# On Gradient-like Explanation under a Black-box Setting: When Black-box Explanations Become as Good as White-box

arXiv: https://arxiv.org/abs/2308.09381 · HTML: https://mlsanity.com/paper/2308.09381/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 33 references that are in the map.
- First posted on arXiv 18 Aug 2023.

## Builds on (most cited first, 19 of 19)

- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [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)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [RISE: Randomized Input Sampling for Explanation of Black-box Models](https://mlsanity.com/paper/1806.07421/) (2018)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [Evaluating the visualization of what a Deep Neural Network has learned](https://mlsanity.com/paper/1509.06321/) (2015)
- [Unmasking Clever Hans Predictors and Assessing What Machines Really Learn](https://mlsanity.com/paper/1902.10178/) (2019)
- [Not Just a Black Box: Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1605.01713/) (2016)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [The Shattered Gradients Problem: If resnets are the answer, then what is the question?](https://mlsanity.com/paper/1702.08591/) (2017)
- [When Explainability Meets Adversarial Learning: Detecting Adversarial Examples using SHAP Signatures](https://mlsanity.com/paper/1909.03418/) (2019)
- [Attack-agnostic Adversarial Detection on Medical Data Using Explainable Machine Learning](https://mlsanity.com/paper/2105.01959/) (2021)

## Built on by (most cited first, 2 of 2)

- [SMA: Who Said That? Auditing Membership Leakage in Semi-Black-box RAG Controlling](https://mlsanity.com/paper/2508.09105/) (2025)
- [Rethinking Explanation Evaluation under the Retraining Scheme](https://mlsanity.com/paper/2511.08281/) (2025)

## Abstract (arXiv)

Attribution methods shed light on the explainability of data-driven approaches such as deep learning models by uncovering the most influential features in a to-be-explained decision. While determining feature attributions via gradients delivers promising results, the internal access required for acquiring gradients can be impractical under safety concerns, thus limiting the applicability of gradient-based approaches. In response to such limited flexibility, this paper presents methodAbr~(gradient-estimation-based explanation), an approach that produces gradient-like explanations through only query-level access. The proposed approach holds a set of fundamental properties for attribution methods, which are mathematically rigorously proved, ensuring the quality of its explanations. In addition to the theoretical analysis, with a focus on image data, the experimental results empirically demonstrate the superiority of the proposed method over state-of-the-art black-box methods and its competitive performance compared to methods with full access.