variable instance log keeps only snapshots of the process variables and not the actual variables. It relies on toString method of the process variable object so if you need to recreate the object make sure your toString gives a representation that you can use to recreate the object.
Though that is bit of an abuse of the variable logs as this is not actual variable storage. Take a look at variable persistence strategies for more advanced ways of achieving such goals.
Okay, thank you, your answer will help me. I will implement a custom variable storage.