arXiv:2404. 17429v4 Announce Type: replace-cross Abstract: A natural hypothesis for the success of reservoir computing in generic tasks is the ability of the untrained reservoir to map distinct input time series to separable reservoir states, a property we term separation capacity.
arXiv:2607. 17858v1 Announce Type: cross Abstract: Reservoir computing exploits nonlinear dynamical systems to encode temporal inputs into high-dimensional state space representations.
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.
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.
arXiv:2606. 28486v1 Announce Type: cross Abstract: The emergence of low-dimensional structures in the spectra of neural network weight matrices is a common empirical feature of trained models, but the dynamical origin of this phenomenon during learning remains an open problem.
arXiv:2607. 14304v1 Announce Type: cross Abstract: We study sparse random geometric graphs generated by connecting pairs of high-dimensional vectors whose inner product exceeds a threshold.
arXiv:2607. 24420v1 Announce Type: cross Abstract: Reservoir computing has emerged as an efficient machine learning framework for predicting time series generated by dynamical systems.
arXiv:2602. 02908v2 Announce Type: replace-cross Abstract: Diffusion models trained on different, non-overlapping subsets of a dataset often produce strikingly similar outputs when given the same noise seed.
arXiv:2607. 18559v1 Announce Type: cross Abstract: Gaussian graphical model selection is usually studied under independent sampling, but in many applications the data arise as a single trajectory of a dependent stochastic process.
arXiv:2506. 08764v3 Announce Type: replace Abstract: Deep neural networks are known to suffer from exploding or vanishing gradients as depth increases, a phenomenon closely tied to the spectral behavior of the input-output Jacobian.
arXiv:2605. 01107v2 Announce Type: replace Abstract: Feedforward neural networks transform data through learned representations whose geometry shapes how classes separate and relate across successive layers.
arXiv:2511. 11927v2 Announce Type: replace-cross Abstract: Principal Component Analysis (PCA) is a standard tool for extracting a low-rank signal from noisy observations.
arXiv:2608. 08350v1 Announce Type: new Abstract: The initialisation of deep neural networks determines whether information and gradients can propagate across depth, yet a unified theory connecting these properties to learning dynamics remains elusive.