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。

通过集成神经感知、语法解析和符号推理实现闭环神经符号学习

Closed Loop Neural-Symbolic Learning via Integrating Neural Perception,  Grammar Parsing, and Symbolic Reasoning

The study and understanding of human behaviour is relevant to computer
science, artificial intelligence, neural computation, cognitive science,
philosophy, psychology, and several other areas. Presupposing cognition as
basis of behaviour, among the most prominent tools in the modelling of
behaviour are computational-logic systems, connectionist models of cognition,
and models of uncertainty. Recent studies in cognitive science, artificial
intelligence, and psychology have produced a number of cognitive models of
reasoning, learning, and language that are underpinned by computation. In
addition, efforts in computer science research have led to the development of
cognitive computational systems integrating machine learning and automated
reasoning. Such systems have shown promise in a range of applications,
including computational biology, fault diagnosis, training and assessment in
simulators, and software verification. This joint survey reviews the personal
ideas and views of several researchers on neural-symbolic learning and
reasoning. The article is organised in three parts: Firstly, we frame the scope
and goals of neural-symbolic computation and have a look at the theoretical
foundations. We then proceed to describe the realisations of neural-symbolic
computation, systems, and applications. Finally we present the challenges
facing the area and avenues for further research.

这篇文章介绍了关于认知科学、人工智能、神经计算的研究，特别是神经符号学习和推理的最新进展，从理论到应用和挑战，以及展望未来。