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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.18863 |
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| _version_ | 1866917608128774144 |
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| author | Simpson, Lachlan Millar, Kyle Cheng, Adriel Lim, Cheng-Chew Chew, Hong Gunn |
| author_facet | Simpson, Lachlan Millar, Kyle Cheng, Adriel Lim, Cheng-Chew Chew, Hong Gunn |
| contents | Explainability models are now prevalent within machine learning to address the black-box nature of neural networks. The question now is which explainability model is most effective. Probabilistic Lipschitzness has demonstrated that the smoothness of a neural network is fundamentally linked to the quality of post hoc explanations. In this work, we prove theoretical lower bounds on the probabilistic Lipschitzness of Integrated Gradients, LIME and SmoothGrad. We propose a novel metric using probabilistic Lipschitzness, normalised astuteness, to compare the robustness of explainability models. Further, we prove a link between the local Lipschitz constant of a neural network and its stable rank. We then demonstrate that the stable rank of a neural network provides a heuristic for the robustness of explainability models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18863 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Probabilistic Lipschitzness and the Stable Rank for Comparing Explanation Models Simpson, Lachlan Millar, Kyle Cheng, Adriel Lim, Cheng-Chew Chew, Hong Gunn Machine Learning Explainability models are now prevalent within machine learning to address the black-box nature of neural networks. The question now is which explainability model is most effective. Probabilistic Lipschitzness has demonstrated that the smoothness of a neural network is fundamentally linked to the quality of post hoc explanations. In this work, we prove theoretical lower bounds on the probabilistic Lipschitzness of Integrated Gradients, LIME and SmoothGrad. We propose a novel metric using probabilistic Lipschitzness, normalised astuteness, to compare the robustness of explainability models. Further, we prove a link between the local Lipschitz constant of a neural network and its stable rank. We then demonstrate that the stable rank of a neural network provides a heuristic for the robustness of explainability models. |
| title | Probabilistic Lipschitzness and the Stable Rank for Comparing Explanation Models |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2402.18863 |