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arXiv · 2508.10490

On the Complexity-Faithfulness Trade-off of Gradient-Based Explanations

Amir Mehrpanah·Matteo Gamba·Kevin Smith·Hossein Azizpour
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Abstract

ReLU networks, while prevalent for visual data, have sharp transitions, sometimes relying on individual pixels for predictions, making vanilla gradient-based explanations noisy and difficult to interpret. Existing methods, such as GradCAM, smooth these explanations by producing surrogate models at the cost of faithfulness. We introduce a unifying spectral framework to systematically analyze and quantify smoothness, faithfulness, and their trade-off in explanations. Using this framework, we quantify and regularize the contribution of ReLU networks to high-frequency information, providing a principled approach to identifying this trade-off. Our analysis characterizes how surrogate-based smoothing distorts explanations, leading to an ``explanation gap'' that we formally define and measure for different post-hoc methods. Finally, we validate our theoretical findings across different design choices, datasets, and ablations.

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Amir Mehrpanah, Matteo Gamba, Kevin Smith, Hossein Azizpour. 2025-08-14. On the Complexity-Faithfulness Trade-off of Gradient-Based Explanations. https://arxiv.org/abs/2508.10490

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