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Enhancing Visual Feature Attribution via Weighted Integrated Gradients

This paper introduces Weighted Integrated Gradients (WG), an enhanced attribution method that adaptively weights baseline images based on an unsupervised suitability criterion to overcome the noise and instability caused by uniform weighting in traditional multi-baseline approaches, thereby achieving up to 36% improvement in explanation reliability across various vision models.

Original authors: Kien Tran Duc Tuan, Tam Nguyen Trong, Son Nguyen Hoang, Khoat Than, Anh Nguyen Duc

Published 2026-06-16

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CC BY 4.0

Original authors: Kien Tran Duc Tuan, Tam Nguyen Trong, Son Nguyen Hoang, Khoat Than, Anh Nguyen Duc

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to explain to a friend why a computer program decided that a picture contains a "dog." You want to point out exactly which pixels (like the ears or the tail) made the computer say "dog" instead of "cat."

In the world of Artificial Intelligence, this process is called Feature Attribution. One popular way to do this is a method called Integrated Gradients (IG).

The Problem: The "Blank Canvas" Issue

To understand how IG works, imagine you are trying to trace a path from a "blank canvas" (a baseline image) to the actual photo of the dog. The computer calculates how the prediction changes as you slowly turn the blank canvas into the dog photo.

The problem is: What does the "blank canvas" look like?

Is it a black screen?
Is it a white screen?
Is it a blurry mess?

The paper points out that the answer matters a lot. If you pick a bad "blank canvas," your explanation might be noisy or wrong.

The Old Fix: "The Average Crowd"

A previous method called Expected Gradients (EG) tried to fix this by saying, "Let's not just pick one blank canvas. Let's pick many different ones (black, white, blurry, random) and average their answers."

Think of this like asking a crowd of 100 people for directions. EG assumes that every single person in the crowd is equally helpful. It gives every person's answer the same weight, whether they are an expert or someone who is just guessing. The paper argues that in high-tech vision models, this is a mistake. Some "blank canvases" are terrible guides, and averaging them with the good ones dilutes the quality of the answer.

The New Solution: Weighted Integrated Gradients (WG)

The authors propose a new method called Weighted Integrated Gradients (WG).

Instead of treating every "blank canvas" equally, WG acts like a smart manager who interviews the crowd before asking for directions.

The Test: For every specific photo, WG tests each "blank canvas" to see how good it is at explaining that specific image. It asks: "If we start with this blank canvas, does it help us understand the dog clearly?"
The Score: It gives a "fitness score" to each canvas. A canvas that leads to a clear, strong explanation gets a high score. A confusing one gets a low score.
The Weight: When calculating the final answer, WG listens more to the high-scoring canvases and less to the low-scoring ones.

The Analogy:
Imagine you are trying to solve a mystery.

EG asks 10 witnesses and averages their stories, even if 5 of them were asleep at the scene.
WG checks which witnesses were actually awake and paying attention. It weights the stories of the alert witnesses much heavier than the stories of the sleeping ones.

How They Tested It

The researchers tested this on many different types of AI models (like ResNet, VGG, and Transformers) using standard image datasets (like ImageNet).

They used two main ways to check if the explanations were better:

The "Delete" Test: They removed the most important pixels identified by the AI. If the explanation was good, the AI should immediately stop recognizing the dog. WG made the AI lose confidence much faster than the old method, meaning it found the real important pixels.
The "Overlap" Test: They compared the AI's explanation to a human-drawn outline of the dog. WG's explanations matched the human outlines better than the old method did.

The Catch: It Takes More Time

The paper is very honest about a trade-off. Because WG has to "interview" every baseline to give it a score, it takes more computer power and time than the old method.

EG is fast but sometimes noisy.
WG is slower (about 5.7 times slower in their tests) but produces much more reliable and accurate explanations.

The Bottom Line

The paper claims that Weighted Integrated Gradients is a smarter way to explain AI decisions in computer vision. By stopping the practice of treating all reference images as equal, and instead weighting them based on how useful they are for a specific picture, the method creates clearer, more trustworthy maps of what the AI is "looking at."

It's not a magic bullet that works instantly, but for situations where getting the right explanation is more important than getting it fast, this new method is a significant upgrade.

Problem Statement

Integrated Gradients (IG) is a foundational method for feature attribution in Explainable AI (XAI), particularly for computer vision. However, its effectiveness is heavily dependent on the choice of a baseline (reference) image. In high-dimensional vision tasks, no universally "neutral" baseline exists; common choices (e.g., black, white, or random noise) often yield inconsistent or noisy explanations.

