arXiv AI September 1, 2026 By Zhichao Hou, Ferhat Erata, Joe Lilien, MohamadAli Torkamani

Stratified Consistency Distillation for Natural Language Formalization

The paper introduces Stratified Consistency Distillation, a fine‑tuning method to improve natural‑language to logical‑formula translations for neurosymbolic reasoning. It generates multiple candidate translations with a large LLM, clusters them by semantic equivalence, and selects pseudo‑labels using entropy‑based strategies—majority voting for low entropy, LLM-as‑Judge for medium entropy, and unification or abstention for high entropy. The selected pseudo‑labels are then used to fine‑tune a smaller model, yielding significant gains in Pass@K and a new Equivalent Logical Similarity metric.

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Related stories

VERGE: Formal Refinement and Guidance Engine for Verifiable LLM Reasoning

NeuroProlog: Multi-Task Fine-Tuning for Neurosymbolic Mathematical Reasoning via the Cocktail Effect

TQLite: Multi-LLM Jury Guided Distillation for Real-time MQM Translation Quality Evaluation

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