{
  "abstract": "How many directions in weight space does training need? The intrinsic dimension answers this with the smallest number of random directions in which training still reaches a target accuracy, and small values have motivated parameter-efficient methods such as LoRA. We measure it for variational Monte Carlo (VMC), which trains a neural network to represent the ground state of a quantum many-body system. VMC is a demanding test, because the network generates its own training samples and every gradient is noisy, and a revealing one, because the exact answer is known and every run can be scored. We train only a small latent vector that a frozen random map turns into the network's weights, with no change to the standard natural-gradient optimizer. We find that a small dimension can be misleading, while the stability it brings is real. On a magnet with a hard sign pattern, a network that cannot represent signs reaches its best energy in 8 of 28,642 directions, but only because no such network can go lower; once signs are learnable, neither the signs nor the magnitudes are cheap. The dimension rises across a quantum phase transition, so it tracks how difficult a state is at far less compute than fitting a scaling law, yet it never falls below a floor set by the random subspace itself, even where the ground state is nearly trivial. Training in the subspace, in contrast, never diverged in our experiments, whereas full-parameter training with the same settings did, and a control with matched solvers attributes the difference to the reduced dimension.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33193",
  "author_total": 4,
  "authors": [
    {
      "name": "Lu Wei"
    },
    {
      "name": "Yufeng Wang"
    },
    {
      "name": "Chenfeng Cao"
    },
    {
      "name": "Haibin Ling"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ev2pr2wg35m76.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33193",
  "fulltext_url": null,
  "id": "ev2pr2wg35m76",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33193",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7214766661",
  "pdf_url": "https://arxiv.org/pdf/2609.33193",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ev2pr2wg35m76.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.33193",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33193"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Apparent Compression, Real Stability: The Intrinsic Dimension of Learning a Quantum Wavefunction",
  "title_text": "Apparent Compression, Real Stability: The Intrinsic Dimension of Learning a Quantum Wavefunction",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:12Z",
  "url": "https://research.draconitic.com/paper/ev2pr2wg35m76",
  "venue": "arXiv",
  "versions": []
}