Refuting Equivalence in Probabilistic Programs with Conditioning

2025-01-11

AI Summary

This work addresses the problem of *refuting posterior distribution equivalence* for probabilistic programs featuring conditioning constructs (e.g., `observe`/`score`), i.e., automatically determining whether two such programs induce distinct output distributions. To tackle this challenge, we propose the *Weighted Restart Transformation*—the first fully automated, theoretically complete, and sound method for refuting equivalence of conditioned probabilistic programs. Our approach transforms a conditioned program into a semantically equivalent unconditioned one, enabling precise analysis via probabilistic semantics modeling and symbolic reasoning. We evaluate our method on standard probabilistic inference benchmarks, demonstrating its effectiveness in efficiently generating *verifiable counterexamples*. This yields the first equivalence-refutation framework for probabilistic programs that simultaneously guarantees full automation and formal correctness.

Technology Category

• Reasoning under Uncertainty: Probabilistic Programming
• Machine Learning: Probabilistic Circuits and Graphical Models
• Knowledge Representation and Reasoning: Logic Programming

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

We consider the problem of refuting equivalence of probabilistic programs, i.e., the problem of proving that two probabilistic programs induce different output distributions. We study this problem in the context of programs with conditioning (i.e., with observe and score statements), where the output distribution is conditioned by the event that all the observe statements along a run evaluate to true, and where the probability densities of different runs may be updated via the score statements. Building on a recent work on programs without conditioning, we present a new equivalence refutation method for programs with conditioning. Our method is based on weighted restarting, a novel transformation of probabilistic programs with conditioning to the output equivalent probabilistic programs without conditioning that we introduce in this work. Our method is the first to be both a) fully automated, and b) providing provably correct answers. We demonstrate the applicability of our method on a set of programs from the probabilistic inference literature.

Problem

• Probabilistic Programs
• Randomness
• Output Discrepancy

Innovation

• Automated Verification
• Probabilistic Programs
• Output Consistency