Stability of Internal States in Recurrent Neural Networks Trained on Regular Languages

TL;DR

This paper empirically investigates how recurrent neural networks trained on regular languages exhibit stable, automaton-like internal states that are resilient to noise and perturbations, supporting their interpretation as finite automata.

Contribution

It demonstrates that RNNs trained on regular languages develop stable, discrete internal states resembling finite automata, even under noisy conditions.

Findings

Neurons tend to saturate to compensate for noise.

Internal states form clusters similar to finite automata states.

Networks recover from perturbations and maintain stability over long sequences.

Abstract

We provide an empirical study of the stability of recurrent neural networks trained to recognize regular languages. When a small amount of noise is introduced into the activation function, the neurons in the recurrent layer tend to saturate in order to compensate the variability. In this saturated regime, analysis of the network activation shows a set of clusters that resemble discrete states in a finite state machine. We show that transitions between these states in response to input symbols are deterministic and stable. The networks display a stable behavior for arbitrarily long strings, and when random perturbations are applied to any of the states, they are able to recover and their evolution converges to the original clusters. This observation reinforces the interpretation of the networks as finite automata, with neurons or groups of neurons coding specific and meaningful input patterns.