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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.26537 |
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| _version_ | 1866911186005524480 |
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| author | Adam, Maxwell Furman, Zach Hoogland, Jesse |
| author_facet | Adam, Maxwell Furman, Zach Hoogland, Jesse |
| contents | We introduce the loss kernel, an interpretability method for measuring similarity between data points according to a trained neural network. The kernel is the covariance matrix of per-sample losses computed under a distribution of low-loss-preserving parameter perturbations. We first validate our method on a synthetic multitask problem, showing it separates inputs by task as predicted by theory. We then apply this kernel to Inception-v1 to visualize the structure of ImageNet, and we show that the kernel's structure aligns with the WordNet semantic hierarchy. This establishes the loss kernel as a practical tool for interpretability and data attribution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_26537 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Loss Kernel: A Geometric Probe for Deep Learning Interpretability Adam, Maxwell Furman, Zach Hoogland, Jesse Machine Learning We introduce the loss kernel, an interpretability method for measuring similarity between data points according to a trained neural network. The kernel is the covariance matrix of per-sample losses computed under a distribution of low-loss-preserving parameter perturbations. We first validate our method on a synthetic multitask problem, showing it separates inputs by task as predicted by theory. We then apply this kernel to Inception-v1 to visualize the structure of ImageNet, and we show that the kernel's structure aligns with the WordNet semantic hierarchy. This establishes the loss kernel as a practical tool for interpretability and data attribution. |
| title | The Loss Kernel: A Geometric Probe for Deep Learning Interpretability |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2509.26537 |