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We present an improved method for symbolic regression that seeks to fit datato formulas that are Pareto-optimal, in the sense of having the best accuracyfor a given complexity. It improves on the previous state-of-the-art bytypically being orders of magnitude more robust toward noise and bad data, andalso by discovering many formulas that stumped previous methods. We develop amethod for discovering generalized symmetries (arbitrary modularity in thecomputational graph of a formula) from gradient properties of a neural networkfit. We use normalizing flows to generalize our symbolic regression method toprobability distributions from which we only have samples, and employstatistical hypothesis testing to accelerate robust brute-force search.

AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity