{
  "domain": "ai.onnx",
  "name": "MeanVarianceNormalization",
  "sinceVersion": 13,
  "description": "Normalizes each group as `(X - mean) / sqrt(variance)`, reducing over `axes` (default `[0, 2, 3]`).",
  "inputs": [{ "role": "X", "dtype": "T", "description": "Input tensor to normalize." }],
  "outputs": [
    {
      "role": "Y",
      "dtype": "T",
      "rank": "ranks.X",
      "description": "Normalized tensor with the same shape as `X`.",
      "shape": "shapes.X"
    }
  ],
  "attributes": { "axes": [0, 2, 3] },
  "attributeDescriptions": { "axes": "Axes that share a mean and variance; negative values count from the back." },
  "typeConstraints": { "T": ["float32", "float16"] },
  "args": {
    "x": { "kind": "tensor", "semantic": "X", "role": "input" },
    "y": { "kind": "tensor", "semantic": "Y", "role": "output" }
  },
  "tunables": {
    "WORKGROUP_SIZE": 256,
    "SERIAL_WORKGROUP_SIZE": 256,
    "SERIAL_TINY_WORKGROUP_SIZE": 64,
    "SERIAL_MAX_REDUCTION": 128,
    "SERIAL_MIN_ROWS": 256,
    "TREE_MEDIUM_WORKGROUP_SIZE": 64,
    "VEC4_MIN_REDUCTION": 8,
    "FLAT_SPLIT_MIN_ELEMENTS": 65536,
    "FLAT_SPLIT_TARGET_ELEMENTS": 4096,
    "MAX_FLAT_SPLITS": 256
  },
  "derive": {
    "deviceWorkgroupCap": "min(device.limits.maxComputeInvocationsPerWorkgroup, device.limits.maxComputeWorkgroupSizeX)",
    "foldedDispatchCapacity": "device.limits.maxComputeWorkgroupsPerDimension * device.limits.maxComputeWorkgroupsPerDimension",
    "shapeContract": "ranks.X >= 3 and ranks.Y == ranks.X and sameShape(shapes.Y, shapes.X) and f16Ok(dtypes.T)",
    "reduceCount": "(dim(shapes.X, 0) if hasAxis(attrs.axes, 0, ranks.X) else 1) * (dim(shapes.X, 1) if hasAxis(attrs.axes, 1, ranks.X) else 1) * (dim(shapes.X, 2) if hasAxis(attrs.axes, 2, ranks.X) else 1) * (dim(shapes.X, 3) if ranks.X >= 4 and hasAxis(attrs.axes, 3, ranks.X) else 1) * (dim(shapes.X, 4) if ranks.X >= 5 and hasAxis(attrs.axes, 4, ranks.X) else 1) * (dim(shapes.X, 5) if ranks.X >= 6 and hasAxis(attrs.axes, 5, ranks.X) else 1)",
    "rowCount": "numel(shapes.X) / max(1, reduceCount)",
    "allAxesReduced": "hasAxis(attrs.axes, 0, ranks.X) and hasAxis(attrs.axes, 1, ranks.X) and hasAxis(attrs.axes, 2, ranks.X) and (ranks.X < 4 or hasAxis(attrs.axes, 3, ranks.X)) and (ranks.X < 5 or hasAxis(attrs.axes, 4, ranks.X)) and (ranks.X < 6 or hasAxis(attrs.axes, 5, ranks.X))",
    "vec4Eligible": "((ranks.X == 3 and hasAxis(attrs.axes, 2, 3) and (dim(shapes.X, 2) % 4 == 0 or (hasAxis(attrs.axes, 1, 3) and dim(shapes.X, 1) * dim(shapes.X, 2) % 4 == 0) or (hasAxis(attrs.axes, 0, 3) and hasAxis(attrs.axes, 1, 3) and numel(shapes.X) % 4 == 0))) or (ranks.X == 4 and hasAxis(attrs.axes, 3, 4) and (dim(shapes.X, 3) % 4 == 0 or (hasAxis(attrs.axes, 2, 4) and dim(shapes.X, 2) * dim(shapes.X, 3) % 4 == 0) or (hasAxis(attrs.axes, 1, 4) and hasAxis(attrs.axes, 2, 4) and dim(shapes.X, 1) * dim(shapes.X, 2) * dim(shapes.X, 3) % 4 == 0) or (hasAxis(attrs.axes, 0, 4) and hasAxis(attrs.axes, 1, 4) and hasAxis(attrs.axes, 2, 4) and numel(shapes.X) % 4 == 0))) or (ranks.X == 5 and hasAxis(attrs.axes, 4, 5) and (dim(shapes.X, 4) % 4 == 0 or (hasAxis(attrs.axes, 3, 5) and dim(shapes.X, 3) * dim(shapes.X, 4) % 4 == 0) or (hasAxis(attrs.axes, 2, 5) and hasAxis(attrs.axes, 3, 5) and dim(shapes.X, 2) * dim(shapes.X, 3) * dim(shapes.X, 4) % 4 == 0) or (hasAxis(attrs.axes, 1, 5) and hasAxis(attrs.axes, 2, 5) and hasAxis(attrs.axes, 3, 5) and dim(shapes.X, 1) * dim(shapes.X, 2) * dim(shapes.X, 3) * dim(shapes.X, 4) % 4 == 0) or (allAxesReduced and numel(shapes.X) % 4 == 0))) or (ranks.X == 6 and hasAxis(attrs.axes, 5, 