{
  "domain": "ai.onnx",
  "name": "LayerNormalization",
  "sinceVersion": 17,
  "description": "Normalizes a tensor along a suffix of axes starting at `axis` by subtracting the mean and dividing by the square root of the variance plus `epsilon`, then scales and optionally shifts the result with learnable `Scale` and `B` tensors. The output `Y` has the same shape as `X`; optional outputs `Mean` and `InvStdDev` expose the per-normalization-group statistics computed during normalization.",
  "inputs": [
    { "role": "X", "dtype": "T", "description": "Tensor to be normalized." },
    { "role": "Scale", "dtype": "T", "description": "Scale tensor applied after normalization." },
    { "role": "B", "dtype": "T", "optional": true, "description": "Optional bias tensor added after scaling." }
  ],
  "outputs": [
    {
      "role": "Y",
      "dtype": "T",
      "rank": "ranks.X",
      "description": "Normalized and scaled output tensor; same shape as X.",
      "shape": "shapes.X"
    },
    {
      "role": "Mean",
      "dtype": "float32",
      "optional": true,
      "description": "Per-normalization-group mean in the ONNX broadcastable keepdims shape: dimensions before `axis` are preserved and dimensions from `axis` onward are 1.",
      "rank": "ranks.X"
    },
    {
      "role": "InvStdDev",
      "dtype": "float32",
      "optional": true,
      "description": "Per-normalization-group reciprocal standard deviation `1 / sqrt(variance + epsilon)`, returned in the same ONNX broadcastable keepdims shape as `Mean`.",
      "rank": "ranks.X"
    }
  ],
  "attributes": { "axis": -1, "epsilon": 0.00001, "stash_type": 1 },
  "attributeDescriptions": {
    "axis": "The first axis of the normalization range; all axes from `axis` to the last are normalized together. Negative values count from the end; the default `-1` normalizes only the last dimension.",
    "epsilon": "Small constant added to the variance before taking the square root to avoid division by zero.",
    "stash_type": "TensorProto element type used for the normalization stage and optional statistics; the implemented ONNX route supports the standard float32 value (`1`)."
  },
  "attributeConstraints": { "stash_type": { "values": [1] } },
  "typeConstraints": { "T": ["float32", "float16"] },
  "args": {
    "x": { "kind": "tensor", "semantic": "X", "role": "input" },
    "scale": { "kind": "tensor", "semantic": "Scale", "role": "input" },
    "b": { "kind": "tensor", "semantic": "B", "role": "input", "required": false },
    "y": { "kind": "tensor", "semantic": "Y", "role": "output" },
    "mean": { "kind": "tensor", "semantic": "Mean", "role": "output", "required": false },
    "invStdDev": { "kind": "tensor", "semantic": "InvStdDev", "role": "output", "required": false }
  },
  "tunables": { "MAX_WORKGROUP_SIZE": 256, "SCALAR_FAST_MAX_HIDDEN": 1024 },
  "derive": {
    "deviceWorkgroupCap": "min(device.limits.maxComputeInvocationsPerWorkgroup, device.limits.maxComputeWorkgroupSizeX)",
    "normWorkgroupCap": "min(tunables.MAX_WORKGROUP_SIZE, deviceWorkgroupCap)",
    "hasSubgroupId": "device.features.has(\"subgroups\") and device.wgslLanguageFeatures.has(\"subgroup_id\")",
    "lastAxisWg": "min(normWorkgroupCap, pow2ceil(dim(shapes.X, -1)))",
    "lastAxisWgVec4": "min(normWorkgroupCap, pow2ceil(dim(shapes.X, -1) / 4))",
    "lastAxisContractOk": "ranks.X >= 1 and ranks.Y == ranks.X and numel(shapes.X) == numel(shapes.Y) and (attrs.axis == -1 or attrs.axis == ranks.X - 1)",
    "suffixAxisContractOk": "ranks.X >= 2 and ranks.Y == ranks.X and numel(shapes.X) == numel(shapes.Y) and attrs.axis + ranks.X >= 0 and attrs.axis < ranks.X and not (attrs.axis == -1 or attrs.axis == ranks.X - 1)",
    "axisNorm": "attrs.axis if attrs.axis >= 0 else attrs.axis + ranks.X",
    "normRows": "numel(shapes.X) / max(1, dim(shapes.X, -1)) if lastAxisContractOk else outer(shapes.X, axisNorm)",
    "normRowStride": "max(1, min(normRows, device.limits.maxComputeWorkgroupsPerDimension))",
    "suffixAxisSize": "numel(shapes.X) / max(1, outer(shapes.X, axisNorm))",
    "suffixAxisWg": "min(normWorkgroupCap, pow2ceil(suffixAxisSize))",
    "suffixAxisWgVec4": "min(normWorkgroupCap, pow2ceil(suffixAxisSize / 4))",
    "genericHiddenSize": "dim(shapes.X, -1) if lastAxisContractOk else suffixAxisSize",
    "genericWorkgroupSize": "lastAxisWg if lastAxisContractOk else suffixAxisWg",
    "scaleExactOk": "ranks.X >= 1 and ranks.Scale >= 1 and numel(shapes.Scale) == dim(shapes.X, -1) and dim(shapes.Scale, -1) == dim(shapes.X, -1)",
