410.04118 · HTML: https://mlsanity.com/paper/2410.04118/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 30 references that are in the map.
- First posted on arXiv 5 Oct 2024.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [nuScenes: A multimodal dataset for autonomous driving](https://mlsanity.com/paper/1903.11027/) (2019)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [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)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [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)
- [RISE: Randomized Input Sampling for Explanation of Black-box Models](https://mlsanity.com/paper/1806.07421/) (2018)
- [Interpretable Explanations of Black Boxes by Meaningful Perturbation](https://mlsanity.com/paper/1704.03296/) (2017)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Real Time Image Saliency for Black Box Classifiers](https://mlsanity.com/paper/1705.07857/) (2017)
- [Visualizing Deep Neural Network Decisions: Prediction Difference Analysis](https://mlsanity.com/paper/1702.04595/) (2017)
- [XRAI: Better Attributions Through Regions](https://mlsanity.com/paper/1906.02825/) (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)
- [IDGI: A Framework to Eliminate Explanation Noise from Integrated Gradients](https://mlsanity.com/paper/2303.14242/) (2023)
- [Computing Linear Restrictions of Neural Networks](https://mlsanity.com/paper/1908.06214/) (2019)
- [Interpretable Deep Learning in Drug Discovery](https://mlsanity.com/paper/1903.02788/) (2019)

## Built on by (most cited first, 1 of 1)

- [Path-Weighted Integrated Gradients for Interpretable Dementia Classification](https://mlsanity.com/paper/2509.17491/) (2025)

## Abstract (arXiv)

Integrated Gradients (IG) is a widely used algorithm for attributing the outputs of a deep neural network to its input features. Due to the absence of closed-form integrals for deep learning models, inaccurate Riemann Sum approximations are used to calculate IG. This often introduces undesirable errors in the form of high levels of noise, leading to false insights in the model's decision-making process. We introduce a framework, RiemannOpt, that minimizes these errors by optimizing the sample point selection for the Riemann Sum. Our algorithm is highly versatile and applicable to IG as well as its derivatives like Blur IG and Guided IG. RiemannOpt achieves up to 20% improvement in Insertion Scores. Additionally, it enables its users to curtail computational costs by up to four folds, thereby making it highly functional for constrained environments.