Stability & Generalisation of Gradient Descent for Shallow Neural Networks without the Neural Tangent Kernel
Datasets and Benchmarks Track
Authors: Dominic Richards, Ilja Kuzborskij

We revisit on-average algorithmic stability of Gradient Descent (GD) for training  overparameterised  shallow  neural  networks  and prove  new  generalisation and  excess  risk  bounds  without  the  Neural  Tangent  Kernel  (NTK)  or  Polyak-Łojasiewicz (PL) assumptions. In particular, we show oracle type bounds which reveal that the generalisation and excess risk of GD is controlled by an interpolating network with the shortest GD path from initialisation (in a sense, an interpolating network with the smallest relative norm).  While this was known for kernelised interpolants, our proof applies directly to networks trained by GD without intermediate kernelisation. At the same time, by relaxing oracle inequalities developed here we recover existing NTK-based risk bounds in a straightforward way, which demonstrates that our analysis is tighter. Finally, unlike most of the NTK-based analyses we focus on regression with label noise and show that GD with early stopping is consistent