Tootfinder

Single-graph inference for fractal Gaussian networks
Chunhao Cai
https://arxiv.org/abs/2610.11597 https://arxiv.org/pdf/2610.11597 https://arxiv.org/html/2610.11597
arXiv:2610.11597v1 Announce Type: new
Abstract: We study inference on the strength of Gaussian multiplicative chaos from one geometric graph with unobserved vertex positions. In the planar model, the edge-count statistic has a piecewise deterministic limit with a transition at $\gamma=1$, whereas degree quantiles consistently estimate $\nu=\gamma^2/2$ throughout the subcritical range. Fractional moments give uniform finite-sample risk bounds. At finite resolution, common graph envelopes calibrate tests over continuous parameter boxes with unknown Poisson intensity. They give simultaneous coverage under adaptive refinement for a fixed statistic, and conditional coverage for an independently piloted size--degree residual on a fixed partition. For the exact periodic FFT--pixel approximation, we prove explicit total-variation rates for the annealed spatial Cox law and the observed graph law, uniformly on every compact subcritical range $0\le\gamma\le\Gamma<2$. The rates allow intensity to grow with resolution and imply uniform asymptotic coverage after recalibration at each resolution. Numerical studies examine parameter refinement, residual calibration, and multiresolution stability.
toXiv_bot_toot

#Sunrise just now
#Sonnenaufgang #Clouds #Wolken

Beyond the Edge of Chaos: Stability-Expressivity Transfer in Reservoir Forecasting
Yao Du, Xingang Wang
https://arxiv.org/abs/2607.17909 https://arxiv.org/pdf/2607.17909 https://arxiv.org/html/2607.17909
arXiv:2607.17909v1 Announce Type: new
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. 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.
toXiv_bot_toot