From Formal Language Theory to Statistical Learning: Finite Observability of Subregular Languages

Generative AI & LLMs

Published: arXiv: 2509.22598v1

Authors

Katsuhiko Hayashi Hidetaka Kamigaito

Abstract

We prove that all standard subregular language classes are linearly separable when represented by their deciding predicates. This establishes finite observability and guarantees learnability with simple linear models. Synthetic experiments confirm perfect separability under noise-free conditions, while real-data experiments on English morphology show that learned features align with well-known linguistic constraints. These results demonstrate that the subregular hierarchy provides a rigorous and interpretable foundation for modeling natural language structure. Our code used in real-data experiments is available at https://github.com/UTokyo-HayashiLab/subregular.

Paper Summary

Problem

The main problem this paper addresses is understanding how natural language patterns can be learned and modeled using simple and interpretable methods. Current machine learning models, such as deep neural networks, are often complex and difficult to understand, but natural language patterns are thought to reside in a more restricted region of the hierarchy.

Key Innovation

The key innovation of this paper is the concept of "finite observability," which shows that all standard subregular language classes are linearly separable when represented by their deciding predicates. This means that these language classes can be learned using simple linear models, which are easy to understand and interpret.

Practical Impact

This research has significant practical implications for natural language processing. By showing that natural language patterns can be learned using simple linear models, this work provides a foundation for developing lightweight, interpretable models that can be used in a variety of applications, such as language learning and text analysis. This could lead to more effective and efficient language models that are easier to understand and use.

Analogy / Intuitive Explanation

Think of natural language patterns as a puzzle with a limited number of pieces. Traditional machine learning models try to solve the puzzle by considering all possible pieces, which can be overwhelming. In contrast, the concept of finite observability shows that the puzzle can be solved by considering only a limited number of pieces, which are the deciding predicates. This approach is more efficient and easier to understand, and it provides a foundation for developing more effective and interpretable language models.

Paper Information

Categories:

cs.CL cs.FL cs.LG

Published Date:

arXiv ID:

2509.22598v1

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