[Paper Review] Closed Loop Neural-Symbolic Learning via Integrating Neural Perception, Grammar Parsing, and Symbolic Reasoning

Qing Li, Siyuan Huang+4 more|arXiv (Cornell University)|Jun 11, 2020

Topic Modeling33 citations

TL;DR

This paper presents a neural-symbolic framework that integrates neural perception, grammar-based parsing, and symbolic reasoning, using reinforcement-based backsearch and posterior approximation to learn valid programs and formulas from data.

ABSTRACT

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 \ extbf{grammar} model as a \ extit{symbolic prior} to bridge neural perception and symbolic reasoning, and (2) proposing a novel \ extbf{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}.

Motivation & Objective

• Motivate closed-loop neural-symbolic learning that combines perception, grammar parsing, and symbolic reasoning.
• Propose a neural-grammar-symbolic model with backsearch and posterior sampling to generate valid programs/formulas.
• Demonstrate learning via synthetic data for handwritten formulas and CLEVR-style VQA using structured grammars.
• Analyze the impact of sampling-based REINFORCE variants and Metropolis-Hastings smoothing on learning accuracy.

Proposed method

• Use LeNet as the neural perception module to extract features from images.
• Apply grammar-based symbolic reasoning with context-free grammars for formulas and CLEVR programs.
• Employ REINFORCE and MAPO-style baselines with reward decay for training.
• Introduce m-BS (multistage backsearch) and 1-BS (single-step backsearch) to correct incorrect predictions via module swaps.
• Formulate posterior approximation p'(z|x,y) as a smoothed version of p(z|x,y) and sample via Metropolis-Hastings; prove KL(p||p') = O(epsilon).
• Train on synthetic datasets generated from CROHME for handwritten formulas and CLEVR-like programs; utilize a scene parser and a Pointer Network as the neural components.

Experimental results

Research questions

• RQ1 Can a closed-loop neural-symbolic system learn valid symbolic programs or formulas from perception data?
• RQ2 How can backsearch and posterior sampling improve learning when the correct symbolic structure is sparse or ambiguous?
• RQ3 What is the effect of Metropolis-Hastings smoothed posteriors on learning efficiency and accuracy?
• RQ4 How well can grammar-driven symbolic reasoning modules be integrated with neural perception in VQA and handwritten formula tasks?

Key findings

• The framework enables learning of neural-symbolic pipelines by integrating perception, grammar parsing, and symbolic execution.
• Backsearch variants (1-BS, m-BS) can correct wrong predictions by swapping modules within grammar-defined groups.
• A Metropolis-Hastings-based posterior approximation p′(z|x,y) smooths the true posterior p(z|x,y) with KL(p||p′)=O(ε) as ε→0, improving sampling stability.
• For handwritten formula recognition, a context-free grammar over digits and basic operators is used with generated synthetic data to train the model.
• For neural-symbolic VQA on CLEVR, a scene parser (Mask-RCNN + ResNet-34) provides structural representations, and a Pointer Network acts as the question parser to extract a valid module sequence.