Conditional Factors: Discovering When to Use a Formula

Formulaic alpha mining produces short, executable predictors, but a formula alone does not say which assets, in which information states, it should rank. We introduce conditional factors: programs that pair an applicability predicate with a ranking formula, discover the two jointly, and execute them as a pair. In U.S. equities, a shared symbolic financial state enters both the predicate and the score; the generator is rewarded by rank correlation measured only on the predicate's support, subject to support-validity constraints. An expected-rank analysis explains why the support matters: changing the comparison set can change the optimal order. We use fixed-formula controls to ask three questions. First, conditional evaluation changes the selected formula for 155 of 192 predicates in a frozen candidate library, although the ranking advantage of the new choice changes sign across years. Second, holding formulas fixed, predicates raise executed returns over always-on use in both markets and, in cryptocurrency, above same-count random support; the U.S. matched-support ranking gain, however, is positive in 2024 and negative in 2025. Third, a signed decomposition of executed returns shows two routes by which predicates help: amplifying favorable use and attenuating unfavorable use. On 2024 cryptocurrency spot data, the 20-day spot-state program earns the highest return among the reported GP, PPO, PS-Tree, and AlphaSAGE-8 comparisons; in a preregistered 2025 extension its gain over always-on use persists while its absolute return trails the external methods. Formula-level applicability is thus an executable and testable part of factor discovery whose value varies across periods.