Residual connections have been proposed as architecture-based inductive bias to mitigate the problem of exploding and vanishing gradients and increase task performance in both feed-forward and recurrent networks (RNNs) when trained with the backpropagation algorithm. Yet, little is known about how residual connections in RNNs influence their dynamics and fading memory properties. Here, we introduce weakly coupled residual recurrent networks (WCRNNs) in which residual connections result in well-defined Lyapunov exponents and allow for studying properties of fading memory. We investigate how the residual connections of WCRNNs influence their performance, network dynamics, and memory properties on a set of benchmark tasks. We show that several distinct forms of residual connections yield effective inductive biases that result in increased network expressivity. In particular, residual connections that (i) result in network dynamics at the proximity of the edge of chaos, (ii) allow networks to capitalize on characteristic spectral properties of the data, and (iii) result in heterogeneous memory properties are shown to increase practical expressivity. In addition, we demonstrate how our results can be extended to non-linear residuals and introduce a weakly coupled residual initialization scheme that can be used for Elman RNNs

通过引入弱耦合残差循环神经网络（WCRNNs），本研究调查了残差连接对性能、网络动力学和记忆属性的影响，并展示了特定形式的残差连接如何提高实用表达能力。

残差循环网络中的褪色记忆作为归纳偏差