mlsanityData to 7 Oct 2026

An Exact Kernel Equivalence for Finite Classification Models

arXiv 2308.00824 ↗First posted 1 Aug 2023cs.LGcited by 5

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Abstract (arXiv)

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.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 22 of its 33 references that are in the map. First posted on arXiv 1 Aug 2023.

Builds on

22 of 33 references.

References · 22

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10 more
  1. 2019Graph Neural Tangent Kernel: Fusing Graph Neural Networks with Graph Kernelscited by 160
  2. 2021A Universal Law of Robustness via Isoperimetrycited by 150
  3. 2020On the Similarity between the Laplace and Neural Tangent Kernelscited by 76
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  6. 2021Do Input Gradients Highlight Discriminative Features?cited by 52
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  10. 2022The Quantum Path Kernel: a Generalized Quantum Neural Tangent Kernel for Deep Quantum Machine Learningcited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 1; 2026: 2.

5 papers.

  1. 2024Persistent Classification: A New Approach to Stability of Data and Adversarial Examplescited by 3
  2. 2025ExPLAIND: Unifying Model, Data, and Training Attribution to Study Model Behaviorcited by 3
  3. 2024Novel Kernel Models and Exact Representor Theory for Neural Networks Beyond the Over-Parameterized Regimecited by 0
  4. 2026The role of parameter Jacobians in the stability of network outputscited by 0
  5. 2026Don't Forget! Decomposing the Training Dynamics of Memorization in Language Modelscited by 0