The edge-of-chaos heuristic has long served as a guiding principle for designing reservoir computers, yet its relevance to machine performance remains elusive. Here, taking the spectral radius of the reservoir network as the control parameter, we show that the radius yielding the best forecasting performance does not coincide with the Lyapunov edge of the isolated, teacher-forced, or closed-loop generative reservoir. By analyzing the collective dynamics of the teacher-forced reservoir, we find that the target dynamics are represented mainly by stable Lyapunov modes whose finite-time stability is strongly modulated by the input. This finding motivates a stability-expressivity transfer index, which balances the stability of these modes against their expressivity in representing the target. Across chaotic and quasiperiodic targets, and for both asymmetric and symmetric reservoirs, this index accurately identifies the optimal spectral radius for autonomous forecasting.
In this paper, we propose a new solution for addressing the content cold-start problem in industry-scale search and recommender systems. Compared to prior approaches, we have made the following new contributions: 1) our solution spans the entire multi-stage funnel and generalizes…
Dysphagia is a debilitating late effect of head and neck cancer (HNC) treatment, yet timely identification of at-risk patients remains challenging in survivorship care. Definitive assessment relies on videofluoroscopic imaging, as captured by the Dynamic Imaging Grade of Swallowi…
We show how large-deviation statistics allows one to obtain reliable estimates of the multiplicity of stable fixed-points in a model of neural ordinary differential equations previously employed in computational tasks. The result is obtained by developing a suitable perturbative…
Singular value soft-thresholding can be computed via a reduction to the matrix polar decomposition, which allows one to exploit GPU-friendly algorithms for computing the polar decomposition. Empirically, there is a significant speed-up on GPUs compared to the standard approach us…
A central design principle in modern machine learning and artificial intelligence is to align a model's inductive bias with the structure of its input data. For matrix-valued inputs, relevant matrix-level relationships can be characterised through spectral values and spectral sub…
Automating theoretical research is constrained not only by the generation of candidate results, but also by their reliable evaluation. A common approach is to close the research loop with a large language model (LLM) reviewer. However, such reviewers remain empirically unreliable…