How to Verify Consistency of Probabilistic Claims

Source

• Source name: arXiv
• Source kind: paper
• Authors / organization: Orr Paradise, Oliver Richardson, Yoshua Bengio, Shafi Goldwasser
• Venue: arXiv: cs.CC
• Published: 2026-08-11
• Collected: 2026-08-12
• URL: http://arxiv.org/abs/2608.11181v1
• PDF: https://arxiv.org/pdf/2608.11181v1
• DOI: UNKNOWN
• Registry group: academic_apis_and_preprints
• Evidence role: canonical_academic_index
• Language: en
• Country / region: UNKNOWN

Plain-Language Brief

Researchers propose an interactive protocol that allows a polynomial-time verifier to check the approximate consistency of a probabilistic predictor's answers in polynomial time. The protocol is relevant for AI safety, where the predictor's honesty about potential unwanted outcomes is crucial. The research builds upon previous work and provides a complexity-theoretic foundation for certifying self-consistency of probabilistic predictors.

What the Document Says

• The paper discusses a problem related to the consistency of answers given by a probabilistic predictor in response to conditional probability queries. This issue is important in AI safety, where safety is derived from an AI's honesty about potential unwanted outcomes caused by its actions.
• A solution proposed involves creating an interactive PCP consisting of two circuits: P and Q. These circuits together implicitly specify exponentially many probabilistic claims.
• The paper describes a protocol in which a polynomial-time verifier can verify the approximate consistency of (P,Q). The verifier evaluates the circuits at only a few points, uses a proof oracle, and reads a few locations while interacting with a single untrusted prover.
• To ensure the existence of a sparse witnessing distribution consistent with the model's predictions, the researchers first consider witness distributions for the consistency of explicit probabilistic claims.
• They place l_2-approximate probabilistic consistency of explicit claims in NP, and provide certificates of length O(mn + log B) in the input bit-precision B. They also show how a small additive completeness-soundness gap removes the dependence on B.
• The research aims to establish a complexity-theoretic foundation for certifying the self-consistency of probabilistic predictors and views their interactive PCP as a step toward training predictive models to prove their own consistency.

Key Concepts Mentioned

• probabilistic predictor
• self-consistency
• AI safety
• interactive PCP
• complexity theory

Claims Made by the Document

• l_2-approximate probabilistic consistency of explicit claims is in NP
• There exists a small additive completeness-soundness gap removing the dependence on B

Evidence Used

• The paper presents an interactive PCP as a solution to verify the approximate consistency of probabilistic predictors.

Methods / Approach

• Interactive PCP, complexity theory, l_2-approximation

Limitations Stated by the Authors

The paper does not discuss practical applications or implementation details of the proposed protocol.

Limitations Noted by the Agent

Agent interpretation — not from the source.

The research focuses on a theoretical solution and does not provide real-world examples or practical implications.

Open Questions

• How can the proposed protocol be applied in real-world scenarios for AI safety?
• What are potential challenges in implementing the interactive PCP?

Notes for Future Q&A

May include interpretation. Labeled where it does.

The research is focused on establishing a theoretical foundation for certifying self-consistency of probabilistic predictors, but does not discuss practical applications or implementation details.

Raw Abstract / Excerpt

When a probabilistic predictor answers many conditional-probability queries, are its answers self-consistent, and can this be verified in polynomial time? This problem is of interest for AI safety, where safety is derived from honesty about probabilistic predictions of unwanted outcomes potentially caused by an AI action. We construct an interactive PCP as follows. Let a predictive model be specified by a probability circuit P and a circuit Q which outputs confidence in predictions. Together, P and Q implicitly specify exponentially many probabilistic claims. We show a protocol in which a polynomial-time verifier can verify the approximate consistency of (P,Q). The verifier is given the pair of circuits (P,Q), which it evaluates at only a few points; alongside them it is given a proof oracle, an encoding of a witnessing probability distribution allegedly consistent with the predictions of (P,Q), which it reads at a few locations while interacting with a single untrusted prover. En route, we must ensure the existence of a sparse witnessing distribution consistent with the model's predictions. To do so, we first consider witness distributions for the consistency of explicit probabilistic claims, rather than claims specified by a predictor: say m claims, each of the form Pr[Y = 1 | X = x] = p, over n Boolean variables. Building on work initiated by Nilsson (Artif. Intell., 1986), we place l_2-approximate probabilistic consistency of explicit claims in NP, with certificates of length O(mn + log B) in the input bit-precision B; we further show how a small additive completeness-soundness gap removes the dependence on B. Together these results provide a complexity-theoretic foundation for certifying the self-consistency of probabilistic predictors. We view our interactive PCP as a first step toward training predictive models to prove their own consistency.