论文标题
输入驱动的复发神经网络中的回声指数和多稳定性
The Echo Index and multistability in input-driven recurrent neural networks
论文作者
论文摘要
复发性神经网络（RNN）具有回声状态属性（ESP），如果对于给定的输入序列，``忘记''''''''''''''''任何内部状态''（非自主）系统的任何内部状态并渐近地遵循独特的，可能是复杂的轨迹。通常，缺乏ESP被理解为RNN中缺乏可靠的行为。在这里，我们表明，RNN可以在更一般的原理下可靠地执行计算，该原则仅解释其在相空间中的本地行为。为此，我们制定了ESP的概括，并引入了回声索引来表征驱动的RNN的同时稳定响应的数量。我们表明，回声索引可能会随输入而变化，这突出了RNN中的潜在计算错误来源，这是由于驱动动力学的输入的特征。
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.
