{
  "abstract": "CoVariance Neural Networks and their extensions have emerged as effective tools for processing multivariate data, deriving graph shift operators directly from second-order statistics. These architectures, however, are designed for independent and identically distributed observations and do not fully capture the joint structure of temporal and cross-variable dependencies in multivariate time series. In this work, we introduce Inverse Cross-Spectral Neural Networks (iCSNNs), a class of graph neural networks for stationary multivariate time series whose shift operators are the inverse cross-spectral density (iCSD) matrices. These operators encode frequency-specific conditional relationships among variables, exploiting the decomposition provided by the spectral representation theorem. Leveraging spectral smoothness, frequencies are grouped into bands sharing a single iCSD operator, yielding a compact parametrisation that retains the frequency-dependent structure of the process. We further propose a joint learning procedure to estimate both the Fourier-domain dependence structure and the iCSNN parameters, adapting the iCSD operators to the downstream task. When tested on synthetic data, iCSNN outperforms baselines from different methodological families.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06630",
  "author_total": 5,
  "authors": [
    {
      "name": "Lorenzo Marinucci"
    },
    {
      "name": "Leonardo Di Nino"
    },
    {
      "name": "Gabriele D'Acunto"
    },
    {
      "name": "Paolo Di Lorenzo"
    },
    {
      "name": "Sergio Barbarossa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6mdv3pk1qnbg0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06630",
  "fulltext_url": null,
  "id": "6mdv3pk1qnbg0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06630",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "eess.SP"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Advanced Graph Neural Networks"
    ]
  ],
  "openalex": "W7220674388",
  "pdf_url": "https://arxiv.org/pdf/2610.06630",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6mdv3pk1qnbg0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:16Z",
      "native_id": "2610.06630",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06630"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Inverse Cross-spectral Neural Networks for Multivariate Time Series",
  "title_text": "Inverse Cross-spectral Neural Networks for Multivariate Time Series",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:16Z",
  "url": "https://research.draconitic.com/paper/6mdv3pk1qnbg0",
  "venue": "arXiv",
  "versions": []
}