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arXiv · 2001.07694

The Echo Index and multistability in input-driven recurrent neural networks

Andrea Ceni·Peter Ashwin·Lorenzo Livi·Claire Postlethwaite
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Abstract

A recurrent neural network (RNN) possesses the echo state property (ESP) if, for a given input sequence, it ``forgets'' any internal states of the driven (nonautonomous) system and asymptotically follows a unique, possibly complex trajectory. The lack of ESP is conventionally understood as a lack of reliable behaviour in RNNs. Here, we show that RNNs can reliably perform computations under a more general principle that accounts only for their local behaviour in phase space. To this end, we formulate a generalisation of the ESP and introduce an echo index to characterise the number of simultaneously stable responses of a driven RNN. We show that it is possible for the echo index to change with inputs, highlighting a potential source of computational errors in RNNs due to characteristics of the inputs driving the dynamics.

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Andrea Ceni, Peter Ashwin, Lorenzo Livi, Claire Postlethwaite. 2020-01-21. The Echo Index and multistability in input-driven recurrent neural networks. https://doi.org/10.1016/j.physd.2020.132609

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