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

• URL: http://arxiv.org/abs/2508.10490v1
• Date: Thu, 14 Aug 2025 09:49:07 GMT
• Title: On the Complexity-Faithfulness Trade-off of Gradient-Based Explanations
• Authors: Amir Mehrpanah, Matteo Gamba, Kevin Smith, Hossein Azizpour,
• Abstract summary: ReLU networks have sharp transitions, sometimes relying on individual pixels for predictions.<n>Existing methods, such as GradCAM, smooth these explanations by producing surrogate models at the cost of faithfulness.<n>We introduce a unifying spectral framework to systematically analyze and quantify smoothness, faithfulness, and their trade-off in explanations.
• Score: 5.528734654854472
• License: http://creativecommons.org/licenses/by/4.0/
• 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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