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Semantically-meaningful Numeric Constants for Genetic Programming

Ephemeral Random Constants (ERCs) are part of the standard SR toolkit. It is well-known that GP is not good at regressing numeric constants as terminal nodes [1] and ERCs thus serve a dual role: both helping to obtain a better fit in the presence of noise and finding constants that rightfully reproduce the semantics of the underlying model. A disadvantage of ERCs is their contribution to overfitting: standard GP mechanisms for introducing ERCs are ‘blind’ in the sense that there is no means of biasing them towards either of these roles. Previous work by Lipson et al. [2] explicitly modelled noise distribution in order to perform better in the presence of asymetric noise. We adopt a contrary approach and explicitly bias the semantically-aware role. By the use of inverse equation solvers, ERCs can be replaced by closed-form expressions involving rationals and fundamental constants (e.g. π, φ, e). With these particular biases, such an approach might be used to help discover physical laws from experimental data.