  Stochastic differential equations (SDEs) have been shown recently to
characterize well the dynamics of training machine learning models with SGD.
When the generalization error of the SDE approximation closely aligns with that
of SGD in expectation, it provides two opportunities for understanding better
the generalization behaviour of SGD through its SDE approximation. Firstly,
viewing SGD as full-batch gradient descent with Gaussian gradient noise allows
us to obtain trajectory-based generalization bound using the
information-theoretic bound from Xu and Raginsky [2017]. Secondly, assuming
mild conditions, we estimate the steady-state weight distribution of SDE and
use information-theoretic bounds from Xu and Raginsky [2017] and Negrea et al.
[2019] to establish terminal-state-based generalization bounds. Our proposed
bounds have some advantages, notably the trajectory-based bound outperforms
results in Wang and Mao [2022], and the terminal-state-based bound exhibits a
fast decay rate comparable to stability-based bounds.