    "scaleBroadcastOk": "ranks.Scale >= 0 and ranks.Scale <= ranks.X and broadcastable(shapes.Scale, shapes.X)",
    "biasExactOk": "present.b and ranks.X >= 1 and ranks.B >= 1 and numel(shapes.B) == dim(shapes.X, -1) and dim(shapes.B, -1) == dim(shapes.X, -1)",
    "biasBroadcastOk": "present.b and ranks.B >= 0 and ranks.B <= ranks.X and broadcastable(shapes.B, shapes.X)",
    "suffixScaleExactOk": "suffixAxisContractOk and scaleBroadcastOk and numel(shapes.Scale) == suffixAxisSize",
    "suffixBiasExactOk": "present.b and suffixAxisContractOk and biasBroadcastOk and numel(shapes.B) == suffixAxisSize",
    "lastAxisExactScaleOk": "lastAxisContractOk and scaleExactOk",
    "lastAxisBroadcastScaleOk": "lastAxisContractOk and scaleBroadcastOk",
    "suffixAxisBroadcastScaleOk": "suffixAxisContractOk and scaleBroadcastOk",
    "suffixAxisExactAffineOk": "suffixAxisContractOk and suffixScaleExactOk and suffixBiasExactOk",
    "lastAxisScalarFastOk": "dtypes.T == \"f16\" or dim(shapes.X, -1) <= tunables.SCALAR_FAST_MAX_HIDDEN",
    "noStatsOutputs": "not present.mean and not present.invStdDev",
    "meanOnlyOutputs": "present.mean and not present.invStdDev",
    "invStdOnlyOutputs": "not present.mean and present.invStdDev",
    "fullStatsOutputs": "present.mean and present.invStdDev",
    "statsRowsOk": "fullStatsOutputs and ranks.X >= 1 and numel(shapes.Mean) == normRows and numel(shapes.InvStdDev) == normRows",
    "meanRowsOk": "present.mean and ranks.X >= 1 and numel(shapes.Mean) == normRows",
    "invStdRowsOk": "present.invStdDev and ranks.X >= 1 and numel(shapes.InvStdDev) == normRows",
    "statsOuterOk": "fullStatsOutputs and ranks.X >= 2 and numel(shapes.Mean) == normRows and numel(shapes.InvStdDev) == normRows"
  },
  "bindingSets": {
    "vec4Affine": [
      {
        "name": "x",
        "arg": "x",
        "semantic": "X",
        "buffer": { "type": "read-only-storage" },
        "elementType": "$vectorScalar"
      },
      {
        "name": "scale",
        "arg": "scale",
        "semantic": "Scale",
        "buffer": { "type": "read-only-storage" },
        "elementType": "$vectorScalar"
      },
      { "name": "y", "arg": "y", "semantic": "Y", "buffer": { "type": "storage" }, "elementType": "$vectorScalar" },
      {
        "name": "params",
        "semantic": "kernel.params",
        "buffer": { "type": "uniform" },
        "struct": {
          "name": "Params",
          "fields": [
            { "name": "rows", "type": "u32", "value": "normRows" },
            { "name": "rowStride", "type": "u32", "value": "normRowStride" }
          ]
        }
      }
    ],
    "vec4AffineBias": [
      {
        "name": "x",
        "arg": "x",
        "semantic": "X",
        "buffer": { "type": "read-only-storage" },
        "elementType": "$vectorScalar"
      },
      {
        "name": "scale",
        "arg": "scale",
        "semantic": "Scale",
        "buffer": { "type": "read-only-storage" },
        "elementType": "$vectorScalar"
      },
      {
        "name": "bias",
        "arg": "b",
        "semantic": "B",
        "buffer": { "type": "read-only-storage" },
        "elementType": "$vectorScalar"
      },
      { "name": "y", "arg": "y", "semantic": "Y", "buffer": { "type": "storage" }, "elementType": "$vectorScalar" },
      {
        "name": "params",
        "semantic": "kernel.params",
        "buffer": { "type": "uniform" },
        "struct": {
          "name": "Params",
          "fields": [
            { "name": "rows", "type": "u32", "value": "normRows" },
            { "name": "rowStride", "type": "u32", "value": "normRowStride" }
          ]
        }
      }
    ],
    "vec4AffineStats": [
      {
        "name": "x",
        "arg": "x",
        "semantic": "X",
        "buffer": { "type": "read-only-storage" },
        "elementType": "$vectorScalar"
      },
      {
        "name": "scale",
        "arg": "scale",
        "semantic": "Scale",
        "buffer": { "type": "read-only-storage" },
        "elementType": "$vectorScalar"
      },
      { "name": "y", "arg": "y", "semantic": "Y", "buffer": { "type": "storage" }, "elementType": "$vectorScalar" },
      { "name": "mean_out", "arg": "mean", "semantic": "Mean", "buffer": { "type": "storage" }, "elementType": "f32" },
      {
        "name": "inv_std_out",
        "arg": "invStdDev",
        "semantic": "InvStdDev",
