Inductive Coherence
Scott Garrabrant, Benya Fallenstein, Abram Demski, Nate Soares

TL;DR
This paper introduces inductive coherence, a new framework for probabilistic reasoning about computational outputs, providing finite approximation guarantees and addressing limitations of traditional coherent distributions.
Contribution
It proposes inductive coherence, a strengthened form of coherence, along with an algorithm that ensures finite approximations satisfy this criterion.
Findings
The algorithm satisfies inductive coherence constraints.
Inductive coherence improves finite approximation quality.
Addresses limitations of traditional coherent distributions.
Abstract
While probability theory is normally applied to external environments, there has been some recent interest in probabilistic modeling of the outputs of computations that are too expensive to run. Since mathematical logic is a powerful tool for reasoning about computer programs, we consider this problem from the perspective of integrating probability and logic. Recent work on assigning probabilities to mathematical statements has used the concept of coherent distributions, which satisfy logical constraints such as the probability of a sentence and its negation summing to one. Although there are algorithms which converge to a coherent probability distribution in the limit, this yields only weak guarantees about finite approximations of these distributions. In our setting, this is a significant limitation: Coherent distributions assign probability one to all statements provable in a…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsBayesian Modeling and Causal Inference · Logic, Reasoning, and Knowledge · Computability, Logic, AI Algorithms