6) and (dim(shapes.X, 5) % 4 == 0 or (hasAxis(attrs.axes, 4, 6) and dim(shapes.X, 4) * dim(shapes.X, 5) % 4 == 0) or (hasAxis(attrs.axes, 3, 6) and hasAxis(attrs.axes, 4, 6) and dim(shapes.X, 3) * dim(shapes.X, 4) * dim(shapes.X, 5) % 4 == 0) or (hasAxis(attrs.axes, 2, 6) and hasAxis(attrs.axes, 3, 6) and hasAxis(attrs.axes, 4, 6) and dim(shapes.X, 2) * dim(shapes.X, 3) * dim(shapes.X, 4) * dim(shapes.X, 5) % 4 == 0) or (hasAxis(attrs.axes, 1, 6) and hasAxis(attrs.axes, 2, 6) and hasAxis(attrs.axes, 3, 6) and hasAxis(attrs.axes, 4, 6) and dim(shapes.X, 1) * dim(shapes.X, 2) * dim(shapes.X, 3) * dim(shapes.X, 4) * dim(shapes.X, 5) % 4 == 0) or (allAxesReduced and numel(shapes.X) % 4 == 0))))",
    "maxWorkgroupSize": "min(tunables.WORKGROUP_SIZE, deviceWorkgroupCap)",
    "minSubgroupSize": "device.adapterInfo.subgroupMinSize if has(device.adapterInfo, \"subgroupMinSize\") else 1",
    "useSubgroups": "device.features.has(\"subgroups\") and has(device.adapterInfo, \"subgroupMinSize\") and minSubgroupSize > 0",
    "scalarWorkgroupSize": "min(maxWorkgroupSize, tunables.TREE_MEDIUM_WORKGROUP_SIZE) if not useSubgroups and reduceCount > tunables.TREE_MEDIUM_WORKGROUP_SIZE and reduceCount <= 2 * tunables.TREE_MEDIUM_WORKGROUP_SIZE else min(maxWorkgroupSize, max(1, pow2ceil(reduceCount)))",
    "vectorWorkgroupSize": "min(maxWorkgroupSize, max(1, pow2ceil(ceilDiv(reduceCount, 4))))",
    "serialWorkgroupSize": "min(device.limits.maxComputeInvocationsPerWorkgroup, device.limits.maxComputeWorkgroupSizeX, (tunables.SERIAL_TINY_WORKGROUP_SIZE if reduceCount <= 4 else tunables.SERIAL_WORKGROUP_SIZE))",
    "rowDispatchFits": "rowCount <= foldedDispatchCapacity",
    "serialDispatchFits": "ceilDiv(rowCount, serialWorkgroupSize) <= foldedDispatchCapacity",
    "applyDispatchFits": "ceilDiv(numel(shapes.Y), maxWorkgroupSize) <= foldedDispatchCapacity",
    "scalarStorageFits": "scalarWorkgroupSize * 8 <= device.limits.maxComputeWorkgroupStorageSize",
    "vectorStorageFits": "vectorWorkgroupSize * 8 <= device.limits.maxComputeWorkgroupStorageSize",
    "flatSplit": "min(tunables.MAX_FLAT_SPLITS, pow2ceil(ceilDiv(numel(shapes.X), tunables.FLAT_SPLIT_TARGET_ELEMENTS)))",
    "flatScratchBytes": "flatSplit * 8",
    "flatPathFits": "flatSplit <= device.limits.maxComputeWorkgroupsPerDimension and flatScratchBytes <= device.limits.maxStorageBufferBindingSize and flatScratchBytes <= device.limits.maxBufferSize and maxWorkgroupSize * 8 <= device.limits.maxComputeWorkgroupStorageSize and applyDispatchFits"
  },
  "bindingSets": {
    "rows": [
      {
        "name": "x",
        "arg": "x",
        "semantic": "X",
        "buffer": { "type": "read-only-storage" },
        "elementType": "$ioElement"
      },
      { "name": "y", "arg": "y", "semantic": "Y", "buffer": { "type": "storage" }, "elementType": "$ioElement" },
      {
        "name": "params",
        "semantic": "kernel.params",
        "buffer": { "type": "uniform" },
        "struct": { "name": "Params", "fields": [{ "name": "rows", "type": "u32", "value": "rowCount" }] }
      }
    ],
    "flatPartials": [
      { "name": "x", "arg": "x", "semantic": "X", "buffer": { "type": "read-only-storage" }, "elementType": "$scalar" },
      { "name": "partials", "semantic": "partials", "buffer": { "type": "storage" }, "elementType": "vec2<f32>" },
      {
        "name": "params",
        "semantic": "kernel.params",
        "buffer": { "type": "uniform" },
        "struct": { "name": "Params", "fields": [{ "name": "count", "type": "u32", "value": "numel(shapes.X)" }] }
      }
    ],
    "flatCombine": [