        "buffer": { "type": "storage" },
        "elementType": "f32"
      },
      {
        "name": "params",
        "semantic": "kernel.params",
        "buffer": { "type": "uniform" },
        "struct": {
          "name": "Params",
          "fields": [
            { "name": "rows", "type": "u32", "value": "normRows" },
            { "name": "rowStride", "type": "u32", "value": "normRowStride" }
          ]
        }
      }
    ],
    "vec4AffineBiasStats": [
      {
        "name": "x",
        "arg": "x",
        "semantic": "X",
        "buffer": { "type": "read-only-storage" },
        "elementType": "$vectorScalar"
      },
      {
        "name": "scale",
        "arg": "scale",
        "semantic": "Scale",
        "buffer": { "type": "read-only-storage" },
        "elementType": "$vectorScalar"
      },
      {
        "name": "bias",
        "arg": "b",
        "semantic": "B",
        "buffer": { "type": "read-only-storage" },
        "elementType": "$vectorScalar"
      },
      { "name": "y", "arg": "y", "semantic": "Y", "buffer": { "type": "storage" }, "elementType": "$vectorScalar" },
      { "name": "mean_out", "arg": "mean", "semantic": "Mean", "buffer": { "type": "storage" }, "elementType": "f32" },
      {
        "name": "inv_std_out",
        "arg": "invStdDev",
        "semantic": "InvStdDev",
        "buffer": { "type": "storage" },
        "elementType": "f32"
      },
      {
        "name": "params",
        "semantic": "kernel.params",
        "buffer": { "type": "uniform" },
        "struct": {
          "name": "Params",
          "fields": [
            { "name": "rows", "type": "u32", "value": "normRows" },
            { "name": "rowStride", "type": "u32", "value": "normRowStride" }
          ]
        }
      }
    ],
    "scalarAffineMean": [
      { "name": "x", "arg": "x", "semantic": "X", "buffer": { "type": "read-only-storage" }, "elementType": "$scalar" },
      {
        "name": "scale",
        "arg": "scale",
        "semantic": "Scale",
        "buffer": { "type": "read-only-storage" },
        "elementType": "$scalar"
      },
      { "name": "y", "arg": "y", "semantic": "Y", "buffer": { "type": "storage" }, "elementType": "$scalar" },
      { "name": "mean_out", "arg": "mean", "semantic": "Mean", "buffer": { "type": "storage" }, "elementType": "f32" },
      {
        "name": "params",
        "semantic": "kernel.params",
        "buffer": { "type": "uniform" },
        "struct": {
          "name": "Params",
          "fields": [
            { "name": "rows", "type": "u32", "value": "normRows" },
            { "name": "rowStride", "type": "u32", "value": "normRowStride" }
          ]
        }
      }
    ],
    "scalarAffineInvStd": [
      { "name": "x", "arg": "x", "semantic": "X", "buffer": { "type": "read-only-storage" }, "elementType": "$scalar" },
      {
        "name": "scale",
        "arg": "scale",
        "semantic": "Scale",
        "buffer": { "type": "read-only-storage" },
        "elementType": "$scalar"
      },
      { "name": "y", "arg": "y", "semantic": "Y", "buffer": { "type": "storage" }, "elementType": "$scalar" },
      {
        "name": "inv_std_out",
        "arg": "invStdDev",
        "semantic": "InvStdDev",
        "buffer": { "type": "storage" },
        "elementType": "f32"
      },
      {
        "name": "params",
        "semantic": "kernel.params",
        "buffer": { "type": "uniform" },
        "struct": {
          "name": "Params",
          "fields": [
            { "name": "rows", "type": "u32", "value": "normRows" },
            { "name": "rowStride", "type": "u32", "value": "normRowStride" }
          ]
        }
      }
    ],
    "scalarAffineBiasMean": [
      { "name": "x", "arg": "x", "semantic": "X", "buffer": { "type": "read-only-storage" }, "elementType": "$scalar" },
      {
        "name": "scale",
        "arg": "scale",
        "semantic": "Scale",
        "buffer": { "type": "read-only-storage" },
        "elementType": "$scalar"
      },
      {
        "name": "bias",
        "arg": "b",
        "semantic": "B",
        "buffer": { "type": "read-only-storage" },
        "elementType": "$scalar"
      },
      { "name": "y", "arg": "y", "semantic": "Y", "buffer": { "type": "storage" }, "elementType": "$scalar" },
      { "name": "mean_out", "arg": "mean", "semantic": "Mean", "buffer": { "type": "storage" }, "elementType": "f32" },
      {
        "name": "params",
        "semantic": "kernel.params",
