Breaking the Simplification Bottleneck in Amortized Neural Symbolic Regression

Abstract

Symbolic Regression (SR) aims to discover interpretable analytical expressions that accurately describe observed data. Amortized SR promises to be much more efficient than the predominant genetic programming SR methods, but currently struggles to scale to realistic scientific complexity. We find that the central obstacle is the *simplification bottleneck*, i.e. its inability to quickly reduce equivalent expressions to a concise normalized form. Amortized SR has addressed this by general-purpose Computer Algebra Systems (CAS) like SymPy, but the high computational cost severely limits training and inference speed. We propose **SimpliPy**, a rule-based simplification engine achieving a 100-fold speed-up over SymPy at comparable quality. This enables substantial improvements in amortized SR, including scalability to much larger training sets, more efficient use of the per-expression token budget, and systematic test-set decontamination with respect to equivalent training expressions. We demonstrate these advantages in our **Flash-ANSR** framework, which achieves much better accuracy than amortized baselines (NeSymReS, E2E) on the FastSRB benchmark. Moreover, it performs on par with state-of-the-art direct optimization (PySR) while recovering more concise instead of more complex expressions with increasing inference budget.