An Exact Kernel Equivalence for Finite Classification Models

Brian Bell, Michael Geyer, David Glickenstein, Amanda Fernandez, Juston Moore

Research output: Contribution to journalConference articlepeer-review


We explore the equivalence between neural networks and kernel methods by deriving the first exact representation of any finite-size parametric classification model trained with gradient descent as a kernel machine. We compare our exact representation to the well-known Neural Tangent Kernel (NTK) and discuss approximation error relative to the NTK and other non-exact path kernel formulations. We experimentally demonstrate that the kernel can be computed for realistic networks up to machine precision. We use this exact kernel to show that our theoretical contribution can provide useful insights into the predictions made by neural networks, particularly the way in which they generalize.

Original languageEnglish (US)
Pages (from-to)206-217
Number of pages12
JournalProceedings of Machine Learning Research
StatePublished - 2023
Event2nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning, TAG-ML 2023, held at the International Conference on Machine Learning, ICML 2023 - Honolulu, United States
Duration: Jul 28 2023 → …

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


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