Abstract
The behavior of simple recurrent neural networks trained on regular languages is analyzed in terms of accuracy and interpretability. We use controlled amounts of noise and L1 regularization to obtain stable and accurate responses that are at the same time highly interpretable, and introduce a shocking mechanism that reactivates silent neurons when learning stops due to an excessive regularization. Proper parameter tuning allows the networks to develop a strong generalization capacity, and at the same time provides solutions that may be interpreted as finite automata. Experiments carried out with different regular languages show that, in all cases, the trained networks display activation patterns that automatically cluster into a set of discrete states without any need to explicitly perform quantization. Analysis of the transitions between states in response to the input symbols reveals that the networks are in fact implementing a finite state machine that in all cases matches the regular expressions used to generate the training data.
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Notes
- 1.
In all the experiments carried out we set C = 5000. Whenever the network’s weights are shocked the number of training epochs is increased in order to give more time for the training to converge.
- 2.
We have performed experiments with different values of the shocking parameter \(\zeta \), and found that any value in the range [0.5, 1.2] provides similar results.
- 3.
The results for the complete set of Tomita grammars, including the activation color plots, the Isomap projections of the hidden layer activation space and the extracted automata (see Sect. 4.3) can be publicly accessed at our GitHub repo: https://github.com/slyder095/coliva_llago_icann2019.
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Acknowledgments
This work has been partially funded by grant S2017/BMD-3688 from Comunidad de Madrid and by Spanish project MINECO/FEDER TIN2017-84452-R (http://www.mineco.gob.es/).
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Oliva, C., Lago-Fernández, L.F. (2019). On the Interpretation of Recurrent Neural Networks as Finite State Machines. In: Tetko, I., Kůrková, V., Karpov, P., Theis, F. (eds) Artificial Neural Networks and Machine Learning – ICANN 2019: Theoretical Neural Computation. ICANN 2019. Lecture Notes in Computer Science(), vol 11727. Springer, Cham. https://doi.org/10.1007/978-3-030-30487-4_25
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