{
  "abstract": "Equivariant graph neural networks have emerged as foundational architectures for machine-learned interatomic potentials, approaching quantum-chemical accuracy at a fraction of the computational cost. These models describe local atomic environments accurately, but finite spatial cutoffs truncate long-range information flow, and stacking message-passing layers can lead to over-smoothing and over-squashing. Existing long-range extensions either prescribe a fixed analytical propagation kernel, restrict long-range communication to scalars or degree-preserving channels, are only approximately equivariant, or incur super-linear computational cost. Combining learnable long-range equivariant transport with multiscale many-body expressivity and efficient scaling for larger systems remains a central challenge. We introduce Neural Equivariant Multipole Operators (NEMORA), a neural equivariant extension of the Fast Multipole Method (FMM) for learning long-range tensorial representations. NEMORA generalizes the FMM's analytical multipole expansion and translation operators to learned equivariant counterparts on an adaptive spatial hierarchy. Its operators couple angular degrees and form many-body interactions across length scales, retaining the FMM's hierarchical organization and analytical radial factors as physical inductive biases while learning data-dependent long-range couplings. NEMORA evaluates in linear time and memory complexity, allowing it to treat larger systems than other long-range methods reaching hundreds of thousands of atoms, and it augments both symmetry-constrained and unconstrained short-range backbones. On non-local benchmarks, it reduces force and energy errors relative to the short-range backbones by over an order of magnitude and up to three orders of magnitude, respectively, which is better than or competitive with existing long-range extensions in accuracy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10776",
  "author_total": 4,
  "authors": [
    {
      "name": "Jay L. Kaplan"
    },
    {
      "name": "Samuel Varner"
    },
    {
      "name": "Rebecca Willett"
    },
    {
      "name": "Juan J. de Pablo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fw44a5gs7h3ze.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10776",
  "fulltext_url": null,
  "id": "fw44a5gs7h3ze",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10776",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "physics.chem-ph"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "openalex",
      "2505|Machine Learning in Materials Science"
    ]
  ],
  "openalex": "W7221187926",
  "pdf_url": "https://arxiv.org/pdf/2610.10776",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fw44a5gs7h3ze.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:54Z",
      "native_id": "2610.10776",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10776"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    }
  ],
  "title": "NEMORA: Neural Equivariant Multipole Operators for Long-Range Atomistic Learning",
  "title_text": "NEMORA: Neural Equivariant Multipole Operators for Long-Range Atomistic Learning",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:54Z",
  "url": "https://research.draconitic.com/paper/fw44a5gs7h3ze",
  "venue": "arXiv",
  "versions": []
}