{
  "abstract": "Accurate measurements of Cosmic Microwave Background (CMB) B-mode polarization, a key probe of inflationary physics, are hindered by complex Galactic dust foregrounds. Traditional foreground removal with Internal Linear Combination (ILC) fully preserves the primordial signal but requires multi-frequency data and is limited to two-point statistics. We present a novel way to estimate and remove foregrounds at single frequency using signal-preserving machine learning that leverages inter-scale correlations. Using the DustFilaments simulations, we train CNNs to reconstruct large-scale foregrounds ($\\ell < 200$) from small-scales ($\\ell > 200$). We quantify the effectiveness of foreground removal with the residual foreground power, $f_{\\rm{resid}}$, which gives the fraction of foreground power remaining after removal. Predictions using only small-scale $B$-modes achieve $f_{\\rm{resid}}\\simeq 0.704$, while adding temperature and $E$-modes decreases it to $f_{\\rm{resid}} \\simeq 0.376$. These results are still higher than the spatial ILC, which leverages multi-frequency data at Simons-Observatory-like frequencies. However, a hybrid network that uses both multi-frequency and inter-scale correlations attains $f_{\\rm{resid}}=4.71\\times10^{-4}$ when using $B$-mode inputs alone, and $3.62\\times10^{-4}$ when using temperature and $E/B$-mode inputs. This network achieves a residual power of $\\sim 7\\times$ lower than ILC, while inheriting ILC's signal-preserving property. This is $\\sim 2$--$3\\times$ lower than a network that only uses multi-frequency inputs, demonstrating that correlations across scale are not redundant with correlations across frequency and that our techniques are complementary to multi-frequency foreground removal. However, this is achieved only for DustFilments and network generalization across simulations remains a key challenge for robust ML-based foreground removal. (abridged)",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.28712",
  "author_total": 5,
  "authors": [
    {
      "name": "Helen Shao"
    },
    {
      "name": "Fiona McCarthy"
    },
    {
      "name": "Blake D. Sherwin"
    },
    {
      "name": "Miles Cranmer"
    },
    {
      "name": "Carlos Hervias-Caimapo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/beawnetgspafy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.28712",
  "fulltext_url": null,
  "id": "beawnetgspafy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.28712",
  "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",
      "astro-ph.CO"
    ],
    [
      "openalex",
      "3103|Cosmology and Gravitation Theories"
    ]
  ],
  "openalex": "W7172310701",
  "pdf_url": "https://arxiv.org/pdf/2607.28712",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/beawnetgspafy.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:30Z",
      "native_id": "2607.28712",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.28712"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.CO",
      "subfield": "cosmology"
    }
  ],
  "title": "Single Frequency CMB Foreground Removal with Inter-scale Machine Learning",
  "title_text": "Single Frequency CMB Foreground Removal with Inter-scale Machine Learning",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:30Z",
  "url": "https://research.draconitic.com/paper/beawnetgspafy",
  "venue": "arXiv",
  "versions": []
}