Evolving Explanations: Complexity-Adaptive Refinement of Faithful Explanations for Symbolic Regression

Natural-language explanations generated by large language models (LLMs) for machine learning models often seem fluent but are not necessarily faithful to the underlying model. We formalize this mismatch as a faithfulness gap and propose a complexity-adaptive refinement framework for symbolic regression that iteratively generates and validates explanations until numerical agreement with the target expression is achieved. The approach follows a two-stage pipeline: an explainer LLM produces textual descriptions at increasing levels of detail, while an independent validator LLM extracts a symbolic expression that is compared against the original model. This process is framed as a discrete search over explanation space, where complexity is minimized subject to a faithfulness constraint. We evaluate the method on real-world and synthetic datasets, with a total of 250 runs across varying model complexities. The explanation refinement loop achieves an overall pass rate of 84.0%, with most explanations converging at low complexity levels and only a small fraction requiring detailed descriptions. Our results demonstrate that faithful explanations can be obtained with minimal necessary complexity by explicitly closing the explanation loop through symbolic validation.