Let SMTM be Turing Machine, but the commands recorded in which can change to others in some random way (for example, choose with a 50/50 probability the command to move to the right or move to the left), and SM-NTM be non-deterministic Turing Machine with same property (note that NTM non-deterministic in sense of choosing next action, but not the rule, which describes this actions). A difference between a self-modifying Turing machine and TM/NTM: instead of one command for any given situation, or a set of commands in a non-deterministic Turing machine, there is a fuzzy set of commands.
In addition to the question from the title: Is there any papers which describes these sort of theoretical models of computation? In particular, I am interested in the applicability of Rice's theorem for a given computational model. Maybe, there is some connection to quantum computers, NP-hardness, etc.?
The problem that prompted me to this question:
There are neural networks that have an element of non-determinism, where at a certain stage the numbers change by adding random numbers (obtained, for example, from weather observations or observation of the decay of unstable atoms, that is, really random numbers) - do such models have restrictions superimposed on a Turing machine?