{"ID":2862944,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.26537","arxiv_id":"2509.26537","title":"The Loss Kernel: A Geometric Probe for Deep Learning Interpretability","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2509.26537","url_pdf":"https://arxiv.org/pdf/2509.26537v1","authors":"[\"Maxwell Adam\",\"Zach Furman\",\"Jesse Hoogland\"]","published":"2025-09-30T17:10:28Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false}