The goal of neural-symbolic computation is to integrate the connectionist and symbolist paradigms. Prior methods learn the neural-symbolic models using reinforcement learning (RL) approaches, which ignore the error propagation in the symbolic reasoning module and thus converge slowly with sparse rewards. In this paper, we address these issues and close the loop of neural-symbolic learning by (1) introducing the grammar model as a symbolic prior to bridge neural perception and symbolic reasoning, and (2) proposing a novel back-search algorithm which mimics the top-down human-like learning procedure to propagate the error through the symbolic reasoning module efficiently. We further interpret the proposed learning framework as maximum likelihood estimation using Markov chain Monte Carlo sampling and the back-search algorithm as a Metropolis-Hastings sampler. The experiments are conducted on two weakly-supervised neural-symbolic tasks: (1) handwritten formula recognition on a newly introduced HWF dataset; (2) visual question answering on the CLEVR dataset. The results show that our approach significantly outperforms the RL methods in terms of performance, converging speed, and data efficiency.

Closed Loop Neural-Symbolic Learning via Integrating Neural Perception, Grammar Parsing, and Symbolic Reasoning
Qing Li, Siyuan Huang, Yining Hong, Yixin Chen, Ying Nian Wu, and Song-Chun Zhu.
International Conference on Machine Learning (ICML) 2020.
Paper / Supplementary / Code


HWF v1.0: 10K training formulas and 2K test formulas.


Qing Li1

Siyuan Huang1

Yining Hong2

Yixin Chen1

Ying Nian Wu1

Song-Chun Zhu1,2

1 Department of Statistics, UCLA

2 Department of Computer Science, UCLA


title={Closed Loop Neural-Symbolic Learning via Integrating Neural Perception, Grammar Parsing, and Symbolic Reasoning},
author={Li, Qing and Huang, Siyuan and Hong, Yining and Chen, Yixin and Wu, Ying Nian and Zhu, Song-Chun.},
booktitle={International Conference on Machine Learning (ICML)},