[Paper Review] A Comparison of Rule Extraction for Different Recurrent Neural Network Models and Grammatical Complexity.

Qinglong Wang, Kaixuan Zhang+4 more|arXiv (Cornell University)|Jan 16, 2018

Natural Language Processing Techniques13 citations

TL;DR

This paper compares rule extraction capabilities across various recurrent neural network (RNN) architectures—particularly Elman networks, second-order RNNs, and newer RNN types—on learning deterministic finite automata (DFA) from the Tomita grammar set. It finds that second-order RNNs consistently outperform others in rule extraction accuracy across all grammars, with a theoretical analysis of grammatical complexity via entropy and averaged edit distance explaining performance inconsistencies.

ABSTRACT

It has been shown that rules can be extracted from highly non-linear, recursive models such as recurrent neural networks (RNNs). The RNN models mostly investigated include both Elman networks and second-order recurrent networks. Recently, new types of RNNs have demonstrated superior power in handling many machine learning tasks, especially when structural data is involved such as language modeling. Here, we empirically evaluate different recurrent models on the task of learning deterministic finite automata (DFA), the seven Tomita grammars. We are interested in the capability of recurrent models with different architectures in learning and expressing regular grammars, which can be the building blocks for many applications dealing with structural data. Our experiments show that a second-order RNN provides the best and stablest performance of extracting DFA over all Tomita grammars and that other RNN models are greatly influenced by different Tomita grammars. To better understand these results, we provide a theoretical analysis of the complexity of different grammars, by introducing the entropy and the averaged edit distance of regular grammars defined in this paper. Through our analysis, we categorize all Tomita grammars into different classes, which explains the inconsistency in the performance of extraction observed across all RNN models.

Motivation & Objective

• To evaluate the rule extraction performance of diverse RNN architectures on learning regular grammars.
• To investigate why certain RNN models perform inconsistently across different Tomita grammars.
• To develop a theoretical framework for quantifying grammatical complexity to explain performance variations in rule extraction.
• To categorize Tomita grammars based on intrinsic structural complexity using entropy and averaged edit distance.

Proposed method

• Empirically evaluate multiple RNN architectures—including Elman and second-order RNNs—on learning deterministic finite automata (DFA) from the seven Tomita grammars.
• Apply rule extraction techniques to convert trained RNN models into interpretable logical rules.
• Define and compute the entropy of regular grammars as a measure of grammatical uncertainty.
• Introduce the averaged edit distance between strings in a grammar as a measure of structural complexity.
• Use these complexity metrics to classify Tomita grammars into distinct performance categories.
• Correlate the theoretical complexity measures with observed rule extraction accuracy across RNN models.

Experimental results

Research questions

• RQ1 How do different RNN architectures compare in extracting interpretable rules from regular grammars?
• RQ2 Why do some RNN models show inconsistent rule extraction performance across different Tomita grammars?
• RQ3 What intrinsic grammatical properties explain the performance variation in rule extraction across RNN models?
• RQ4 Can grammatical complexity be formally quantified using entropy and edit distance to predict rule extraction difficulty?
• RQ5 Which RNN architecture demonstrates the most stable and accurate rule extraction across all Tomita grammars?

Key findings

• Second-order RNNs achieve the most consistent and highest rule extraction accuracy across all seven Tomita grammars.
• Elman networks and other RNN variants show significant performance variation depending on the specific Tomita grammar, indicating sensitivity to grammatical structure.
• The proposed complexity metrics—entropy and averaged edit distance—successfully explain performance disparities across grammars.
• Tomita grammars can be meaningfully categorized into complexity classes based on these metrics, aligning with empirical rule extraction outcomes.
• Grammars with higher entropy and greater averaged edit distance tend to be more difficult to extract rules from, especially in simpler RNN architectures.
• The theoretical framework enables prediction of rule extraction difficulty without training, based solely on grammar structure.