{
  "oags": "0.2",
  "status": "alpha",
  "entry": {
    "id": "IB-attention-hopfield",
    "type": "evidence",
    "claim": "Softmax self-attention (the Transformer's core operation) is exactly ONE update step of a continuous modern Hopfield network with an exponential energy — i.e. associative-memory attractor retrieval — with pattern-storage capacity scaling ~2^(d/2) and the softmax inverse-temperature beta as the retrieval-sharpness knob.",
    "evidence_grade": "E2",
    "state": "verified",
    "primary_source_ref": [
      "Ramsauer et al. 2020, ICLR — 'Hopfield Networks is All You Need'"
    ],
    "quantities": "attention = 1 modern-Hopfield update; pattern-storage capacity ~2^(d/2); knob = softmax inverse-temperature beta",
    "declared_loss": "FORMAL result (Petrovich flag): a proven mathematical equivalence + capacity bound about an ENGINEERED system, not a measurement of a natural system. Included as the transformer domain's evidence anchor; the broad 'attention IS memory retrieval everywhere' generalization is NOT asserted here as a natural law."
  },
  "expand": [
    {
      "rel": "relates",
      "target": "IB-transmission-prior-attractor",
      "href": "https://infoblock.org/b/IB-transmission-prior-attractor/oags.json"
    }
  ],
  "incoming": [
    {
      "rel": "relates",
      "from": "IB-transmission-prior-attractor",
      "href": "https://infoblock.org/b/IB-transmission-prior-attractor/oags.json"
    }
  ],
  "links": [
    "https://infoblock.org/b/IB-transmission-prior-attractor/",
    "https://infoblock.org/b/IB-transmission-prior-attractor/"
  ],
  "declared_losses": [
    "Public evidence-graph projection: internal analytic/theory edges and private provenance are withheld by design.",
    "Alpha: some primary-source refs await precise citation verification."
  ],
  "generated": "2026-08-02"
}