The paper investigates how training shapes the geometry of recurrent network dynamics in Reservoir Computing (RC) networks used for temporal forecasting. It demonstrates that, in a linear continuous-time reservoir with infinite data, training data create an invariant subspace whose dimension matches the number of dominant modes. For a simplified diagonal linear reservoir, the study connects dominant eigenvalues and eigenvectors to the spectrum of a backward Dynamic Mode Decomposition matrix, providing a finite-dimensional approximation of the backward-time Koopman operator, and illustrates these phenomena through simulation while suggesting extensions to nonlinear RC.
By Noa Kaplan, Alberto Padoan, Anastasia Bizyaeva
arXiv:2607. 17858v1 Announce Type: cross Abstract: Reservoir computing exploits nonlinear dynamical systems to encode temporal inputs into high-dimensional state space representations.
By Mohab Abdalla, Damien Rontani
arXiv:2512.12767v2 Announce Type: replace-cross
Abstract: Training recurrent neuronal networks consisting of excitatory (E) and inhibitory (I) units with additive noise for working memory computation...
By Thiparat Chotibut, Oleg Evnin, Weerawit Horinouchi
arXiv:2608. 14638v1 Announce Type: new Abstract: In this paper we study autoencoders, a special class of deep neural nets (DNNs) whose performance can be characterized via their fixed points.
By Leonid Berlyand, Roman Sarapin, Yitzchak Shmalo, Victor Slavin, Sasha Sodin
arXiv:2609.13920v1 Announce Type: cross
Abstract: Persistent Gaussian perturbations have been shown to prevent asymptotic oversmoothing in recurrent Graph Neural Networks (GNNs) by ensuring a positiv...
By Mostafa Haghir Chehreghani
arXiv:2607. 17909v1 Announce Type: cross Abstract: The edge-of-chaos heuristic has long served as a guiding principle for designing reservoir computers, yet its relevance to machine performance remains elusive.
By Yao Du, Xingang Wang