Pith Number

pith:PABWDLMH

pith:2024:PABWDLMHXFCUTQM72IFAQYYX2V

not attested not anchored not stored refs pending

From Lazy to Rich: Exact Learning Dynamics in Deep Linear Networks

Alexandra M. Proca, Andrew M. Saxe, Cl\'ementine C. J. Domin\'e, Daniel Kunin, Lukas Braun, Nicolas Anguita, Pedro A. M. Mediano

arxiv:2409.14623 v2 · 2024-09-22 · cs.LG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PABWDLMHXFCUTQM72IFAQYYX2V}

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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

4 papers in Pith

Signal-to-Noise Ratio and Sample Size Govern Representational Alignment in Neural Networks

Spectral Dynamics in Deep Networks: Feature Learning, Outlier Escape, and Learning Rate Transfer

You Had One Job: Per-Task Quantization Using LLMs' Hidden Representations

Spectral Dynamics in Deep Networks: Feature Learning, Outlier Escape, and Learning Rate Transfer

Receipt and verification

First computed	2026-07-05T10:23:56.571924Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

780361ad87b94549c19fd20a086317d56b33e8efa4421c5f541e2d41fe3424f5

Aliases

arxiv: 2409.14623 · arxiv_version: 2409.14623v2 · doi: 10.48550/arxiv.2409.14623 · pith_short_12: PABWDLMHXFCU · pith_short_16: PABWDLMHXFCUTQM7 · pith_short_8: PABWDLMH

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/PABWDLMHXFCUTQM72IFAQYYX2V \
  | 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: 780361ad87b94549c19fd20a086317d56b33e8efa4421c5f541e2d41fe3424f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b3ab22a37e4a80b593b2d6f9280432d4d836eb1d0a9b39eca4e9f33a64fd00f2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2024-09-22T23:19:04Z",
    "title_canon_sha256": "0a8a2bab9542d2487f9e2fb57cfcff7040120efd80ab09e00c5291f3111813f0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2409.14623",
    "kind": "arxiv",
    "version": 2
  }
}