{
  "id": 19301758,
  "title": "Pricing Symbolic Rules by What GNNs Leave Unlearned",
  "url": "https://urgent.news/2026/11/09/pricing-symbolic-rules-by-what-gnns-leave-unlearned",
  "topic": "ai",
  "section": "AI",
  "published": "2026-11-09T14:03:25.000Z",
  "source": {
    "name": "arXiv cs.AI",
    "slug": "arxiv-cs-ai",
    "url": "https://arxiv.org/abs/2611.12446v1"
  },
  "original_language": "en",
  "account": null,
  "summary": "Symbolic knowledge (motif counts, ring counts, label constraints) is routinely added to graph neural networks (GNNs) and justified by their limited expressivity. We replace this yardstick with an exact one. The largest log-loss reduction a rule $S$ can give a model family is $I(Y;S\\midσ)$ given what the family computes; every realised gain splits exactly into this term plus repaid neural debt;…",
  "key_points": [],
  "editors_take": null,
  "illustration": null,
  "coverage": {
    "outlets": 1,
    "also_reported_by": []
  },
  "ai_generated": true,
  "disclaimer": "Summaries, key points and the editor’s take are written by software from other outlets’ reporting and may contain errors — always check the linked original."
}