2026/07/19 by Ritam Basu
#hep-th #cond-mat.dis-nn #cond-mat.stat-mech #math-ph #math.MP #quant-ph
We employ machine learning to quantify the information carried by three Krylov-space observables: the spread complexity C(t), the discrete Wigner negativity N(t), and the normalized negativity χ(t)=N(t)/|S(t)|, with S(t) the survival amplitude, recently proposed as a second-moment infall probe (arXiv:2607.04065). Small residual networks (16-32 neurons) and boosted trees are trained on half of ∼ 57,000 labeled evolutions spanning the GUE, GOE and Poisson ensembles, the integrable SL(2,ℝ)/CFT sector, and the chaos interpolation H(ε)=HSL(2,ℝ)+ε R0 WGUE. Either moment determines the thermofield temperature at R2≃ 0.999. Neither reconstructs the fine spectral form factor (R2≃ 0.18 in every ensemble); smoothing the target does not repair this, and windows wide enough to help erase the dip-ramp physics itself: the SFF strictly refines both moments. The coarse eS plateau is nevertheless recovered at R2=0.861, mostly from the first 20% of C(t). A single curve identifies the symmetry class at up to 98% accuracy. In the integrable sector the observables are informationally equivalent, as exact negative-binomial slaving demands, while the negativity best resolves the (h,α) degeneracy (N→ h: 0.999). Along the interpolation the asymmetry gap of χ over C switches on with chaos, growing from +0.33 to +0.77 as the level statistics cross to GUE, while the raw-N gap decays to zero. The second-moment informational surplus is therefore a signature of chaos, carried specifically by the normalized negativity, and we derive an analytical mechanism and a quantitative bound for it.