Closed Loop Neural-Symbolic Learning via Integrating Neural Perception, Grammar Parsing, and Symbolic Reasoning
This work addresses the problem of inefficient learning in neural-symbolic integration for researchers and practitioners, offering a novel method that is incremental but impactful in specific domains.
The paper tackles the slow convergence and sparse reward issues in neural-symbolic learning by introducing a grammar model as a symbolic prior and a back-search algorithm for error propagation, resulting in significant performance improvements, faster convergence, and better data efficiency on tasks like handwritten formula recognition and visual question answering.
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 \url{https://liqing-ustc.github.io/NGS}.