{
  "analytic": "lora-rank",
  "kind": "declared_analytical_or_constructed_example",
  "experimental_model_result": false,
  "panels": [
    {
      "kind": "line",
      "x": [
        4,
        8,
        16,
        32,
        64,
        128
      ],
      "series": [
        {
          "label": "Trainable fraction",
          "y": [
            0.001953125,
            0.00390625,
            0.0078125,
            0.015625,
            0.03125,
            0.0625
          ]
        }
      ],
      "xlabel": "Rank r",
      "ylabel": "Fraction of one 4096 x 4096 matrix",
      "logx": false,
      "logy": false
    }
  ],
  "title": "Low-rank parameter counts and a linear merge check",
  "assumptions": "Counts for one square matrix only; numerical merge uses deterministic float64 arrays, seed 42, not a language model.",
  "worked": "4096×4096矩阵在r=16时低秩因子有131072参数，约占0.78125%。独立小矩阵浮点核对的最大绝对差为3.55e-15；这验证线性实现，不证明量化合并无损或下游能力。",
  "merge_max_abs_error": 3.552713678800501e-15,
  "source_ids": [
    "lora",
    "qlora",
    "flash",
    "arxiv-1503.02531"
  ],
  "formula_source": "Article equations and this versioned script",
  "diagram_nodes": [
    "固定基础权重与目标任务",
    "选择层 / 投影 / rank",
    "低秩因子与初始化",
    "受约束梯度更新",
    "任务质量和资源分项",
    "合并等价与部署复核"
  ]
}