{
  "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 $b_n=α\\sqrt{n(n+2h-1)}$. To introduce chaos we add a GUE random matrix to the integrable chain, $H(\\varepsilon)=H_{SL(2,R)}+\\varepsilon R_0 W_{GUE}$, where $R_0$ is its spectral half-width. Either $C(t)$ or $N(t)$ alone determines the thermofield temperature, with $R^2\\simeq0.999$. 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 $S$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.17346",
  "author_total": 1,
  "authors": [
    {
      "name": "Ritam Basu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/basdhagq5s7y8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.17346",
  "fulltext_url": null,
  "id": "basdhagq5s7y8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.17346",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.dis-nn"
    ],
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      "arxiv",
      "cond-mat.stat-mech"
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      "arxiv",
      "quant-ph"
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      "openalex",
      "3109|Quantum chaos and dynamical systems"
    ]
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  "openalex": "W7169838277",
  "pdf_url": "https://arxiv.org/pdf/2607.17346",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/basdhagq5s7y8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2607.17346",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.17346"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "The Information Content of Krylov Observables: A Machine Learning Approach",
  "title_text": "The Information Content of Krylov Observables: A Machine Learning Approach",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/basdhagq5s7y8",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1103/hqts-lp2n",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}