To mitigate this, Expected Gradients (EG) averages IG attributions over multiple baselines. While EG reduces sensitivity to a single baseline choice, it relies on a critical limitation: it assigns uniform weights to all baselines, implicitly assuming they are equally informative. The authors argue that in complex vision models, baselines vary significantly in their relevance to a specific input. Uniform averaging can allow low-quality or noisy baselines to dilute the final attribution, leading to unstable and less faithful explanations.

Methodology: Weighted Integrated Gradients (WG)

The paper proposes Weighted Integrated Gradients (WG), a principled extension of IG that assigns input-dependent weights to different baselines based on their suitability for explaining a specific input.

1. Unsupervised Fitness Measure ( $D_\alpha$ ):
WG introduces an unsupervised criterion to evaluate baseline suitability without requiring manual annotations or domain knowledge. It defines a "fitness" score based on perturbation:

Definition: $D_\alpha$ is the minimum number of features that must be masked to reduce the model's output score to $\alpha\%$ of its original value.
Logic: A baseline with a lower $D_\alpha$ is considered more "fit" because fewer features need to be removed to significantly impact the model's confidence. This implies the baseline effectively highlights the influential features.
Weighting: The weight $w_k$ for the $k$ -th baseline is inversely proportional to its fitness score ( $w_k \propto 1/D_\alpha$ ). Baselines that yield more faithful explanations (lower $D_\alpha$ ) receive higher weights.

2. Efficient Computation (Algorithm 1):
Calculating $D_\alpha$ via exhaustive search is computationally prohibitive ( $O(n)$ ). The authors propose a binary search strategy that leverages the monotonicity of score reduction upon feature removal. By iteratively masking features based on importance scores (e.g., IG attributions), the algorithm achieves a time complexity of $O(\log n)$ per baseline.

3. Theoretical Justification:

Axiomatic Properties: WG preserves the core axioms of IG (Implementation Invariance and Sensitivity) and satisfies a generalized completeness property.
Probabilistic Analysis: Under an assumption of Expected Proxy Fitness–Relevance Monotonicity (i.e., baselines with better fitness scores tend to place more probability mass on truly relevant features), the authors prove that WG increases the expected relevance of the aggregated attribution compared to uniform averaging (EG).
Finite-Sample Guarantees: The paper provides a theorem showing that when WG achieves a positive relevance margin over the average EG relevance, the empirical relevance fraction concentrates above the EG average at an exponential rate.

Key Contributions

Formulation: The authors reformulate baseline selection in IG as an input-dependent weighting problem, moving beyond the uniform assumption of EG.
Mechanism: They propose a perturbation-based, unsupervised fitness score ( $D_\alpha$ ) to estimate baseline usefulness and derive adaptive weights.
Analysis: They provide a theoretical analysis showing that, under specific monotonicity assumptions, fitness-weighted aggregation yields higher expected relevance mass than uniform averaging.
Empirical Evaluation: They evaluate WG across diverse architectures (Convolutional and Transformer) on standard datasets (ImageNet, COCO), reporting both attribution fidelity gains and computational overhead.

Experimental Results

The authors evaluated WG against EG using seven backbone models (DenseNet121, MobileNetV2, ResNet50/101, VGG16/19, and ViT-B/16).

Metrics:
- AUC of Deletion (Lower is better): Measures how rapidly model confidence drops when top-attributed features are removed. WG consistently outperformed EG, with relative improvements ranging from 19.36% to 36.01% across models.
- AUC of Overlap (Higher is better): A supervised metric measuring spatial alignment with ground-truth segmentation masks. WG showed improvements ranging from 5.69% to 18.55%.
Visual Quality: Qualitative analysis (saliency maps) indicates that WG produces sharper and more focused attributions on main objects compared to EG.
Trade-off: The authors explicitly note that WG incurs additional computational cost due to the fitness evaluation step (approximately 5.7 $\times$ slower than EG in their measurements).

Significance and Claims

The paper positions WG not as a faster alternative to EG, but as an attribution-fidelity trade-off. Its primary significance lies in:

Reliability: By adaptively down-weighting low-quality baselines, WG ensures more reliable attributions without manual baseline curation.
Principled Approach: It offers a data-driven mechanism to address the "baseline problem" in path-based attribution, moving beyond the assumption that all baselines contribute equally.
Applicability: The method is particularly suited for settings where improved explanation quality justifies the additional runtime, enhancing the usability of XAI in critical vision applications.

The authors maintain a modest tone regarding their theoretical claims, acknowledging that the probabilistic guarantees rely on an "expected, proxy-based" assumption and that the fitness-relevance monotonicity is empirically verified but not guaranteed for every individual input instance. They conclude that WG is a step toward clearer and more reliable explanations for deep learning systems, provided the computational overhead is acceptable for the specific use case.