Hi @<1663354518726774784:profile|CrookedSeal85>

However, I systematically notice a jump of some number of "ghost iterations" when resuming my trainings...

Try the following:

task = Task.init(..., continue_last_task=0

from the Task.init docstring (Notice this value can be both boolean and integer)

        :param bool continue_last_task: Continue the execution of a 
...
          - An integer - Specify initial iteration offset (override the auto automatic last_iteration_offset). Pass 0, to disable the automatic last_iteration_offset or specify a different initial offset. You can specify a Task ID to be used with `reuse_last_task_id='task_id_here'`