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The SMILE framework achieves the highest symbol resolution in the SRBench benchmark by combining continuous gradient optimization with discrete symbol recovery techniques. The framework consists of three stages: first, analyzing the data to identify the hierarchical structure of the target expressions; second, using interpretable activation functions to continuously optimize the network parameters of the encoded target expressions; finally, pruning the network into compact expressions containing precise symbolic constants through structured pruning, coefficient optimization, and rounding. Experiments show that SMILE exhibits strong robustness under maximum noise levels and always lies on the Pareto frontier between accuracy and complexity, capable of recovering significantly simpler expressions in less time than competing methods.
SMILE 框架通过结合连续梯度优化与离散符号恢复，在 SRBench 基准测试中实现了最高的符号解率。该框架包含三个阶段：首先分析数据以识别目标表达式的组合层级结构；其次利用可解释激活函数对编码目标表达式的网络参数进行连续优化；最后通过结构化剪枝、系数优化和取整将网络蒸馏为包含精确符号常数的紧凑表达式。实验表明，SMILE 在最大噪声水平下表现出强鲁棒性，且始终位于精度与复杂度之间的帕累托前沿，能在比竞争方法少的时间段内恢复出显著更简单的表达式。