A New Baseline Assumption of Integated Gradients Based on Shaply value

TL;DR

This work identifies a fundamental sensitivity of Integrated Gradients (IG) to the choice of a single baseline and reframes attribution through the lens of the Shapley Value. It shows that IG can be viewed as a path-based approximation to the Aumann-Shapley Value, but per-feature attributions can be biased by this shortcut. To address this, the authors propose Shapley Integrated Gradients (SIG), which uses proportional sampling over coalitions to approximate Shapley contributions while treating coalitions as baselines, enabling efficient, parallelizable computation with $O(n^2)$ complexity. Across GridWorld simulations and image-based tasks (e.g., facial expression codes and ImageNet with ResNet), SIG yields more accurate and consistent feature attributions, validating its generic applicability to diverse data types and instances. This approach offers a practical, principled pathway to more robust explanations without substantial computational overhead, improving interpretability in real-world AI systems.

Abstract

Efforts to decode deep neural networks (DNNs) often involve mapping their predictions back to the input features. Among these methods, Integrated Gradients (IG) has emerged as a significant technique. The selection of appropriate baselines in IG is crucial for crafting meaningful and unbiased explanations of model predictions in diverse settings. The standard approach of utilizing a single baseline, however, is frequently inadequate, prompting the need for multiple baselines. Leveraging the natural link between IG and the Aumann-Shapley Value, we provide a novel outlook on baseline design. Theoretically, we demonstrate that under certain assumptions, a collection of baselines aligns with the coalitions described by the Shapley Value. Building on this insight, we develop a new baseline method called Shapley Integrated Gradients (SIG), which uses proportional sampling to mirror the Shapley Value computation process. Simulations conducted in GridWorld validate that SIG effectively emulates the distribution of Shapley Values. Moreover, empirical tests on various image processing tasks show that SIG surpasses traditional IG baseline methods by offering more precise estimates of feature contributions, providing consistent explanations across different applications, and ensuring adaptability to diverse data types with negligible additional computational demand.

Figures (13)

• Figure 1: ($a$) For a two-features input, red lines represent calculation of Shapley Value for feature $S_1$ and blue lines represent that for feature $S_2$. While Path $P_2$ is calculation path of IG. ($b$) Red paths are the calculation path of Shapley Value while blue path is the calculation path of IG for a $n$-features input.
• Figure 2: ($a$) Proportional sampling in our SIG. Different colored nodes represent different weights defined by Equation \ref{['Eq_4']}. ($b$) Construction of new players. A patch of pixels is considered as a new player/feature on which we search the baseline set.
• Figure 3: Average Spearmanr metric of four baseline methods in GridWorld. $(a)$ and $(b)$ depict the results for 2 $\times$ 2 GridWorld, and $(c)$ and $(d)$ are the results for 2 $\times$ 3 GridWorld. The yellow line indicates the variance of the Spearmanr metric.
• Figure 4: Average 1-Spearmanr metric of four baseline methods in GridWorld. $(a), (b)$ denote the impacts of hyterparameters $N$ with fixed $Q$$40\%$ and $Q$ with fixed $N$ 200 respectively in a 2$\times 2$ GridWorld. (Details are documented in the Appendix)
• Figure 5: Saliency map of four baseline methods in Expression Code Task where red pixels indicate positive values, while blue pixels denote negative values.

Theorems & Definitions (2)

• Theorem 1
• proof