Language models reveal uncertainty in scientific model building
Transformed in Translation: Two-Stage Structural Uncertainty in LLM-Based Scientific Autoformalization
Software Engineering
Summary
Scientists often turn words into math to understand how things work, but this math can still be uncertain. The authors studied how two types of uncertainty appear: one from how language models create mathematical descriptions and another from how those descriptions predict future behavior. They found that different models and methods leave identifiable traces in the math, meaning the process of turning words into math doesn’t erase where it came from. This understanding helps improve how we check and compare scientific models made by computers.
What this means in practice
- •For data scientists: Identify distinct model sources and their behaviors when converting text-based scientific descriptions into executable mathematical forms.
- •For software developers: Design tools that track and compare different computational models generated from natural language to improve scientific model validation.
Authors
Andre Panossian
Abstract
Scientific autoformalization turns verbal accounts into executable mathematics, but executable code does not settle which model has been constructed. We examine two sources of structural uncertainty: the formalizer that generates a response law, and the recurrence that turns that law into trajectories. In secondary analyses of an openly archived crossed experiment, we studied 320 response maps generated by two pinned language-model formalizers from five engineered cognitive accounts within one sparse quadratic grammar and 16 randomized blocks. With whole blocks held out, source-account identity was recovered at 78.8% accuracy (chance 20.0%) and formalizer identity at 96.3% (chance 50.0%; both p < 0.001). Program size was the stronger single feature family; a pre-specified exploratory comparison found no stable source-account predictive gain from local geometry beyond size. Holding every response map fixed, we then evaluated five recurrence families spanning 33 configurations and 1,013,760 finite-horizon trajectories. Added feedback, projection and leak produced sharply different outcome distributions. The consequential distinction was which comparisons survived: median cross-recurrence rank concordance was 0.73 for endpoint magnitude but 0.05 for settling, among the configuration pairs with defined rankings. Thus a common mathematical language did not erase translation provenance, and robust ordering under one observable did not transfer to another. Scientific autoformalization is usefully studied as model-space construction: the generated ensemble and its dynamical embedding are both part of the specification supporting a scientific claim.