Alessandro has many cool research directions you could check out:

(a) Irreversible learning dynamics during the initial learning transient (critical periods, critical periods for regularization, evolution of usable information during training)

(b) Reversibility of learning dynamics near convergence (reverse the dynamics to make the network forget a sample, practical linearization of fine-tuning dynamics)

(c) Connection between dynamics and information (emergence, distance between learning tasks, path integral approximation)