Research map / Optimization / Implicit bias and generalization
Asymptotics of Wide Networks from Feynman Diagrams
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Feynman-diagram cluster counting to bound correlation-function scaling | Wide neural-network correlation functions · Fully connected networks with linear, ReLU, and tanh activations | fitted width exponent | No clear effect |
| Use the derived finite-width bound instead of the existing gradient-flow bound | NTK change during gradient flow · Wide-network training | width scaling bound: O(n^{-1/2}) -> O(n^{-1}) | Helped |
| Extend the asymptotic analysis from gradient flow to SGD | Wide-network training · NTK change during SGD | width scaling bound: O(n^{-1}) | Helped |
| Use the predicted first finite-width correction | Network function and NTK evolution · Two-class MNIST | agreement with empirical evolution: O(n^{-1}) | No clear effect |
| Replace Gaussian initialization with uniform {±1} initialization | Wide-network correlation functions · Three-hidden-layer networks | fitted width exponent | No clear effect |
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