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

arXiv: https://arxiv.org/abs/2009.13101 · HTML: https://mlsanity.com/paper/2009.13101/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Sep 2020.

## Built on by (most cited first, 6 of 6)

- [On the Tractability of SHAP Explanations under Markovian Distributions](https://mlsanity.com/paper/2405.02936/) (2024)
- [Linguistically inspired roadmap for building biologically reliable protein language models](https://mlsanity.com/paper/2207.00982/) (2022)
- [Implicit N-grams Induced by Recurrence](https://mlsanity.com/paper/2205.02724/) (2022)
- [Simulating Weighted Automata over Sequences and Trees with Transformers](https://mlsanity.com/paper/2403.09728/) (2024)
- [Extracting Weighted Automata for Approximate Minimization in Language Modelling](https://mlsanity.com/paper/2106.02965/) (2021)
- [PDFA Distillation via String Probability Queries](https://mlsanity.com/paper/2406.18328/) (2024)

## Abstract (arXiv)

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.