Integrated Gradients

Description

Integrated Gradients is an attribution technique that explains a model's prediction by quantifying the contribution of each input feature. It works by accumulating gradients along a straight path from a user-defined baseline input (e.g., a black image or an all-zero vector) to the actual input. This path integral ensures that the attributions satisfy fundamental axioms like completeness (attributions sum up to the difference between the prediction and the baseline prediction) and sensitivity (non-zero attributions for features that change the prediction). The output is a set of importance scores, often visualised as heatmaps, indicating which parts of the input were most influential for the model's decision.

Example Use Cases

Explainability

Analysing a medical image classification model to understand which specific pixels or regions in an X-ray image contribute most to a diagnosis of pneumonia, ensuring the model focuses on relevant pathological features rather than artifacts.

Explaining the sentiment prediction of a natural language processing model by highlighting which words or phrases in a review most strongly influenced its classification as positive or negative, revealing the model's interpretative focus.

Limitations

Requires a carefully chosen and meaningful baseline input; an inappropriate baseline can lead to misleading or uninformative attributions.
The model must be differentiable, which limits its direct application to models with non-differentiable components or discrete inputs without workarounds.
Computationally more expensive than simple gradient-based methods, as it requires multiple gradient calculations along the integration path.
While satisfying completeness, the attributions can sometimes be visually noisy or difficult for humans to interpret intuitively, especially for complex inputs.

Resources

Research Papers

Maximum Entropy Baseline for Integrated Gradients

Hanxiao Tan•Apr 12, 2022

Integrated Gradients (IG), one of the most popular explainability methods available, still remains ambiguous in the selection of baseline, which may seriously impair the credibility of the explanations. This study proposes a new uniform baseline, i.e., the Maximum Entropy Baseline, which is consistent with the "uninformative" property of baselines defined in IG. In addition, we propose an improved ablating evaluation approach incorporating the new baseline, where the information conservativeness is maintained. We explain the linear transformation invariance of IG baselines from an information perspective. Finally, we assess the reliability of the explanations generated by different explainability methods and different IG baselines through extensive evaluation experiments.

Understanding Integrated Gradients with SmoothTaylor for Deep Neural Network Attribution

Gary S. W. Goh et al.•Apr 22, 2020

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.

Software Packages

Integrated-Gradients

Nov 4, 2016

Attributing predictions made by the Inception network using the Integrated Gradients method

captum

Aug 27, 2019

Model interpretability and understanding for PyTorch

Tutorials

Integrated Gradients from Scratch | Towards Data Science

Alexey Kravets•Oct 14, 2021

Related Techniques

Name	Description	Assurance Goals
DeepLIFT	DeepLIFT (Deep Learning Important FeaTures) explains neural network predictions by decomposing the difference between the actual output and a reference output back to individual input features. It compares each neuron's activation to a reference activation (typically from a baseline input like all zeros or the dataset mean) and propagates these differences backwards through the network using chain rule modifications. Unlike gradient-based methods, DeepLIFT satisfies the sensitivity property (zero input gets zero attribution) and provides more stable attributions by using discrete differences rather than gradients.	Explainability Transparency
Layer-wise Relevance Propagation	Layer-wise Relevance Propagation (LRP) explains neural network predictions by working backwards through the network to show how much each input feature contributed to the final decision. It follows a simple conservation rule: the total contribution scores always add up to the original prediction. Starting from the output, LRP distributes 'relevance' backwards through each layer using different rules depending on the layer type. This creates a detailed breakdown showing which input features helped or hindered the prediction, making it easier to understand why the network made a particular decision.	Explainability Transparency
Taylor Decomposition	Taylor Decomposition is a mathematical technique that explains neural network predictions by computing first-order and higher-order derivatives of the network's output with respect to input features. It decomposes the prediction into relevance scores that indicate how much each input feature and feature interaction contributes to the final decision. The method uses Layer-wise Relevance Propagation (LRP) principles to trace prediction contributions backwards through the network layers, providing precise mathematical attributions for each input element.	Explainability
Saliency Maps	Saliency maps are visual explanations for image classification models that highlight which pixels in an image most strongly influence the model's prediction. Computed by calculating gradients of the model's output with respect to input pixels, saliency maps produce heatmaps where brighter regions indicate pixels that, when changed, would most significantly affect the prediction. This technique helps users understand which parts of an image the model is 'looking at' when making decisions.	Explainability Fairness