Pith Number

pith:E2GIVSWF

pith:2019:E2GIVSWFJFP653GQQ4BN3UCHDN

not attested not anchored not stored refs pending

Error bounds for approximations with deep ReLU neural networks in $W^{s,p}$ norms

Gitta Kutyniok, Ingo G\"uhring, Philipp Petersen

arxiv:1902.07896 v1 · 2019-02-21 · math.FA · cs.LG

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\usepackage{pith}
\pithnumber{E2GIVSWFJFP653GQQ4BN3UCHDN}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Cited by

1 paper in Pith

Deep neural network approximation theory for high-dimensional functions

Receipt and verification

First computed	2026-05-17T23:53:03.554764Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

268c8acac5495feeecd08702ddd0471b7f56fe3c53fa0ea69db83edcbe53ff6c

Aliases

arxiv: 1902.07896 · arxiv_version: 1902.07896v1 · doi: 10.48550/arxiv.1902.07896 · pith_short_12: E2GIVSWFJFP6 · pith_short_16: E2GIVSWFJFP653GQ · pith_short_8: E2GIVSWF

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/E2GIVSWFJFP653GQQ4BN3UCHDN \
  | 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: 268c8acac5495feeecd08702ddd0471b7f56fe3c53fa0ea69db83edcbe53ff6c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7fc6f1b05dee7412a95f8fb013f3a7b2633ff8ea3a3f9726a18ffabe12a0253c",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2019-02-21T07:45:40Z",
    "title_canon_sha256": "e2902c97e9f20438281ee6b52ae1748e4ef6554047475b7b7ae9306a37763ecc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1902.07896",
    "kind": "arxiv",
    "version": 1
  }
}