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Life sciences · Preprint
arXiv · September 4, 2026
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SMILE is a novel hybrid framework for symbolic regression that combines continuous optimization with discrete symbolic recovery, evaluated on benchmark datasets. The work is a methodological contribution to machine learning for equation discovery and has not been peer reviewed. No clinical, biological, or applied life-science outcomes are reported.
Algorithm development with benchmark evaluation. Intervention: SMILE framework: three-stage hybrid approach combining structural analysis, continuous gradient-based optimization with interpretable activations, and symbolic recovery via structured pruning, coefficient optimization, and rounding.. Compared with: Competing symbolic regression methods evaluated on SRBench.
SMILE achieves the highest symbolic solution rate at the largest noise levels compared to competing methods. SMILE consistently lies on the Pareto front of accuracy versus complexity. SMILE recovers significantly simpler expressions in a fraction of the time required by competing methods.
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An unreviewed methodological paper proposing a new symbolic regression algorithm with benchmark evaluation but no clinical, biological, or real-world application demonstrated.
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Symbolic regression (SR) discovers closed-form mathematical expressions from data, offering interpretability beyond black-box models. Existing methods suffer from slow convergence in combinatorial search spaces and lack mechanisms to exploit compositional structure in the data. We introduce SMILE (Sine, Multiplication, Identity, Logarithm, Exponential), a hybrid framework that unifies continuous gradient-based optimization with discrete symbolic recovery through three stages: structural analysis of the data to identify the compositional hierarchy of the target expression, continuous optimization to learn parameters of a network that encodes the target expression using interpretable activations, and symbolic recovery through structured pruning, coefficient optimization, and rounding. This final stage distills the learned network into a compact expression with exact symbolic constants. We evaluate SMILE on SRBench across ground-truth and black-box datasets, with ablation studies validating each component. SMILE achieves the highest symbolic solution rate at the largest noise levels, demonstrating strong robustness where competing methods degrade substantially. It consistently lies on the Pareto front of accuracy versus complexity, recovering significantly simpler expressions in a fraction of the time required by the competing methods.
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