{
  "abstract": "Can attention move a shock across several cells in one update without breaking it? We develop a conservative, fixed grid finite-volume scheme in which a CFL-conditioned attention flux selects upstream information according to the transport required by the current time step. One-dimensional inviscid Burgers transport is used as the central mechanism test: the same learned flux remains reliable in the conventional small-step regime and, with a time step four times larger, preserves sharp shocks while using one stage per update. A standard fifth-order WENO scheme with third-order strong-stability-preserving Runge-Kutta time integration (WENO-5+SSP-RK3) is included alongside controlled Forward Euler comparisons to separate flux selection from time integration. The learned attention shifts upstream with the local transport reach and becomes more selective near shocks; inference-time interventions and retrained ablations show that transport-scale information and state-dependent selection contribute directly to performance. Directional two-dimensional scalar Burgers transport and the one-dimensional shallow-water system then test whether the conservation-scale-selection principle transfers beyond the original scalar setting. The results support attention as a learnable information stencil for conservative large-step shock transport, while identifying finite candidate reach and problem-dependent robustness as the present limits.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13531",
  "author_total": 6,
  "authors": [
    {
      "name": "Jinyoung Jeong"
    },
    {
      "name": "Joseph B. Choi"
    },
    {
      "name": "Xinlun Cheng"
    },
    {
      "name": "H. S. Udaykumar"
    },
    {
      "name": "Sanghun Choi"
    },
    {
      "name": "Stephen S. Baek"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e6kesxtnc7rya.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13531",
  "fulltext_url": null,
  "id": "e6kesxtnc7rya",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13531",
  "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.AI"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "2206|Computational Fluid Dynamics and Aerodynamics"
    ]
  ],
  "openalex": "W7213371172",
  "pdf_url": "https://arxiv.org/pdf/2609.13531",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e6kesxtnc7rya.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:48Z",
      "native_id": "2609.13531",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13531"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Attention Is All You Need (to Avoid Spurious Oscillations)",
  "title_text": "Attention Is All You Need (to Avoid Spurious Oscillations)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:48Z",
  "url": "https://research.draconitic.com/paper/e6kesxtnc7rya",
  "venue": "arXiv",
  "versions": []
}