Finite-Width Neural Tangent Kernels from Feynman Diagrams
Researchers have developed a novel method using Feynman diagrams to compute finite-width corrections to neural tangent kernels (NTKs). This approach simplifies algebraic manipulations and enables layer-wise recursion relations for predicting training dynamics at the leading order. The framework has been demonstrated to extend stability results for deep networks and confirm the absence of finite-width corrections for scale-invariant nonlinearities like ReLU on the Gram matrix diagonal. Numerical implementations show that these corrections align with sampled neural network statistics for widths greater than approximately 20. AI
IMPACT Introduces a new theoretical framework for analyzing neural network training dynamics, potentially leading to deeper understanding and more stable models.