Faithful model explanations improved by adaptive complexity refinement
Evolving Explanations: Complexity-Adaptive Refinement of Faithful Explanations for Symbolic Regression
Machine Learning
Summary
Explaining how machine learning models work can be tricky because sometimes explanations sound good but don’t match the actual model’s math. The paper’s authors created a method that tries to explain symbolic regression models by generating simple explanations first, checking if they match the model’s output, and then making them more detailed only if needed. They use two large language models: one to create explanations in words and another to turn those words back into math expressions to verify accuracy. Their approach usually finds accurate explanations at low complexity, ensuring the explanations truly reflect the model’s function.
What this means in practice
- •For machine learning engineers: Ensure that symbolic regression model explanations accurately reflect model behavior with minimal complexity for better model trust.
- •For data science teams: Improve interpretation of complex symbolic models by iteratively refining explanations to match model formulas numerically.
Authors
Elisabeth Mayrhuber, Ting Hu, Stephan Winkler
Abstract
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.