Then suppose that the system decides to make burritos filled with nano-machines that carefully filter out some carbon 12 atoms. These are now valid candidates for b, and the unnaturalness of the set ff has gone down.
Wouldn't these burritos be very unnatural since they contain nanomachines, and natural burritos don't?
Yes. But allows for burritos with metal in them and for some without. So they are pretty unnatural, but not ruled out. But all the example burritos have the same level of radioactivity, so all normal burritos are ruled.
Maybe I should have chosen a better example.
A putative new idea for AI control; index here.
Jessica presented a system learning only from positive examples. Given examples of burritos, it computes a distribution over possible burritos. When it comes to creating its own burritos, however, it can only construct them from the feasible set .
The thing to do then seems to be to sample from the distribution . Then the idea is to measure the ``unnaturalness'' or the danger of as , where is a random burrito configuration sampled from .
An obviously contrived example: suppose that there is some distant gamma ray burst that sprays the Earth with cosmic rays, resulting in an increase in Carbon 14 () throughout the food chain.
All burritos sampled for have come from high radiation ingredients, and the system has learnt this is a feature of . But by the time the system has to make its own burritos, the excess radiation has faded, and is literally the zero distribution: there is no burrito in the feasible set that corresponds to anything in . The unnaturalness of is infinite.
But what if, noticing this, we tried to present a larger, less unnatural ? Just let the system have more options, for instance.
Now suppose, for example, that the burritos were wrapped in tin foil, and sometimes this ended up mixed with the food. Then would learn that some flexibility in the amount of metal in the burrito is possible.
Then suppose that the system decides to make burritos filled with nano-machines that carefully filter out some carbon 12 atoms. These are now valid candidates for , and the unnaturalness of the set has gone down.
To emphasise: by allowing the system to stuff burritos full of nano-machines, we've increased the measured naturalness of the burritos.
Those examples are, of course, convoluted and unlikely. But the general problem hasn't gone away. What we were hoping for with a measure of unnaturalness, is to rule out the system deploying illicit optimsation power in the burrito. But if the training distribution is biased in a particular way, then illicit optimisation power can seem more natural, according to the definition, than anything we would informally define as natural.
That's because building natural burritos won't remove the bias, but illicit optimisation power could.