Pith Number

pith:LMABHWB4

pith:2026:LMABHWB4WBMACZ44ENLJZU5DGJ

not attested not anchored not stored refs pending

Stochastic Dimension-Free Zeroth-Order Estimator for High-Dimensional and High-Order PINNs

Huanhuan Gao, Zhangyong Liang

A stochastic zeroth-order estimator trains physics-informed neural networks with up to 10 million dimensions using memory and computation costs that stay independent of dimension and derivative order.

arxiv:2603.24002 v2 · 2026-03-25 · cs.LG

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\usepackage{pith}
\pithnumber{LMABHWB4WBMACZ44ENLJZU5DGJ}

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Record completeness

1 Bitcoin timestamp

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.

Claims

C1strongest claim

SDZE achieves dimension-independent complexity in both space and memory, enabling the training of 10-million-dimensional PINNs on a single NVIDIA A100 GPU.

C2weakest assumption

That Common Random Numbers Synchronization algebraically cancels the O(1/ε²) variance explosion while preserving unbiasedness and convergence of the zeroth-order estimator for the specific randomized spatial operators used in high-order PINNs.

C3one line summary

SDZE uses common random number synchronization and implicit subspace projection to enable training of 10-million-dimensional PINNs on a single GPU with O(1) space and memory complexity.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:45:04.579245Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5b0013d83cb05801679c23569cd3a33279b5c8b90576da24f7d372de0760dcd0

Aliases

arxiv: 2603.24002 · arxiv_version: 2603.24002v2 · doi: 10.48550/arxiv.2603.24002 · pith_short_12: LMABHWB4WBMA · pith_short_16: LMABHWB4WBMACZ44 · pith_short_8: LMABHWB4

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/LMABHWB4WBMACZ44ENLJZU5DGJ \
  | 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: 5b0013d83cb05801679c23569cd3a33279b5c8b90576da24f7d372de0760dcd0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "35aefff33b98dddb4aabfc15dd074a35d9c24e7e349417c66c60e7238f691209",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-03-25T07:02:34Z",
    "title_canon_sha256": "0d1dfed630c218512aec11a4d0fbf3a0e7513e1746b76ccea3a1266d44d3b4c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.24002",
    "kind": "arxiv",
    "version": 2
  }
}