On Interpolation Formulas Describing Neural Network Generalization
In 2020 Domingos introduced an interpolation formula valid for "every model trained by gradient descent". He concluded that such models behave approximately as kernel machines. In this work, we extend the Domingos formula to stochastic training. We introduce a stochastic gradient kernel that extends the deterministic version via a continuous-time diffusion approximation. We prove stochastic Domingos theorems and show that the expected network output admits a kernel-machine representation with optimizer-specific weighting. It reveals that training samples contribute through loss-dependent weights and gradient alignment along the training trajectory. We then link the generalization error to...
| Authors | Jin Guo, Roy Y. He, Jean-Michel Morel |
|---|---|
| Primary category | cs.LG |
| Published | 14 March 2026 |
| Last updated at source | 14 March 2026 |
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