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.
@article{arxiv.2509.26537,
title = {The Loss Kernel: A Geometric Probe for Deep Learning Interpretability},
author = {Maxwell Adam and Zach Furman and Jesse Hoogland},
journal= {arXiv preprint arXiv:2509.26537},
year = {2025}
}