The Information Content of Krylov Observables: A Machine Learning Approach
Abstract
We employ machine learning techniques to estimate the amount of information contained in 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)|, where S(t) is the survival amplitude. We study thermofield-double evolutions on GUE, GOE and Poisson spectra, and on the integrable SL(2,R) Krylov chain of a two-dimensional CFT primary, with Lanczos coefficients bn=α√(n(n+2h−1)). To introduce chaos we add a GUE random matrix to the integrable chain, H(ε)=HSL(2,R)+ε R0 WGUE, where R0 is its spectral half-width. Either C(t) or N(t) alone determines the thermofield temperature, with R2≃0.999. However, neither can reconstruct the fine structure of the spectral form factor. In the integrable sector all three observables carry the same information. When we turn on chaos an asymmetry appears: χ predicts C better than C predicts χ. This gap grows from +0.33 to +0.77, while the same gap for the raw negativity decays to zero. The extra information comes from the survival amplitude, and χ(t) carries it while C(t) can still be recovered from χ(t). We derive a lower bound on this gap, set by the fraction of the variance of χ that comes from S.
Versions
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BibTeX
@misc{basu2026information,
title = {{The Information Content of Krylov Observables: A Machine Learning Approach}},
author = {Ritam Basu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.17346},
eprint = {2607.17346},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.17346},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Information Content of Krylov Observables: A Machine Learning Approach
AU - Ritam Basu
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2607.17346
UR - https://arxiv.org/abs/2607.17346
AB - We employ machine learning techniques to estimate the amount of information contained in 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)|, where S(t) is the survival amplitude. We study thermofield-double evolutions on GUE, GOE and Poisson spectra, and on the integrable SL(2,R) Krylov chain of a two-dimensional CFT primary, with Lanczos coefficients b_n=α√(n(n+2h−1)). To introduce chaos we add a GUE random matrix to the integrable chain, H(ε)=H_SL(2,R)+ε R_0 W_GUE, where R_0 is its spectral half-width. Either C(t) or N(t) alone determines the thermofield temperature, with R^2≃0.999. However, neither can reconstruct the fine structure of the spectral form factor. In the integrable sector all three observables carry the same information. When we turn on chaos an asymmetry appears: χ predicts C better than C predicts χ. This gap grows from +0.33 to +0.77, while the same gap for the raw negativity decays to zero. The extra information comes from the survival amplitude, and χ(t) carries it while C(t) can still be recovered from χ(t). We derive a lower bound on this gap, set by the fraction of the variance of χ that comes from S.
ER -