  We revisit on-average algorithmic stability of GD for training
overparameterised shallow neural networks and prove new generalisation and
excess risk bounds without the NTK or 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.
