We propose an approach to symbolic regression based on a novel variational autoencoder for generating hierarchical structures, HVAE. It combines simple atomic units with shared weights to recursively encode and decode the individual nodes in the hierarchy. Encoding is performed bottom-up and decoding top-down. We empirically show that HVAE can be trained efficiently with small corpora of mathematical expressions and can accurately encode expressions into a smooth low-dimensional latent space. The latter can be efficiently explored with various optimization methods to address the task of symbolic regression. Indeed, random search through the latent space of HVAE performs better than random search through expressions generated by manually crafted probabilistic grammars for mathematical expressions. Finally, EDHiE system for symbolic regression, which applies an evolutionary algorithm to the latent space of HVAE, reconstructs equations from a standard symbolic regression benchmark better than a state-of-the-art system based on a similar combination of deep learning and evolutionary algorithms.\v{z}
翻译:我们提出一种基于新型变异自动编码器的象征性回归方法,用于生成等级结构,HVAE。它将简单的原子单位和共有的重量结合起来,对等级中的各个节点进行递归编码和解码。编码是自下而上和自下地进行的。我们从经验上表明,HVAE可以用小数学表达体进行高效率的培训,并将表达体准确地编码成一个平滑的低维潜层。后者可以用各种优化方法有效地探索,以解决符号回归的任务。事实上,通过HVAE潜在空间的随机搜索比通过数学表达式手动生成的概率语法生成的表达式进行随机搜索要好。最后,EDHIE的符号回归系统将进化算法应用于HVAE的潜在空间,将方程式从一个比基于类似深度学习和进化算法组合的状态系统更好的标准符号回归基准重塑方程式。\vz}