        "buffer": { "type": "uniform" },
        "struct": {
          "name": "Params",
          "fields": [
            { "name": "rows", "type": "u32", "value": "normRows" },
            { "name": "rowStride", "type": "u32", "value": "normRowStride" }
          ]
        }
      }
    ],
    "scalarAffineBiasInvStd": [
      { "name": "x", "arg": "x", "semantic": "X", "buffer": { "type": "read-only-storage" }, "elementType": "$scalar" },
      {
        "name": "scale",
        "arg": "scale",
        "semantic": "Scale",
        "buffer": { "type": "read-only-storage" },
        "elementType": "$scalar"
      },
      {
        "name": "bias",
        "arg": "b",
        "semantic": "B",
        "buffer": { "type": "read-only-storage" },
        "elementType": "$scalar"
      },
      { "name": "y", "arg": "y", "semantic": "Y", "buffer": { "type": "storage" }, "elementType": "$scalar" },
      {
        "name": "inv_std_out",
        "arg": "invStdDev",
        "semantic": "InvStdDev",
        "buffer": { "type": "storage" },
        "elementType": "f32"
      },
      {
        "name": "params",
        "semantic": "kernel.params",
        "buffer": { "type": "uniform" },
        "struct": {
          "name": "Params",
          "fields": [
            { "name": "rows", "type": "u32", "value": "normRows" },
            { "name": "rowStride", "type": "u32", "value": "normRowStride" }
          ]
        }
      }
    ]
  },
  "variants": [
    {
      "id": "last_axis_row_vec4",
      "priority": 110,
      "when": ["f16Ok(dtypes.T)", "not present.b and noStatsOutputs", "lastAxisExactScaleOk", "dim(shapes.X, -1) % 4 == 0"],
      "constants": { "scalar": "dtypes.T", "vectorScalar": "\"vec4<\" ~ dtypes.T ~ \">\"" },
      "passes": [
        {
          "id": "main",
          "name": "LayerNormalization.LastAxisRowVec4",
          "source": {
            "shader": "norm-row-stats.wgsl.jinja",
            "inputs": {
              "mode": "\"layer\"",
              "vec4": true,
              "hasBias": false,
              "writeStats": false,
              "scalar": "dtypes.T",
              "usesF16": "dtypes.T == \"f16\"",
              "hidden": "dim(shapes.X, -1)",
              "wg": "lastAxisWgVec4",
              "epsilon": "attrs.epsilon",
              "hiddenVec": "dim(shapes.X, -1) / 4",
              "vecType": "\"vec4<\" ~ dtypes.T ~ \">\"",
              "combineSubgroups": "hasSubgroupId"
            }
          },
          "subgroupCollectivesWidth": "portable",
          "bindings": "vec4Affine",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
    },
    {
      "id": "last_axis_row",
      "priority": 100,
      "when": ["not present.b and noStatsOutputs", "lastAxisExactScaleOk", "f16Ok(dtypes.T)"],
      "demoteWhen": ["not lastAxisScalarFastOk"],
      "constants": { "scalar": "dtypes.T", "vectorScalar": "dtypes.T" },
      "passes": [
        {
          "id": "main",
          "name": "LayerNormalization.LastAxisRow",
          "source": {
            "shader": "norm-row-stats.wgsl.jinja",
            "inputs": {
              "mode": "\"layer\"",
              "vec4": false,
              "hasBias": false,
              "writeStats": false,
              "scalar": "dtypes.T",
              "usesF16": "dtypes.T == \"f16\"",
              "hidden": "dim(shapes.X, -1)",
              "wg": "lastAxisWg",
              "epsilon": "attrs.epsilon",
              "combineSubgroups": "hasSubgroupId"
            }
          },
          "subgroupCollectivesWidth": "portable",
          "bindings": "vec4Affine",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
    },
    {
      "id": "last_axis_bias_row_vec4",
      "priority": 111,
      "when": ["f16Ok(dtypes.T)", "present.b and noStatsOutputs and biasExactOk", "lastAxisExactScaleOk", "dim(shapes.X, -1) % 4 == 0"],
      "constants": { "scalar": "dtypes.T", "vectorScalar": "\"vec4<\" ~ dtypes.T ~ \">\"" },
      "passes": [
        {
          "id": "main",
          "name": "LayerNormalization.LastAxisRowVec4",
          "source": {
            "shader": "norm-row-stats.wgsl.jinja",
            "inputs": {
              "mode": "\"layer\"",
              "vec4": true,
              "hasBias": true,
              "writeStats": false,
              "scalar": "dtypes.T",
              "usesF16": "dtypes.T == \"f16\"",
              "hidden": "dim(shapes.X, -1)",
              "wg": "lastAxisWgVec4",
