The Loss Kernel: A Geometric Probe for Deep Learning Interpretability

@article{adam2025the,
  title = {The Loss Kernel: A Geometric Probe for Deep Learning Interpretability},
  author = {Maxwell Adam and Zach Furman and Jesse Hoogland},
  year = {2025},
  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.},
  eprint = {2509.26537},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2509.26537}
}