If the AI used a efficient method to scheming and then calculated a semi-efficent "legit" computation and then faked of a really energy ineffficent log it could fit extra baggage within the energy budjet.
It could do a punch of stuff that could be dangerous. It could plan to be dangerously neglectfull. Identifying and objecting to all that spectra of misbehaviour isn't a trivial matter. I think a big danger is a human reading a legit log of harmful activity and approving of it. " I guess murdering babies is a legit step on this friendly calculation" when the subject matter on whether a particular thing is warranted or not requires expert oppinion. In a way you want it not to raise your suspisions you want it to try to be friendly. For example if it wants you to build a certain molecyle it could either be a good miracle nanobot or a highly virulent virus. If there is no info why it wants to do it judging this molecyle migth fall outside the expertise of the human. However the reasoning why it wants to be that kind could be a generic goodness principle that sounds fine on paper "Nanobots improve health therefore I want to make a nanobot" (a failure mode could be that the health conception of it could be too indexical, healthy for him to propagate his likeness into biological computer substrata). Would the illegit goal detector catch on to the too indexical health conception?
If the AI knows that is being analysed in practise the cognitive decisions it does is a form of output as the analysis is causally dependent on the cognitive choices.
It can't fake a log without actually doing work >= the purported work of the log.
If the AI knows that is being analysed in practise the cognitive decisions it does is a form of output as the analysis is causally dependent on the cognitive choices.
What I'm aparantly failing to get across to you is that meta-level thinking wlil also be reflected in the output of the deception detector. The deception detector always by design operates one level higher than the program being audited.
Assume you had access to:
1. a self-improving artificial general intelligence (AGI) of at least human-capability or better; and
2. a lie detector that the AGI is known to be susceptible to. A lie for this purpose is any intentional deception.
The AI is not omnipotent. It is running on a physical machine in the real world with limited inputs. One of these inputs is mechanism by which you can ask it questions, and receive answers filtered through the lie detector. A little light on the box turns red if the machine was intentionally deceptive in any way, or green otherwise. As it happens the lie detector is probabilistic, but the chance of a false negative (lie escaping detection) is infinitesimal—1 in 10^40, let's say, but assume you could make it even smaller if you needed to. The chance of a false positive (non-deception being labeled a lie) is effectively zero.
What could you do with this setup?
EDIT: Some of the details above are provided simply to make the problem tractable. E.g. having the deception detector be probabilistic allows its operating requirements to be less than the AI itself. If the AI is running on a supercomputer, it seems intractable to require a super-supercomputer for the deception detector.
EDIT2: Deception in this case simply means falsifying or omitting information. Loosely speaking, if the AI falsifies the computational traces fed into the deception detector, or leaves out any information in its response, this is detectable. Presumably the UFAI could output a very nice, very convincing plan of action with very tiny fine print hidden somewhere along the lines of "PS: This is all a lie! You implement this and I'm going to turn you all into meaty paperclips. Haha!" and it would get past the deception detector. But I would rather discussion not get sidetracked by such legalistic, nitpicky scenarios. Assume the humans involved are competent, conservative, responsible people who have setup institutional safeguards to prevent hasty action and make sure that output is sufficiently analyzed down to the very last digital bit by a competent, international team of highly rational people before being acted upon.