{
  "annotation_id": "aafc0479-5b19-45f8-a32b-4cde5e2f86d9",
  "date_created": "2026-02-17T05:53:23.004000Z",
  "date_modified": "2026-02-17T05:53:23.004000Z",
  "file_hash": "c215326302f5b52edc43df061d5f0887cc0b3576b779b38553d2e2c24221558f",
  "private": false,
  "record": {
    "abstract": "We prove that the Transformer self-attention mechanism in the high-confidence regime ($\\beta \\to \\infty$, where $\\beta$ is an inverse temperature) operates in the tropical semiring (max-plus algebra). In particular, we show that taking the tropical limit of the softmax attention converts it into a tropical matrix product. This reveals that the Transformer\u0027s forward pass is effectively executing a dynamic programming recurrence (specifically, a Bellman-Ford path-finding update) on a latent graph defined by token similarities. Our theoretical result provides a new geometric perspective for chain-of-thought reasoning: it emerges from an inherent shortest-path (or longest-path) algorithm being carried out within the network\u0027s computation.",
    "arxiv_id": "2601.09775",
    "authors": [
      "Faruk Alpay",
      "Bilge Senturk"
    ],
    "categories": [
      "cs.LG",
      "cs.CL"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "The Geometry of Thought: Disclosing the Transformer as a Tropical Polynomial Circuit",
    "url": "https://arxiv.org/abs/2601.09775",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3a708a0d-caf7-45fc-aa33-86e308e3f26b",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}