              "epsilon": "attrs.epsilon",
              "hiddenVec": "dim(shapes.X, -1) / 4",
              "vecType": "\"vec4<\" ~ dtypes.T ~ \">\"",
              "combineSubgroups": "hasSubgroupId"
            }
          },
          "subgroupCollectivesWidth": "portable",
          "bindings": "vec4AffineBias",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
    },
    {
      "id": "last_axis_bias_row",
      "priority": 101,
      "when": ["present.b and noStatsOutputs and biasExactOk", "lastAxisExactScaleOk", "f16Ok(dtypes.T)"],
      "demoteWhen": ["not lastAxisScalarFastOk"],
      "constants": { "scalar": "dtypes.T", "vectorScalar": "dtypes.T" },
      "passes": [
        {
          "id": "main",
          "name": "LayerNormalization.LastAxisRow",
          "source": {
            "shader": "norm-row-stats.wgsl.jinja",
            "inputs": {
              "mode": "\"layer\"",
              "vec4": false,
              "hasBias": true,
              "writeStats": false,
              "scalar": "dtypes.T",
              "usesF16": "dtypes.T == \"f16\"",
              "hidden": "dim(shapes.X, -1)",
              "wg": "lastAxisWg",
              "epsilon": "attrs.epsilon",
              "combineSubgroups": "hasSubgroupId"
            }
          },
          "subgroupCollectivesWidth": "portable",
          "bindings": "vec4AffineBias",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
    },
    {
      "id": "last_axis_stats_row_vec4",
      "priority": 112,
      "when": ["f16Ok(dtypes.T)", "not present.b and fullStatsOutputs and statsRowsOk", "lastAxisExactScaleOk", "dim(shapes.X, -1) % 4 == 0"],
      "constants": { "scalar": "dtypes.T", "vectorScalar": "\"vec4<\" ~ dtypes.T ~ \">\"" },
      "passes": [
        {
          "id": "main",
          "name": "LayerNormalization.LastAxisRowVec4",
          "source": {
            "shader": "norm-row-stats.wgsl.jinja",
            "inputs": {
              "mode": "\"layer\"",
              "vec4": true,
              "hasBias": false,
              "writeStats": true,
              "scalar": "dtypes.T",
              "usesF16": "dtypes.T == \"f16\"",
              "hidden": "dim(shapes.X, -1)",
              "wg": "lastAxisWgVec4",
              "epsilon": "attrs.epsilon",
              "hiddenVec": "dim(shapes.X, -1) / 4",
              "vecType": "\"vec4<\" ~ dtypes.T ~ \">\"",
              "combineSubgroups": "hasSubgroupId"
            }
          },
          "subgroupCollectivesWidth": "portable",
          "bindings": "vec4AffineStats",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
    },
    {
      "id": "last_axis_stats_row",
      "priority": 102,
      "when": ["not present.b and fullStatsOutputs and statsRowsOk", "lastAxisExactScaleOk", "f16Ok(dtypes.T)"],
      "demoteWhen": ["not lastAxisScalarFastOk"],
      "constants": { "scalar": "dtypes.T", "vectorScalar": "dtypes.T" },
      "passes": [
        {
          "id": "main",
          "name": "LayerNormalization.LastAxisRow",
          "source": {
            "shader": "norm-row-stats.wgsl.jinja",
            "inputs": {
              "mode": "\"layer\"",
              "vec4": false,
              "hasBias": false,
              "writeStats": true,
              "scalar": "dtypes.T",
              "usesF16": "dtypes.T == \"f16\"",
              "hidden": "dim(shapes.X, -1)",
              "wg": "lastAxisWg",
              "epsilon": "attrs.epsilon",
              "combineSubgroups": "hasSubgroupId"
            }
          },
          "subgroupCollectivesWidth": "portable",
          "bindings": "vec4AffineStats",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
    },
    {
      "id": "last_axis_bias_stats_row_vec4",
      "priority": 113,
      "when": ["f16Ok(dtypes.T)", "present.b and fullStatsOutputs and biasExactOk and statsRowsOk", "lastAxisExactScaleOk", "dim(shapes.X, -1) % 4 == 0"],
      "constants": { "scalar": "dtypes.T", "vectorScalar": "\"vec4<\" ~ dtypes.T ~ \">\"" },
      "passes": [
        {
          "id": "main",
          "name": "LayerNormalization.LastAxisRowVec4",
          "source": {
            "shader": "norm-row-stats.wgsl.jinja",
            "inputs": {
              "mode": "\"layer\"",
              "vec4": true,
              "hasBias": true,
              "writeStats": true,
              "scalar": "dtypes.T",
              "usesF16": "dtypes.T == \"f16\"",
              "hidden": "dim(shapes.X, -1)",
