Sharpness-Aware Minimization (SAM) was recently introduced as a regularization procedure for training deep neural networks. It simultaneously minimizes the fitness (or loss) function and the so-called fitness sharpness. The latter serves as a measure of the nonlinear behavior of a solution and does so by finding solutions that lie in neighborhoods having uniformly similar loss values across all fitness cases. In this contribution, we adapt SAM for tree Genetic Programming (TGP) by exploring the semantic neighborhoods of solutions using two simple approaches. By capitalizing upon perturbing input and output of program trees, sharpness can be estimated and used as a second optimization criterion during the evolution. To better understand the impact of this variant of SAM on TGP, we collect numerous indicators of the evolutionary process, including generalization ability, complexity, diversity, and a recently proposed genotype-phenotype mapping to study the amount of redundancy in trees. The experimental results demonstrate that using any of the two proposed SAM adaptations in TGP allows (i) a significant reduction of tree sizes in the population and (ii) a decrease in redundancy of the trees. When assessed on real-world benchmarks, the generalization ability of the elite solutions does not deteriorate.

翻译：锐度感知最小化（SAM）是近年来提出的一种用于深度神经网络训练的正则化方法。该方法同时最小化适应度（或损失）函数与所谓的适应度锐度——后者通过寻找位于邻域内所有适应度案例损失值均匀相似的解，来度量解的非线性行为。本研究通过两种简单方法探索解的语义邻域，将SAM适配至树形遗传规划（TGP）。通过扰动程序树的输入与输出，可估算锐度并将其作为进化过程中的第二优化准则。为深入理解该变体对TGP的影响，我们收集了多项进化过程指标，包括泛化能力、复杂度、多样性以及近期提出的用于研究树冗余度的基因型-表型映射。实验结果表明，在TGP中采用所提两种SAM适配方法均能：（i）显著减小种群中树的规模，（ii）降低树的冗余度。在真实世界基准测试中，精英解的泛化能力未出现退化。