  We establish disintegrated PAC-Bayesian generalisation bounds for models
trained with gradient descent methods or continuous gradient flows. Contrary to
standard practice in the PAC-Bayesian setting, our result applies to
optimisation algorithms that are deterministic, without requiring any
de-randomisation step. Our bounds are fully computable, depending on the
density of the initial distribution and the Hessian of the training objective
over the trajectory. We show that our framework can be applied to a variety of
iterative optimisation algorithms, including stochastic gradient descent (SGD),
momentum-based schemes, and damped Hamiltonian dynamics.