              "wg": "lastAxisWgVec4",
              "epsilon": "attrs.epsilon",
              "hiddenVec": "dim(shapes.X, -1) / 4",
              "vecType": "\"vec4<\" ~ dtypes.T ~ \">\"",
              "combineSubgroups": "hasSubgroupId"
            }
          },
          "subgroupCollectivesWidth": "portable",
          "bindings": "vec4AffineBiasStats",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
    },
    {
      "id": "last_axis_bias_stats_row",
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      "demoteWhen": ["not lastAxisScalarFastOk"],
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        {
          "id": "main",
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            "shader": "norm-row-stats.wgsl.jinja",
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              "mode": "\"layer\"",
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              "hidden": "dim(shapes.X, -1)",
              "wg": "lastAxisWg",
              "epsilon": "attrs.epsilon",
              "combineSubgroups": "hasSubgroupId"
            }
          },
          "subgroupCollectivesWidth": "portable",
          "bindings": "vec4AffineBiasStats",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
    },
    {
      "id": "suffix_axis_bias_exact_row_vec4",
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      "when": ["f16Ok(dtypes.T)", "present.b", "noStatsOutputs", "suffixAxisExactAffineOk", "suffixAxisSize % 4 == 0"],
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            "shader": "norm-row-stats.wgsl.jinja",
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              "hidden": "suffixAxisSize",
              "wg": "suffixAxisWgVec4",
              "epsilon": "attrs.epsilon",
              "hiddenVec": "suffixAxisSize / 4",
              "vecType": "\"vec4<\" ~ dtypes.T ~ \">\"",
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            }
          },
          "subgroupCollectivesWidth": "portable",
          "bindings": "vec4AffineBias",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
    },
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      "id": "last_axis",
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      "when": ["not present.b", "noStatsOutputs", "lastAxisBroadcastScaleOk", "f16Ok(dtypes.T)"],
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        "writeInvStdDev": false,
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        "epsilon": "attrs.epsilon"
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      "passes": [
        {
          "id": "main",
          "name": "LayerNormalization",
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            "shader": "layer-normalization.wgsl.jinja",
            "inputs": { "xShape": "shapes.X", "scaleShape": "shapes.Scale" }
          },
          "bindings": "vec4Affine",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
    },
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      "id": "last_axis_bias",
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      "when": ["present.b", "noStatsOutputs", "lastAxisBroadcastScaleOk", "biasBroadcastOk", "f16Ok(dtypes.T)"],
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        "writeMean": false,
        "writeInvStdDev": false,
        "scalar": "dtypes.T",
        "vectorScalar": "dtypes.T",
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        "hiddenSize": "dim(shapes.X, -1)",
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        "epsilon": "attrs.epsilon"
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      "passes": [
        {
          "id": "main",
          "name": "LayerNormalization",
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            "shader": "layer-normalization.wgsl.jinja",
            "inputs": { "xShape": "shapes.X", "scaleShape": "shapes.Scale", "biasShape": "shapes.B" }
          },
          "bindings": "vec4AffineBias",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
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      "id": "last_axis_stats",
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      "when": ["not present.b", "fullStatsOutputs", "lastAxisBroadcastScaleOk", "statsRowsOk", "f16Ok(dtypes.T)"],
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        "writeMean": true,
        "writeInvStdDev": true,
        "scalar": "dtypes.T",
        "vectorScalar": "dtypes.T",