      { "name": "x", "arg": "x", "semantic": "X", "buffer": { "type": "read-only-storage" }, "elementType": "$scalar" },
      {
        "name": "partials",
        "semantic": "partials",
        "buffer": { "type": "read-only-storage" },
        "elementType": "vec2<f32>"
      },
      { "name": "stats", "semantic": "stats", "buffer": { "type": "storage" }, "elementType": "f32", "length": 2 },
      {
        "name": "params",
        "semantic": "kernel.params",
        "buffer": { "type": "uniform" },
        "struct": { "name": "Params", "fields": [{ "name": "count", "type": "u32", "value": "numel(shapes.X)" }] }
      }
    ],
    "flatApply": [
      { "name": "x", "arg": "x", "semantic": "X", "buffer": { "type": "read-only-storage" }, "elementType": "$scalar" },
      {
        "name": "stats",
        "semantic": "stats",
        "buffer": { "type": "read-only-storage" },
        "elementType": "f32",
        "length": 2
      },
      { "name": "y", "arg": "y", "semantic": "Y", "buffer": { "type": "storage" }, "elementType": "$scalar" },
      {
        "name": "params",
        "semantic": "kernel.params",
        "buffer": { "type": "uniform" },
        "struct": { "name": "Params", "fields": [{ "name": "count", "type": "u32", "value": "numel(shapes.Y)" }] }
      }
    ],
    "noopParams": [
      {
        "name": "params",
        "semantic": "kernel.params",
        "buffer": { "type": "uniform" },
        "struct": { "name": "Params", "fields": [{ "name": "dummy", "type": "u32", "value": 0 }] }
      }
    ]
  },
  "variants": [
    {
      "id": "empty_noop",
      "priority": 200,
      "when": ["shapeContract", "numel(shapes.X) == 0"],
      "passes": [
        {
          "id": "noop",
          "name": "MeanVarianceNormalization.Empty",
          "shader": "noop.wgsl.jinja",
          "bindings": "noopParams",
          "dispatch": { "x": 0 }
        }
      ]
    },
    {
      "id": "all_axes_flat_split",
      "priority": 120,
      "when": ["shapeContract", "numel(shapes.X) > 0", "allAxesReduced", "numel(shapes.X) >= tunables.FLAT_SPLIT_MIN_ELEMENTS", "flatPathFits"],
      "constants": { "scalar": "dtypes.T" },
      "intermediates": [
        { "id": "partials", "dtype": "float32", "shape": "[flatSplit, 2]" },
        { "id": "stats", "dtype": "float32", "shape": "[2]" }
      ],
      "passes": [
        {
          "id": "partials",
          "name": "MeanVarianceNormalization.FlatPartials",
          "source": {
            "shader": "norm-flat-splitk-partials.wgsl.jinja",
            "inputs": { "workgroupSize": "maxWorkgroupSize", "split": "flatSplit", "usesF16": "dtypes.T == \"f16\"" }
          },
          "bindings": "flatPartials",
          "dispatch": { "workgroups": "flatSplit" }
        },
        {
          "id": "combine",
          "name": "MeanVarianceNormalization.FlatCombine",
          "source": {
            "shader": "norm-flat-splitk-combine.wgsl.jinja",
            "inputs": { "split": "flatSplit", "usesF16": "dtypes.T == \"f16\"" }
          },
          "bindings": "flatCombine",
          "dispatch": { "workgroups": 1 }
        },
        {
          "id": "apply",
          "name": "MeanVarianceNormalization.FlatApply",
          "source": {
            "shader": "norm-flat-apply.wgsl.jinja",
            "inputs": { "workgroupSize": "maxWorkgroupSize", "scalar": "dtypes.T", "usesF16": "dtypes.T == \"f16\"" }
          },
          "bindings": "flatApply",
          "dispatch": { "threads": "numel(shapes.Y)", "workgroupSize": "maxWorkgroupSize" }
        }
      ]
    },
    {
      "id": "serial_rows",
