{
  "story_id": "de1f8a4ec18cc2c878e132fa42dd546b",
  "desk": "drm3",
  "revision": 1,
  "published_at": "2026-09-03T04:00:00.000Z",
  "content_hash": "92aaeb26c320520cf541f4645a2a0b5780421981b9f8648bfd08555ef04ce5b2",
  "hash_basis": "sha256 over `headline\\ndek\\nprose`, plus `\\n` + the canonical citations JSON when any source is placed, plus `\\n#blog` for blogs",
  "basis": {
    "headline": "Gradient Descent Converges to Cycles in Non-Separable Logistic Regression",
    "dek": "Research shows gradient descent converges to stable cycles rather than minima in non-separable logistic regression with large step sizes.",
    "prose": "For linearly-separable data, gradient descent is known to converge to the minimizer with arbitrarily large step sizes. [^1]\n\nThe study investigates gradient descent dynamics on logistic regression problems utilizing large, constant step sizes. [^2]\n\nThis convergence property no longer holds when the logistic regression problem is not separable. [^3]\n\nDevelopers commonly treat AGENTS.md or CLAUDE.md files as simple README documents containing static rules for AI coding agents. [^4]\n\nThe article proposes a conceptual framework where AGENTS.md files are viewed as neural networks rather than just static configuration. [^5]\n\nA sequence of period-doubling bifurcations begins at the critical step size of 2 divided by lambda, where lambda is the largest eigenvalue of the Hessian at the solution. [^6]\n\nThe author suggests that gradient descent could be utilized as a training method for these AI agent configurations. [^7]\n\nThe content implies that current rule-based approaches may be insufficient compared to trainable network models. [^8]",
    "cited": "[{\"statement\":\"For linearly-separable data, gradient descent is known to converge to the minimizer with arbitrarily large step sizes.\",\"source\":\"arXiv.org\",\"instrument\":\"News\",\"claim_key\":null,\"published_at\":\"2026-09-03T04:00:00.000Z\",\"publisher_count\":1,\"sources\":[\"arXiv.org\"]},{\"statement\":\"The study investigates gradient descent dynamics on logistic regression problems utilizing large, constant step sizes.\",\"source\":\"arXiv.org\",\"instrument\":\"News\",\"claim_key\":null,\"published_at\":\"2026-09-03T04:00:00.000Z\",\"publisher_count\":1,\"sources\":[\"arXiv.org\"]},{\"statement\":\"This convergence property no longer holds when the logistic regression problem is not separable.\",\"source\":\"arXiv.org\",\"instrument\":\"News\",\"claim_key\":null,\"published_at\":\"2026-09-03T04:00:00.000Z\",\"publisher_count\":1,\"sources\":[\"arXiv.org\"]},{\"statement\":\"Developers commonly treat AGENTS.md or CLAUDE.md files as simple README documents containing static rules for AI coding agents.\",\"source\":\"medium.com\",\"instrument\":\"News\",\"claim_key\":null,\"published_at\":\"2026-09-01T15:27:13.000Z\",\"publisher_count\":1,\"sources\":[\"medium.com\"]},{\"statement\":\"The article proposes a conceptual framework where AGENTS.md files are viewed as neural networks rather than just static configuration.\",\"source\":\"medium.com\",\"instrument\":\"News\",\"claim_key\":null,\"published_at\":\"2026-09-01T15:27:13.000Z\",\"publisher_count\":1,\"sources\":[\"medium.com\"]},{\"statement\":\"A sequence of period-doubling bifurcations begins at the critical step size of 2 divided by lambda, where lambda is the largest eigenvalue of the Hessian at the solution.\",\"source\":\"arXiv.org\",\"instrument\":\"News\",\"claim_key\":null,\"published_at\":\"2026-09-03T04:00:00.000Z\",\"publisher_count\":1,\"sources\":[\"arXiv.org\"]},{\"statement\":\"The author suggests that gradient descent could be utilized as a training method for these AI agent configurations.\",\"source\":\"medium.com\",\"instrument\":\"News\",\"claim_key\":null,\"published_at\":\"2026-09-01T15:27:13.000Z\",\"publisher_count\":1,\"sources\":[\"medium.com\"]},{\"statement\":\"The content implies that current rule-based approaches may be insufficient compared to trainable network models.\",\"source\":\"medium.com\",\"instrument\":\"News\",\"claim_key\":null,\"published_at\":\"2026-09-01T15:27:13.000Z\",\"publisher_count\":1,\"sources\":[\"medium.com\"]}]",
    "kind": "news"
  },
  "receipt_verify": "Ed25519 over the dot-joined string `slice_hash.cursor_from.cursor_to.view.view_version.row_count`; public_key and sig are base64url of the raw 32-byte key / 64-byte signature",
  "receipt": null,