        "usesF16": "dtypes.T == \"f16\"",
        "hiddenSize": "dim(shapes.X, -1)",
        "workgroupSize": "lastAxisWg",
        "epsilon": "attrs.epsilon"
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      "passes": [
        {
          "id": "main",
          "name": "LayerNormalization",
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            "shader": "layer-normalization.wgsl.jinja",
            "inputs": { "xShape": "shapes.X", "scaleShape": "shapes.Scale" }
          },
          "bindings": "vec4AffineStats",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
    },
    {
      "id": "last_axis_bias_stats",
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        "writeMean": true,
        "writeInvStdDev": true,
        "scalar": "dtypes.T",
        "vectorScalar": "dtypes.T",
        "usesF16": "dtypes.T == \"f16\"",
        "hiddenSize": "dim(shapes.X, -1)",
        "workgroupSize": "lastAxisWg",
        "epsilon": "attrs.epsilon"
      },
      "passes": [
        {
          "id": "main",
          "name": "LayerNormalization",
          "source": {
            "shader": "layer-normalization.wgsl.jinja",
            "inputs": { "xShape": "shapes.X", "scaleShape": "shapes.Scale", "biasShape": "shapes.B" }
          },
          "bindings": "vec4AffineBiasStats",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
    },
    {
      "id": "suffix_axis",
      "priority": 40,
      "when": ["not present.b", "noStatsOutputs", "suffixAxisBroadcastScaleOk", "f16Ok(dtypes.T)"],
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        "hasBias": false,
        "writeMean": false,
        "writeInvStdDev": false,
        "scalar": "dtypes.T",
        "vectorScalar": "dtypes.T",
        "usesF16": "dtypes.T == \"f16\"",
        "hiddenSize": "suffixAxisSize",
        "workgroupSize": "suffixAxisWg",
        "epsilon": "attrs.epsilon"
      },
      "passes": [
        {
          "id": "main",
          "name": "LayerNormalization.SuffixAxis",
          "source": {
            "shader": "layer-normalization.wgsl.jinja",
            "inputs": { "xShape": "shapes.X", "scaleShape": "shapes.Scale" }
          },
          "bindings": "vec4Affine",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
    },
    {
      "id": "suffix_axis_bias",
      "priority": 50,
      "when": ["present.b", "noStatsOutputs", "suffixAxisBroadcastScaleOk", "biasBroadcastOk", "f16Ok(dtypes.T)"],
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        "hasBias": true,
        "writeMean": false,
        "writeInvStdDev": false,
        "scalar": "dtypes.T",
        "vectorScalar": "dtypes.T",
        "usesF16": "dtypes.T == \"f16\"",
        "hiddenSize": "suffixAxisSize",
        "workgroupSize": "suffixAxisWg",
        "epsilon": "attrs.epsilon"
      },
      "passes": [
        {
          "id": "main",
          "name": "LayerNormalization.SuffixAxisBias",
          "source": {
            "shader": "layer-normalization.wgsl.jinja",
            "inputs": { "xShape": "shapes.X", "scaleShape": "shapes.Scale", "biasShape": "shapes.B" }
          },
          "bindings": "vec4AffineBias",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
    },
    {
      "id": "suffix_axis_stats",
      "priority": 45,
      "when": ["not present.b", "fullStatsOutputs", "suffixAxisBroadcastScaleOk", "statsOuterOk", "f16Ok(dtypes.T)"],
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        "writeMean": true,
        "writeInvStdDev": true,
        "scalar": "dtypes.T",
        "vectorScalar": "dtypes.T",
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        "hiddenSize": "suffixAxisSize",
        "workgroupSize": "suffixAxisWg",
        "epsilon": "attrs.epsilon"
      },
      "passes": [
        {
          "id": "main",
          "name": "LayerNormalization.SuffixAxisStats",
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            "shader": "layer-normalization.wgsl.jinja",
            "inputs": { "xShape": "shapes.X", "scaleShape": "shapes.Scale" }
          },
          "bindings": "vec4AffineStats",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
    },
    {
      "id": "suffix_axis_bias_stats",
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      "when": ["present.b", "fullStatsOutputs", "suffixAxisBroadcastScaleOk", "biasBroadcastOk", "statsOuterOk", "f16Ok(dtypes.T)"],
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        "hasBias": true,
