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 \textbf{grammar} model as a \textit{symbolic
prior} to bridge neural perception and symbolic reasoning, and (2) proposing a
novel \textbf{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 the 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. Our code and data are released at
https://liqing-ustc.github.io/NGS.

本文介绍了一种新的用于神经符号计算的学习框架，其中引入了语法模型和反向搜索算法来优化符号推理模块中的误差传播，本文将所提出的学习框架解释为最大似然估计，算法则解释为 Metropolis-Hastings 采样器，实验结果表明，本文方法相对于强化学习方法在性能、收敛速度和数据效率等方面均有显著提升。