Sorry, I’m not quite clear what you mean by this, so I might be answering the wrong question.
I believe counterfactuals on the input space are a subset of counterfactuals on the predictor’s state, because the input space’s influence is through the predictor’s state, but modifying the predictor’s state can also reach states that don’t correspond to any input. As such, I don’t think counterfactuals on the input space add any power to the proposal.
Yea, I agree with this description—input space is a strict subset of predictor-state counterfactuals.
In particular, I would be interested to hear if restricting to input space counterfactuals is clearly insufficient for a known reason. It appears to me that you can still pull the trick you describe in “the proposal” sub-section (constructing counterfactuals which change some property in a way that a human simulator would not pick up on) at least in some cases.
Ah, ok, I see what you’re saying now. I don’t see any reason why restricting to input space counterfactuals wouldn’t work, beyond the issues described with predictor-state counterfactuals. Possibly a performance hit from needing to make larger changes. In the worst case, a larger minimum change size might hurt with specifying the direct reporter.
What part of the proposal breaks if we do counterfactuals in input space rather than on the predictor’s state?
Sorry, I’m not quite clear what you mean by this, so I might be answering the wrong question.
I believe counterfactuals on the input space are a subset of counterfactuals on the predictor’s state, because the input space’s influence is through the predictor’s state, but modifying the predictor’s state can also reach states that don’t correspond to any input. As such, I don’t think counterfactuals on the input space add any power to the proposal.
Yea, I agree with this description—input space is a strict subset of predictor-state counterfactuals.
In particular, I would be interested to hear if restricting to input space counterfactuals is clearly insufficient for a known reason. It appears to me that you can still pull the trick you describe in “the proposal” sub-section (constructing counterfactuals which change some property in a way that a human simulator would not pick up on) at least in some cases.
Ah, ok, I see what you’re saying now. I don’t see any reason why restricting to input space counterfactuals wouldn’t work, beyond the issues described with predictor-state counterfactuals. Possibly a performance hit from needing to make larger changes. In the worst case, a larger minimum change size might hurt with specifying the direct reporter.