Pith Number

pith:IEFRZGWU

pith:2026:IEFRZGWURRC2JC45M2MO2PPU7N

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Local Hessian Spectral Filtering for Robust Intrinsic Dimension Estimation

Genki Osada

Spectral filtering on the log-density Hessian counts only tangent directions to estimate local intrinsic dimension even when noise fills most of high-dimensional space.

arxiv:2605.01221 v2 · 2026-05-02 · cs.LG

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Claims

C1strongest claim

We propose Local Hessian Spectral Dimension (LHSD), which resolves this by applying spectral filtering to the log-density Hessian, explicitly cutting off large eigenvalues associated with normal directions to count zero-curvature tangent directions. Implemented using Stochastic Lanczos Quadrature (SLQ), LHSD avoids full Hessian construction, achieving linear scalability with dimension D.

C2weakest assumption

That the log-density Hessian exhibits a clear spectral separation where large eigenvalues reliably correspond to noise-dominated normal directions and near-zero eigenvalues to the tangent space, and that a fixed or simple cutoff can be applied without losing signal or introducing bias.

C3one line summary

LHSD uses spectral filtering on the log-density Hessian to isolate tangent directions from noise and estimate local intrinsic dimension scalably via Stochastic Lanczos Quadrature.

Receipt and verification

First computed	2026-06-23T02:13:24.479379Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

410b1c9ad48c45a48b9d6698ed3df4fb4a93c487c516bef99aee1694a88f190c

Aliases

arxiv: 2605.01221 · arxiv_version: 2605.01221v2 · doi: 10.48550/arxiv.2605.01221 · pith_short_12: IEFRZGWURRC2 · pith_short_16: IEFRZGWURRC2JC45 · pith_short_8: IEFRZGWU

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/IEFRZGWURRC2JC45M2MO2PPU7N \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 410b1c9ad48c45a48b9d6698ed3df4fb4a93c487c516bef99aee1694a88f190c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fde7e1acb8f2c26671760df365b2c1d97c1b2033bf117fae7789e9945af279ee",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-02T03:30:55Z",
    "title_canon_sha256": "ebc936ae33f4a20b982d25965bf77207ce3d7a80f1957d24d95fcf93509e1e5b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.01221",
    "kind": "arxiv",
    "version": 2
  }
}