        "writeMean": true,
        "writeInvStdDev": true,
        "scalar": "dtypes.T",
        "vectorScalar": "dtypes.T",
        "usesF16": "dtypes.T == \"f16\"",
        "hiddenSize": "suffixAxisSize",
        "workgroupSize": "suffixAxisWg",
        "epsilon": "attrs.epsilon"
      },
      "passes": [
        {
          "id": "main",
          "name": "LayerNormalization.SuffixAxisBiasStats",
          "source": {
            "shader": "layer-normalization.wgsl.jinja",
            "inputs": { "xShape": "shapes.X", "scaleShape": "shapes.Scale", "biasShape": "shapes.B" }
          },
          "bindings": "vec4AffineBiasStats",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
    },
    {
      "id": "mean_only",
      "priority": 31,
      "when": ["not present.b and meanOnlyOutputs and meanRowsOk", "lastAxisBroadcastScaleOk or suffixAxisBroadcastScaleOk", "f16Ok(dtypes.T)"],
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        "writeMean": true,
        "writeInvStdDev": false,
        "scalar": "dtypes.T",
        "usesF16": "dtypes.T == \"f16\"",
        "hiddenSize": "genericHiddenSize",
        "workgroupSize": "genericWorkgroupSize",
        "epsilon": "attrs.epsilon"
      },
      "passes": [
        {
          "id": "main",
          "name": "LayerNormalization.MeanOnly",
          "source": {
            "shader": "layer-normalization.wgsl.jinja",
            "inputs": { "xShape": "shapes.X", "scaleShape": "shapes.Scale" }
          },
          "bindings": "scalarAffineMean",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
    },
    {
      "id": "bias_mean_only",
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      "when": ["present.b and meanOnlyOutputs and biasBroadcastOk and meanRowsOk", "lastAxisBroadcastScaleOk or suffixAxisBroadcastScaleOk", "f16Ok(dtypes.T)"],
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        "writeMean": true,
        "writeInvStdDev": false,
        "scalar": "dtypes.T",
        "usesF16": "dtypes.T == \"f16\"",
        "hiddenSize": "genericHiddenSize",
        "workgroupSize": "genericWorkgroupSize",
        "epsilon": "attrs.epsilon"
      },
      "passes": [
        {
          "id": "main",
          "name": "LayerNormalization.BiasMeanOnly",
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            "shader": "layer-normalization.wgsl.jinja",
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          },
          "bindings": "scalarAffineBiasMean",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
    },
    {
      "id": "inv_std_dev_only",
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      "when": ["not present.b and invStdOnlyOutputs and invStdRowsOk", "lastAxisBroadcastScaleOk or suffixAxisBroadcastScaleOk", "f16Ok(dtypes.T)"],
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        "writeInvStdDev": true,
        "scalar": "dtypes.T",
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        "hiddenSize": "genericHiddenSize",
        "workgroupSize": "genericWorkgroupSize",
        "epsilon": "attrs.epsilon"
      },
      "passes": [
        {
          "id": "main",
          "name": "LayerNormalization.InvStdDevOnly",
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            "shader": "layer-normalization.wgsl.jinja",
            "inputs": { "xShape": "shapes.X", "scaleShape": "shapes.Scale" }
          },
          "bindings": "scalarAffineInvStd",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
    },
    {
      "id": "bias_inv_std_dev_only",
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      "when": ["present.b and invStdOnlyOutputs and biasBroadcastOk and invStdRowsOk", "lastAxisBroadcastScaleOk or suffixAxisBroadcastScaleOk", "f16Ok(dtypes.T)"],
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        "writeInvStdDev": true,
        "scalar": "dtypes.T",
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        "hiddenSize": "genericHiddenSize",
        "workgroupSize": "genericWorkgroupSize",
        "epsilon": "attrs.epsilon"
      },
      "passes": [
        {
          "id": "main",
          "name": "LayerNormalization.BiasInvStdDevOnly",
          "source": {
            "shader": "layer-normalization.wgsl.jinja",
            "inputs": { "xShape": "shapes.X", "scaleShape": "shapes.Scale", "biasShape": "shapes.B" }
          },
          "bindings": "scalarAffineBiasInvStd",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
    }
  ]
}