  "receipt_note": "this revision predates receipt-keeping (before v0.37.0); the filed row lives in the record",
  "generation_chain": {
    "wire": {
      "stream": "fountain_news",
      "story_id": "ead869088c3331c0ddb842570405dba6",
      "thread_id": "744e12470f156760443848d452dcc48e",
      "thread_label": "Gradient Descent",
      "novelty": "UPDATE",
      "content_hash": "5d3b875cf1c41f7867799ab778f0b10024aa948e5c49180cd9dbd2c523ea228b",
      "last_published_at": "2026-09-03T04:00:00.000Z",
      "read_receipt": {
        "slice_hash": "a6974819026a155e1c79c99aba73ab29d5f9d0aaa9cffb05e88a08023354a690",
        "cursor_from": "eyJ0cyI6IjIwMjYtMDktMDNUMDM6MzI6MTkuMDAwMDAwWiIsImlkIjoiNzMzZDYyYTFiNGQwMmJmNjYzNTk3YjhmN2JhZDBiZTIiLCJ2IjoiMSJ9",
        "cursor_to": "eyJ0cyI6IjIwMjYtMDktMDNUMDQ6MDk6MDAuMDAwMDAwWiIsImlkIjoiNjQ5MjI3ZDNmNWQyMGQ3NmI1ZTE1NGNhODNlMTI0ZTMiLCJ2IjoiMSJ9",
        "view": "v_fountain_news",
        "view_version": "1",
        "row_count": 100,
        "window_days": 3,
        "bytes_scanned": 12568115,
        "credits": 8,
        "price_per_100_rows": 8,
        "sig": "k4fkL1dHRNIJwSawY8K6wWBrTSdTIRM-buyZr56gcruiCoH5_IdJUeMzPH7d51ZTXAE0Qe6xSFoDys5UGTzsAw",
        "public_key": "bMUigy8O0jOnBxQ4Sc-5lwhIZ8LQVAhxMbR7qESVuUE",
        "signer_path": "lakehouse/data-extract/v1",
        "alg": "Ed25519",
        "signed": true
      }
    },
    "written_at": "2026-09-03T06:46:31.042Z"
  },
  "cited_facts": [
    {
      "statement": "For linearly-separable data, gradient descent is known to converge to the minimizer with arbitrarily large step sizes.",
      "source": "arXiv.org",
      "instrument": "News",
      "claim_key": null,
      "published_at": "2026-09-03T04:00:00.000Z",
      "publisher_count": 1,
      "sources": [
        "arXiv.org"
      ]
    },
    {
      "statement": "The study investigates gradient descent dynamics on logistic regression problems utilizing large, constant step sizes.",
      "source": "arXiv.org",
      "instrument": "News",
      "claim_key": null,
      "published_at": "2026-09-03T04:00:00.000Z",
      "publisher_count": 1,
      "sources": [
        "arXiv.org"
      ]
    },
    {
      "statement": "This convergence property no longer holds when the logistic regression problem is not separable.",
      "source": "arXiv.org",
      "instrument": "News",
      "claim_key": null,
      "published_at": "2026-09-03T04:00:00.000Z",
      "publisher_count": 1,
      "sources": [
        "arXiv.org"
      ]
    },
    {
      "statement": "Developers commonly treat AGENTS.md or CLAUDE.md files as simple README documents containing static rules for AI coding agents.",
      "source": "medium.com",
      "instrument": "News",
      "claim_key": null,
      "published_at": "2026-09-01T15:27:13.000Z",
      "publisher_count": 1,
      "sources": [
        "medium.com"
      ]
    },
    {
      "statement": "The article proposes a conceptual framework where AGENTS.md files are viewed as neural networks rather than just static configuration.",
      "source": "medium.com",
      "instrument": "News",
      "claim_key": null,
      "published_at": "2026-09-01T15:27:13.000Z",
      "publisher_count": 1,
      "sources": [
        "medium.com"
      ]
    },
    {
      "statement": "A sequence of period-doubling bifurcations begins at the critical step size of 2 divided by lambda, where lambda is the largest eigenvalue of the Hessian at the solution.",
      "source": "arXiv.org",
      "instrument": "News",
      "claim_key": null,
      "published_at": "2026-09-03T04:00:00.000Z",
      "publisher_count": 1,
      "sources": [
        "arXiv.org"
      ]
    },
    {
      "statement": "The author suggests that gradient descent could be utilized as a training method for these AI agent configurations.",
      "source": "medium.com",
      "instrument": "News",
      "claim_key": null,
      "published_at": "2026-09-01T15:27:13.000Z",
      "publisher_count": 1,
      "sources": [
        "medium.com"
      ]
    },
    {
      "statement": "The content implies that current rule-based approaches may be insufficient compared to trainable network models.",
      "source": "medium.com",
      "instrument": "News",
      "claim_key": null,
      "published_at": "2026-09-01T15:27:13.000Z",
      "publisher_count": 1,
      "sources": [
        "medium.com"
      ]
    }
  ],
  "note": "A signature proves who filed this and that it has not changed since. It never makes a claim true."
}