Re-visiting the echo state property

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Randomness in neural networks: an overview (2017, background): “in 2012.(106,107) Taking into account the random initialization of the reservoir, Zhang et al.”
Echo state networks are universal (2018, background): “…3.2 Consider echo state network given by Remark 3.3 The hypothesis (cid:107) A 2 L σ 1 appears in the literature as a suﬃcient condition to ensure the echo state property, which has been extensively studied in the ESN literature [Jaeg 10, Jaeg 04, Bueh 06, Bai 12, Yild 12, Wain 16, Manj 13].”
Controlling Recurrent Neural Networks by Conceptors (2014, background): “The echo state property is a fundamental condition for RNNs to be useful in learning tasks [54, 13, 46, 110, 99, 71].”
Recent Advances in Physical Reservoir Computing: A Review (2018, background): “It is also referred to as the echo state property, indicating that the influence of past inputs on the current reservoir states and outputs asymptotically fades out (Jaeger, 2001; Yildiz, Jaeger, & Kiebel, 2012).”
Physical reservoir computing—an introductory perspective (2020, background): “[42–44]) and understanding its relation to the nonlinear dynamical systems ﬁeld are still ongoing research topics (e.g., Ref.”