New verification system audits AI reasoning step-by-step to catch hidden flaws formal tools miss

When evaluating whether to trust an AI system's answer, researchers face a difficult choice. Formal proof assistants can guarantee correctness but work only on narrow problem domains; large language model judges can handle broad questions but produce unauditable scores prone to the same flaws as the systems they evaluate. A new approach called Theoria aims to split the difference.

How Theoria Works#

Rather than assigning an opaque confidence score, Theoria rewrites a candidate solution as a sequence of typed state transitions—essentially, a chain of logical steps. Each step must be justified by an explicit source: a citation to external material, a computational result, or a given fact from the problem itself. The system enforces a strict rule: every difference between consecutive reasoning states must be accounted for. This means hidden premises cannot slip through undetected; instead, they surface as unlicensed changes that the system flags.

The outcome is an auditable proof trace where humans can challenge each individual step independently, rather than accepting or rejecting the entire answer wholesale.

Performance on Real and Adversarial Problems#

Testing on HLE-Verified Gold (a dataset of 185 expert-written problems), Theoria certified 105 solutions at 91.4% precision according to strict standards. On a harder benchmark of 95 deliberately corrupted proofs across 15 domains, the structured approach caught 94.7% of errors compared to 83.2% for traditional holistic LLM judges—an 11.5 percentage-point improvement.

Notably, Theoria's advantage concentrates in the error classes it was designed to catch. It detected hidden premises in 90.6% of cases versus 62.5% for LLM judges (a 28 percentage-point gap) and caught all fabricated citations versus 90% for traditional judges. However, both methods performed identically on arithmetic mistakes and theorem-misapplication errors, categories where the formal structure offers no predicted edge.

On GPQA Diamond, a smaller but highly selective dataset (n=65), Theoria achieved certified precision of 97.1%.

Complementary Strengths#

The methods fail on different problems—the Jaccard overlap in errors is only 0.14–0.36—suggesting they capture different failure modes. Rather than replacing holistic LLM judges, Theoria functions as a specialized tool that excels at exposing the kinds of errors formal structure can detect while remaining transparent enough for human review at every stage.