Neural programming involves training neural networks to learn programs from data. Previous works have failed to achieve good generalization performance, especially on programs with high complexity or on large domains. This is because they mostly rely either on black-box function evaluations that do not capture the structure of the program, or on detailed execution traces that are expensive to obtain, and hence the training data has poor coverage of the domain under consideration. We present a novel framework that utilizes black-box function evaluations, in conjunction with symbolic expressions that integrate relationships between the given functions. We employ tree LSTMs to incorporate the structure of the symbolic expression trees. We use tree encoding for numbers present in function evaluation data, based on their decimal representation. We present an evaluation benchmark for this task to demonstrate our proposed model combines symbolic reasoning and function evaluation in a fruitful manner, obtaining high accuracies in our experiments. Our framework generalizes significantly better to expressions of higher depth and is able to fill partial equations with valid completions.

该论文提出了一种基于黑盒函数评估和符号表达式的神经编程方法，利用树LSTMs结合符号表达式树结构进行编码，基于数字的十进制表示进行树编码，评估表明该模型能够成功地结合符号推理和函数评估，填补部分方程并获得高精度。

在神经程序中将符号表达式和黑盒函数评估相结合