PFDE: Population-Feedback-Driven Evaluation for Automated LID Estimator Design

Designing local intrinsic dimensionality (LID) estimators that remain accurate across diverse geometries and finite-sample conditions requires substantial domain expertise and repeated experimentation. Large language model (LLM)-driven evolutionary program search offers a way to automate this process, with the evaluator providing supervision for candidate selection and revision. Existing methods already leverage population information and search history, but the resulting supervision is often summarized as candidate fitness or mediated by evaluator revision and downstream validation. We propose Population-Feedback-Driven Evaluation (PFDE), which turns comparisons among programs and with historical performance directly into the fitness signals and feedback used to evaluate and revise subsequent programs. This allows the supervision guiding search to reflect both differences among current candidates and capabilities gained or lost over time. Experiments on LID-Benchmarks show improved estimation accuracy over conventional evaluation strategies, with benefits extending to downstream adversarial-example detection. Ablations and counterfactual analyses support the contributions of population feedback and historical information, while experiments with general-purpose coding agents demonstrate applicability beyond the dedicated evolutionary framework. Together, these results highlight the value of using search experience directly as supervision, supporting automated LID estimator design and more effective program optimization.