Decorrelated Is Not Diversified: Style-Robust Selection and Search of Formulaic Alpha Factors

Formulaic alpha factors are interpretable predictive signals mined from market data, and recent work explores the formula space with reinforcement learning and generative models rather than genetic programming. The mined pools, however, are still screened by the information coefficient (IC) and de-duplicated by pairwise correlation of factor values, and the resulting portfolios lose predictive power when market style rotates. We trace this to a blind spot in the selection criterion: IC measures fit to the prevailing regime, and mutual-IC screening removes redundancy only in factor values, so a value-decorrelated set can still concentrate on a single capitalization exposure and fail in unison when that exposure rotates. We propose the Exposure–Cycle Residual (ECR), a behavioral descriptor that characterizes a factor by the direction of its net exposure across capitalization layers and by the phase and period of its capitalization tilt, and defines a candidate's novelty as its residual energy relative to the factors already admitted. Screening on ECR produces factor sets whose measured IC converts into realized return more stably across style regimes than IC or mutual-IC screening. We further embed the residual into search itself as a reward-shaping term over an online pool, steering generation toward exposures and cycles not yet covered. Finally, we present a controlled comparison of formulaic miners at high feature dimensionality, with hundreds of tick-derived fields, a shared single-formula evaluator, and both linear and nonlinear combiners, re-running random search, genetic programming, and recent reinforcement-learning and generative miners under identical screening. Across screens, miners and combiners, ECR-based selection and ECR-guided search consistently improve out-of-sample predictive power and portfolio return, with the largest gains during style-rotation periods.