Distillation of Weighted Automata from Recurrent Neural Networks using a Spectral Approach

TL;DR

This paper introduces a spectral method to distill weighted automata from trained recurrent neural networks, enabling more efficient computation and offering insights into RNN behavior for language modeling.

Contribution

It presents a novel spectral algorithm that extracts weighted automata from RNNs without internal access, bridging deep learning and grammatical inference.

Findings

Extracted automata closely approximate RNN outputs

Method improves interpretability of RNNs

Validated on 62 diverse datasets

Abstract

This paper is an attempt to bridge the gap between deep learning and grammatical inference. Indeed, it provides an algorithm to extract a (stochastic) formal language from any recurrent neural network trained for language modelling. In detail, the algorithm uses the already trained network as an oracle -- and thus does not require the access to the inner representation of the black-box -- and applies a spectral approach to infer a weighted automaton. As weighted automata compute linear functions, they are computationally more efficient than neural networks and thus the nature of the approach is the one of knowledge distillation. We detail experiments on 62 data sets (both synthetic and from real-world applications) that allow an in-depth study of the abilities of the proposed algorithm. The results show the WA we extract are good approximations of the RNN, validating the approach. Moreover, we show how the process provides interesting insights toward the behavior of RNN learned on data, enlarging the scope of this work to the one of explainability of deep learning models.