# Understanding Integrated Gradients with SmoothTaylor for Deep Neural Network Attribution

arXiv: https://arxiv.org/abs/2004.10484 · HTML: https://mlsanity.com/paper/2004.10484/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Apr 2020.

## Built on by (most cited first, 19 of 19)

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- [Improving Attribution Methods by Learning Submodular Functions](https://mlsanity.com/paper/2104.09073/) (2021)
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- [Noise-Free Explanation for Driving Action Prediction](https://mlsanity.com/paper/2407.06339/) (2024)
- [Attribution assignment for deep-generative sequence models enables interpretability analysis using positive-only data](https://mlsanity.com/paper/2506.23182/) (2025)
- [DDSA: Dual-Domain Strategic Attack for Spatial-Temporal Efficiency in Adversarial Robustness Testing](https://mlsanity.com/paper/2601.14302/) (2026)
- [Localizing Prompt Ambiguity in Large Language Models with Probe-Targeted Attribution](https://mlsanity.com/paper/2606.05486/) (2026)

## Abstract (arXiv)

Integrated Gradients as an attribution method for deep neural network models offers simple implementability. However, it suffers from noisiness of explanations which affects the ease of interpretability. The SmoothGrad technique is proposed to solve the noisiness issue and smoothen the attribution maps of any gradient-based attribution method. In this paper, we present SmoothTaylor as a novel theoretical concept bridging Integrated Gradients and SmoothGrad, from the Taylor's theorem perspective. We apply the methods to the image classification problem, using the ILSVRC2012 ImageNet object recognition dataset, and a couple of pretrained image models to generate attribution maps. These attribution maps are empirically evaluated using quantitative measures for sensitivity and noise level. We further propose adaptive noising to optimize for the noise scale hyperparameter value. From our experiments, we find that the SmoothTaylor approach together with adaptive noising is able to generate better quality saliency maps with lesser noise and higher sensitivity to the relevant points in the input space as compared to Integrated Gradients.