# Combining Symbolic Expressions and Black-box Function Evaluations in Neural Programs

arXiv: https://arxiv.org/abs/1801.04342 · HTML: https://mlsanity.com/paper/1801.04342/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jan 2018.

## Built on by (most cited first, 3 of 3)

- [AlphaIntegrator: Transformer Action Search for Symbolic Integration Proofs](https://mlsanity.com/paper/2410.02666/) (2024)
- [Understanding in Artificial Intelligence](https://mlsanity.com/paper/2101.06573/) (2021)
- [Bridging the Gap: Representation Spaces in Neuro-Symbolic AI](https://mlsanity.com/paper/2411.04393/) (2024)

## Abstract (arXiv)

Neural programming involves training neural networks to learn programs, mathematics, or logic from data. Previous works have failed to achieve good generalization performance, especially on problems and 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 define 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.