The Information Content of Krylov Observables: A Machine Learning Approach

• URL: http://arxiv.org/abs/2607.17346v1
• Date: Sun, 19 Jul 2026 17:17:21 GMT
• Title: The Information Content of Krylov Observables: A Machine Learning Approach
• Abstract summary: We quantify the spread complexity $mathcalC(t)$, the discrete Wigner negativity $N(t)$, and the normalized negativity $(t)=N(t)/|S(t)|$, with $S(t)$ the survival amplitude, recently proposed as a second-moment infall probe (arXiv:2607.04065).<n>Small residual networks (16-32 neurons) and boosted trees are trained on half of $sim 57,000$ labeled evolutions spanning the GUE, GOE and Poisson ensembles, the integrable $SL
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We employ machine learning to quantify the information carried by three Krylov-space observables: the spread complexity $\mathcal{C}(t)$, 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 $\sim 57{,}000$ labeled evolutions spanning the GUE, GOE and Poisson ensembles, the integrable $SL(2,\mathbb{R})$/CFT sector, and the chaos interpolation $H(\varepsilon)=H_{SL(2,\mathbb{R})}+\varepsilon R_0 W_{GUE}$. Either moment determines the thermofield temperature at $R^2\simeq 0.999$. Neither reconstructs the fine spectral form factor ($R^2\simeq 0.18$ 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 $e^S$ plateau is nevertheless recovered at $R^2=0.861$, mostly from the first 20% of $\mathcal{C}(t)$. 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 ($N\to h$: 0.999). Along the interpolation the asymmetry gap of $χ$ over $\mathcal{C}$ 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.

Related papers

• Zero-SNR Analyticity of the Scalar MMSE Is Equivalent to Gaussianity [0.7499255435598924]
  We prove that the minimum mean-square error $operatornamemmse_X(s)$ is analytic at zero signal-to-noise ratio if and only if $X$ is Gaussian.<n>A zero of $mgeq 2$ splits according to the roots of a Hermitemath and instead contributes a prefactor $n-m/2er_msqrt2n$.
  arXiv  Detail & Related papers  (2026-09-14T05:07:20Z)
• Solving Stochastic Fixed-Point Equations with High Probability [22.376855234542813]
  We study oracle fixed-point equations $mathbfT(mathbfx) = mathbfx$ over normed spaces.<n>We introduce VR-GHAL, a variance-reduced gradual Halpern method for quadratically smoothable Banach spaces.
  arXiv  Detail & Related papers  (2026-07-10T04:59:20Z)
• Activation Saturation and Floquet Spectrum Collapse in Neural ODEs [0.0]
  This is a collapse of the Floquet spectrum: as saturation deepens, all exponents are driven to zero.<n>As a secondary contribution, a saturation- spectral factorisation yields a refined bound $widetildeC(U)le C(U)$ whose improvement is exponentially amplified in$T$ at the flow level.
  arXiv  Detail & Related papers  (2026-04-01T06:39:56Z)
• Rényi exponent landscape of multipartite entanglement in free-fermion systems [51.56484100374058]
  We show that the Rényi tripartite information $I_3() exhibits a qualitatively $exclusion-dependent scaling at small Fermi momentum.<n>A direct consequence is a replica obstruction: $I_m(n)/I_m(1) sim zm-1 to 0$ for all integer $n geq 2$, so the leading von Neumann signal cannot be reconstructed from integer Rényi data.
  arXiv  Detail & Related papers  (2026-03-09T22:27:00Z)
• Spectral statistics and energy-gap scaling in $k-$local spin Hamiltonians [0.0]
  We investigate the spectral properties of all-to-all interacting spin Hamiltonians acting on exactly $k$ spins.<n>For $mu = 0$, we demonstrate that the random matrix ensemble is determined by the parity of system size $L$ and locality $k$.<n>Our work introduces a semi-solvable model that captures universal features of random-matrix statistics, and spectral gap formation.
  arXiv  Detail & Related papers  (2025-10-17T17:11:38Z)
• Information-Computation Tradeoffs for Noiseless Linear Regression with Oblivious Contamination [65.37519531362157]
  We show that any efficient Statistical Query algorithm for this task requires VSTAT complexity at least $tildeOmega(d1/2/alpha2)$.
  arXiv  Detail & Related papers  (2025-10-12T15:42:44Z)
• A Unified Framework for Uniform Signal Recovery in Nonlinear Generative Compressed Sensing [68.80803866919123]
  Under nonlinear measurements, most prior results are non-uniform, i.e., they hold with high probability for a fixed $mathbfx*$ rather than for all $mathbfx*$ simultaneously. Our framework accommodates GCS with 1-bit/uniformly quantized observations and single index models as canonical examples. We also develop a concentration inequality that produces tighter bounds for product processes whose index sets have low metric entropy.
  arXiv  Detail & Related papers  (2023-09-25T17:54:19Z)
• Statistical Learning under Heterogeneous Distribution Shift [71.8393170225794]
  Ground-truth predictor is additive $mathbbE[mathbfz mid mathbfx,mathbfy] = f_star(mathbfx) +g_star(mathbfy)$.
  arXiv  Detail & Related papers  (2023-02-27T16:34:21Z)
• Optimal Robust Linear Regression in Nearly Linear Time [97.11565882347772]
  We study the problem of high-dimensional robust linear regression where a learner is given access to $n$ samples from the generative model $Y = langle X,w* rangle + epsilon$ We propose estimators for this problem under two settings: (i) $X$ is L4-L2 hypercontractive, $mathbbE [XXtop]$ has bounded condition number and $epsilon$ has bounded variance and (ii) $X$ is sub-Gaussian with identity second moment and $epsilon$ is
  arXiv  Detail & Related papers  (2020-07-16T06:44:44Z)
• Agnostic Learning of a Single Neuron with Gradient Descent [92.7662890047311]
  We consider the problem of learning the best-fitting single neuron as measured by the expected square loss. For the ReLU activation, our population risk guarantee is $O(mathsfOPT1/2)+epsilon$. For the ReLU activation, our population risk guarantee is $O(mathsfOPT1/2)+epsilon$.
  arXiv  Detail & Related papers  (2020-05-29T07:20:35Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.