{
  "$schema": "https://themachinepress.com/schemas/story-v1.schema.json",
  "schema_version": "1.0.0",
  "document_type": "machine_press_story",
  "story": {
    "story_id": "mp-2026-09-12-015",
    "source_story_id": "tmp-sidebar-grokking-scaling-boundary",
    "edition_id": "mp-2026-09-12-morning-0065",
    "edition_url": "https://themachinepress.com/edition/2026-09-12",
    "position": 17,
    "story_type": "ticker",
    "section": "research",
    "editorial_classification": "editorial",
    "headline": "Doubling Data Brought Grokking Four Times Sooner",
    "slug": "doubling-data-brought-grokking-four-times-sooner",
    "dek": "Across 384 modular-arithmetic runs, data complexity dominated width in the fitted transition law.",
    "summary": "Across 384 modular-arithmetic runs, data complexity dominated width in the fitted transition law.",
    "body_text": "The reported scaling fit assigns data a minus-2.04 exponent, versus minus-0.27 for hidden width: doubling data moved generalization onset about fourfold, while doubling width shifted it roughly 1.2-fold. A sharp weight-decay boundary separated grokking from non-grokking in this small-model setting.",
    "why_it_matters": "Across 384 modular-arithmetic runs, data complexity dominated width in the fitted transition law.",
    "limitations": [],
    "importance": 7,
    "canonical_url": "https://themachinepress.com/story/mp-2026-09-12-015/doubling-data-brought-grokking-four-times-sooner",
    "json_url": "https://themachinepress.com/story/mp-2026-09-12-015.json",
    "first_published_at": "2026-09-12T09:00:00.000-04:00",
    "modified_at": "2026-09-12T09:00:00.000-04:00",
    "content_status": "new",
    "is_carryover": false,
    "carryover_reason": null,
    "key_claims": [
      {
        "claim_id": "claim-mp-2026-09-12-015-001",
        "text": "Across 384 modular-arithmetic runs, data complexity dominated width in the fitted transition law.",
        "source_ids": [
          "source-2026-09-12-017"
        ],
        "qualification": null
      }
    ],
    "source_ids": [
      "source-2026-09-12-017"
    ],
    "tags": [
      "grokking",
      "scaling laws",
      "generalization"
    ],
    "image_url": null,
    "corrections": []
  },
  "sources": [
    {
      "source_id": "source-2026-09-12-017",
      "title": "arXiv preprint 2609.10657",
      "publisher": "arXiv",
      "url": "https://arxiv.org/abs/2609.10657",
      "canonical_url": "https://arxiv.org/abs/2609.10657",
      "source_type": "primary_research",
      "is_primary_source": true,
      "published_at": null,
      "accessed_at": "2026-09-12T08:27:00.000-04:00",
      "supports_claim_ids": [
        "claim-mp-2026-09-12-015-001"
      ]
    }
  ],
  "corrections": [],
  "publisher": {
    "name": "The Machine Press",
    "url": "https://themachinepress.com",
    "description": "A daily newspaper for the age of artificial intelligence."
  },
  "cite_this_report": {
    "title": "Doubling Data Brought Grokking Four Times Sooner",
    "publisher": "The Machine Press",
    "published_at": "2026-09-12T09:00:00.000-04:00",
    "canonical_url": "https://themachinepress.com/story/mp-2026-09-12-015/doubling-data-brought-grokking-four-times-sooner"
  }
}