# The Loss Kernel: A Geometric Probe for Deep Learning Interpretability

Source: [The Loss Kernel: A Geometric Probe for Deep Learning Interpretability](<https://www.sota2.com/research/paper/68fa7bcc1e209131cea8a87c>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-26T05:48:24.291Z

Authors: Maxwell Adam, Zach Furman, Jesse Hoogland

Published: 2025-09-30T17:10:28.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2509.26537>)

[PDF](<https://arxiv.org/pdf/2509.26537.pdf>)