Pith Number

pith:I23EX2FI

pith:2024:I23EX2FIKGT3S7L4DKA2R6P7DC

not attested not anchored not stored refs pending

Information-Theoretic Progress Measures reveal Grokking is an Emergent Phase Transition

Daniele Marinazzo, Kenzo Clauw, Sebastiano Stramaglia

arxiv:2408.08944 v1 · 2024-08-16 · cs.LG · cs.IT · math.IT

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{I23EX2FIKGT3S7L4DKA2R6P7DC}

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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

7 papers in Pith

Deciphering Two Training Clocks in Grokking via Deep Linear Network Theory with Conditional ReLU Reduction

Scalar Representations of Neural Network Training Dynamics

Emergence via Phase Transitions: Mechanism Landscapes and Universal Convergence Across Complex Systems

Phase Transitions in Driven Informational Systems: A Two-Field Perspective on Learning Theory and Non-Equilibrium Chemistry

Model Capacity Determines Grokking through Competing Memorisation and Generalisation Speeds

Receipt and verification

First computed	2026-07-05T08:56:25.932302Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

46b64be8a851a7b97d7c1a81a8f9ff189c39ee61c554443777ca8e2f4dbe2ca4

Aliases

arxiv: 2408.08944 · arxiv_version: 2408.08944v1 · doi: 10.48550/arxiv.2408.08944 · pith_short_12: I23EX2FIKGT3 · pith_short_16: I23EX2FIKGT3S7L4 · pith_short_8: I23EX2FI

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/I23EX2FIKGT3S7L4DKA2R6P7DC \
  | 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: 46b64be8a851a7b97d7c1a81a8f9ff189c39ee61c554443777ca8e2f4dbe2ca4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7246d29a2b9070242d3d048763fa39ae862fe85cab1d7d5642514e8afd63238f",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2024-08-16T16:33:46Z",
    "title_canon_sha256": "12ee0f4a1c20770e221e0b86c8fb9552a21fa037e42f553503352ee78051f49a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2408.08944",
    "kind": "arxiv",
    "version": 1
  }
}