Pith Number

pith:KXNY45KN

pith:2020:KXNY45KN6QFO5CBN5RJHN7WDGZ

not attested not anchored not stored refs pending

On the Banach spaces associated with multi-layer ReLU networks: Function representation, approximation theory and gradient descent dynamics

Stephan Wojtowytsch, Weinan E

arxiv:2007.15623 v1 · 2020-07-30 · stat.ML · cs.LG · math.FA

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KXNY45KN6QFO5CBN5RJHN7WDGZ}

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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

2 papers in Pith

A First-Principles Theory of Slow Thinking and Active Perception

Path Regularization: A Near-Complete and Optimal Nonasymptotic Generalization Theory for Multilayer Neural Networks and Double Descent Phenomenon

Receipt and verification

First computed	2026-07-05T01:23:32.431742Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

55db8e754df40aee882dec5276fec336550c9f24f4128097fdcbf12b7908f62e

Aliases

arxiv: 2007.15623 · arxiv_version: 2007.15623v1 · doi: 10.48550/arxiv.2007.15623 · pith_short_12: KXNY45KN6QFO · pith_short_16: KXNY45KN6QFO5CBN · pith_short_8: KXNY45KN

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/KXNY45KN6QFO5CBN5RJHN7WDGZ \
  | 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: 55db8e754df40aee882dec5276fec336550c9f24f4128097fdcbf12b7908f62e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3689f4ca8ec9c79c248a1a5dae7dfc25ca2d55bbd526cd52b7f7fd5fde652bd0",
    "cross_cats_sorted": [
      "cs.LG",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2020-07-30T17:47:05Z",
    "title_canon_sha256": "87238f3b8d29f798bb8d289bb874df683ac724a50ecc7201586bf199ec95b279"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2007.15623",
    "kind": "arxiv",
    "version": 1
  }
}