On Computability, Learnability and Extractability of Finite State Machines from Recurrent Neural Networks

TL;DR

This paper explores the theoretical and practical connections between recurrent neural networks and finite state machines, focusing on extractability, learnability, and computational equivalence, with new insights and formal frameworks.

Contribution

It introduces a new framework for approximating RNNs with FSMs, extends active learning methods, and provides computational results on RNN-FSM equivalence.

Findings

Insights into the clustering hypothesis of RNN hidden states.

A new active learning framework for RNN approximation.

Computational results on RNN and FSM distance and equivalence.

Abstract

This work aims at shedding some light on connections between finite state machines (FSMs), and recurrent neural networks (RNNs). Examined connections in this master's thesis is threefold: the extractability of finite state machines from recurrent neural networks, learnability aspects and computationnal links. With respect to the former, the long-standing clustering hypothesis of RNN hidden state space when trained to recognize regular languages was explored, and new insights into this hypothesis through the lens of recent advances of the generalization theory of Deep Learning are provided. As for learnability, an extension of the active learning framework better suited to the problem of approximating RNNs with FSMs is proposed, with the aim of better formalizing the problem of RNN approximation by FSMs. Theoretical analysis of two possible scenarions in this framework were performed. With regard to computability, new computational results on the distance and the equivalence problem between RNNs trained as language models and different types of weighted finite state machines were given.