Pith Number

pith:TTSE4RZ3

pith:2017:TTSE4RZ3V7QL73ZY6HKYBRJ5XT

not attested not anchored not stored refs pending

Universal Function Approximation by Deep Neural Nets with Bounded Width and ReLU Activations

Boris Hanin

arxiv:1708.02691 v3 · 2017-08-09 · stat.ML · cs.CG · cs.LG · math.FA · math.ST · stat.TH

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\usepackage{pith}
\pithnumber{TTSE4RZ3V7QL73ZY6HKYBRJ5XT}

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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.

Cited by

5 papers in Pith

A Theory on Flow Matching with Neural Networks

Invariance-inducing regularization using worst-case transformations suffices to boost accuracy and spatial robustness

Deep neural network approximation theory for high-dimensional functions

DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators

Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models

Receipt and verification

First computed	2026-07-05T00:13:11.754410Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ce44e473bafe0bfef38f1d580c53dbce0f55f10766611365c77a06b2df85446

Aliases

arxiv: 1708.02691 · arxiv_version: 1708.02691v3 · doi: 10.48550/arxiv.1708.02691 · pith_short_12: TTSE4RZ3V7QL · pith_short_16: TTSE4RZ3V7QL73ZY · pith_short_8: TTSE4RZ3

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/TTSE4RZ3V7QL73ZY6HKYBRJ5XT \
  | 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: 9ce44e473bafe0bfef38f1d580c53dbce0f55f10766611365c77a06b2df85446

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1b41af95f97357f6a8e2817e51063d45a2df781560aca167c0cb362033d4655e",
    "cross_cats_sorted": [
      "cs.CG",
      "cs.LG",
      "math.FA",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2017-08-09T01:37:21Z",
    "title_canon_sha256": "ac093a691aa3d220ef67b248554e694f141eeeb158092dd749278c5381e9adea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.02691",
    "kind": "arxiv",
    "version": 3
  }
}