Cycle-Consistent Neural Explanation of Formal Verification Certificates

2026-06-23

AI Summary

This work addresses the limited interpretability of formal verification certificates for non-experts by proposing a cycle-consistent neural architecture. The framework integrates a forward network that generates natural language explanations with an inverse network that reconstructs the original certificate, forming a closed loop validated by a symbolic verifier to ensure faithfulness. Combining pointer-generation mechanisms with feedback from symbolic verification and employing a hybrid reasoning routing strategy, the method achieves high-fidelity, deterministic, and efficient inference on structured certificate explanation tasks. Evaluated on 420 test certificates, the approach attains a cycle-consistency accuracy of 90.0%, outperforming the strongest multi-LLM baseline by 13.9 percentage points while accelerating inference by 860×, enabling offline deployment with zero marginal cost.

Abstract

Formal verification produces machine-checkable certificates that attest to the satisfaction or violation of temporal properties, yet these certificates remain opaque to non-specialist stakeholders. We propose a cycle-consistent neural architecture that generates faithful natural language explanations of verification certificates. A forward network NN1 maps certificates to explanations, and an inverse network NN2 reconstructs certificates from explanations; a symbolic verifier closes the loop, providing a differentiable faithfulness proxy. A pointer-generator mechanism ensures lexical grounding by copying state names directly from the certificate. We evaluate on 420 test certificates spanning six verification methods (bounded proof, k-induction, inductive invariant, lasso, reachability, witness pair) in both YES and NO verdict variants, drawn from a financial compliance domain with 207 named states. Our trained architecture, combined with a hybrid inference-time routing strategy, achieves 90.0% cycle-verified soundness, surpassing a multi- LLM few-shot baseline (76.1% for the best of 16 LLM combinations across four frontier models) by 13.9 percentage points. The neural model wins on 10 of 12 verdict/kind categories, with three categories reaching 100% soundness. The architecture offers 860x faster inference (185 ms vs. 160 s per certificate for the full multi-LLM baseline), offline operation, deterministic outputs, and zero per-inference cost. These results demonstrate that trained specialization outperforms general-purpose LLM prompting for structured certificate explanation, while eliminating the deployment constraints of cloud-based inference.

Problem

• formal verification
• certificates
• explainability
• natural language explanation
• temporal properties

Innovation

• cycle-consistent neural explanation
• formal verification certificates
• symbolic verifier
• pointer-generator mechanism
• hybrid inference routing