If I understand correctly, you want a way of thinking about a reference class of programs that has some specific, perhaps interpretability-relevant or compression-related properties in common with the deterministic program you’re studying?
I think in this case I’d actually say the tempered Bayesian posterior by itself isn’t enough, since even if you work locally in a basin, it might not preserve the specific features you want. In this case I’d probably still start with the tempered Bayesian posterior, but then also condition on the specific properties/explicit features/ etc. that you want to preserve. (I might be misunderstanding your comment though)
If I understand correctly, you want a way of thinking about a reference class of programs that has some specific, perhaps interpretability-relevant or compression-related properties in common with the deterministic program you’re studying?
I think in this case I’d actually say the tempered Bayesian posterior by itself isn’t enough, since even if you work locally in a basin, it might not preserve the specific features you want. In this case I’d probably still start with the tempered Bayesian posterior, but then also condition on the specific properties/explicit features/ etc. that you want to preserve. (I might be misunderstanding your comment though)