      "priority": 115,
      "when": ["shapeContract", "numel(shapes.X) > 0", "reduceCount <= tunables.SERIAL_MAX_REDUCTION", "rowCount >= tunables.SERIAL_MIN_ROWS", "serialDispatchFits"],
      "constants": { "scalar": "dtypes.T", "ioElement": "dtypes.T" },
      "passes": [
        {
          "id": "main",
          "name": "MeanVarianceNormalization.SerialRows",
          "source": {
            "shader": "mean-variance-normalization-serial-rows.wgsl.jinja",
            "inputs": {
              "xShape": "shapes.X",
              "reduce": ["hasAxis(attrs.axes, 0, ranks.X)", "hasAxis(attrs.axes, 1, ranks.X)", "hasAxis(attrs.axes, 2, ranks.X)", "hasAxis(attrs.axes, 3, ranks.X)", "hasAxis(attrs.axes, 4, ranks.X)", "hasAxis(attrs.axes, 5, ranks.X)"],
              "reduceCount": "reduceCount",
              "workgroupSize": "serialWorkgroupSize",
              "scalar": "dtypes.T",
              "usesF16": "dtypes.T == \"f16\""
            }
          },
          "bindings": "rows",
          "dispatch": { "threads": "rowCount", "workgroupSize": "serialWorkgroupSize" }
        }
      ]
    },
    {
      "id": "cooperative_vec4",
      "priority": 110,
      "when": ["shapeContract", "numel(shapes.X) > 0", "reduceCount >= tunables.VEC4_MIN_REDUCTION", "vec4Eligible", "rowDispatchFits", "vectorStorageFits"],
      "constants": {
        "scalar": "dtypes.T",
        "vectorScalar": "\"vec4<\" ~ dtypes.T ~ \">\"",
        "ioElement": "\"vec4<\" ~ dtypes.T ~ \">\""
      },
      "passes": [
        {
          "id": "main",
          "name": "MeanVarianceNormalization.CooperativeVec4",
          "source": {
            "shader": "mean-variance-normalization-subgroup.wgsl.jinja",
            "inputs": {
              "xShape": "shapes.X",
              "reduce": ["hasAxis(attrs.axes, 0, ranks.X)", "hasAxis(attrs.axes, 1, ranks.X)", "hasAxis(attrs.axes, 2, ranks.X)", "hasAxis(attrs.axes, 3, ranks.X)", "hasAxis(attrs.axes, 4, ranks.X)", "hasAxis(attrs.axes, 5, ranks.X)"],
              "reduceCount": "reduceCount",
              "wg": "vectorWorkgroupSize",
              "minSubgroupSize": "minSubgroupSize",
              "maxSubgroups": "ceilDiv(vectorWorkgroupSize, minSubgroupSize)",
              "scalar": "dtypes.T",
              "vecType": "\"vec4<\" ~ dtypes.T ~ \">\"",
              "usesF16": "dtypes.T == \"f16\"",
              "useSubgroups": "useSubgroups",
              "vectorized": true
            }
          },
          "bindings": "rows",
          "dispatch": { "workgroups": "rowCount" }
        }
      ]
    },
    {
      "id": "cooperative_scalar",
      "priority": 100,
      "when": ["shapeContract", "numel(shapes.X) > 0", "rowDispatchFits", "scalarStorageFits"],
      "constants": { "scalar": "dtypes.T", "ioElement": "dtypes.T" },
      "passes": [
        {
          "id": "main",
          "name": "MeanVarianceNormalization.CooperativeScalar",
          "source": {
            "shader": "mean-variance-normalization-subgroup.wgsl.jinja",
            "inputs": {
              "xShape": "shapes.X",
              "reduce": ["hasAxis(attrs.axes, 0, ranks.X)", "hasAxis(attrs.axes, 1, ranks.X)", "hasAxis(attrs.axes, 2, ranks.X)", "hasAxis(attrs.axes, 3, ranks.X)", "hasAxis(attrs.axes, 4, ranks.X)", "hasAxis(attrs.axes, 5, ranks.X)"],
              "reduceCount": "reduceCount",
              "wg": "scalarWorkgroupSize",
              "minSubgroupSize": "minSubgroupSize",
              "maxSubgroups": "ceilDiv(scalarWorkgroupSize, minSubgroupSize)",
              "scalar": "dtypes.T",
              "usesF16": "dtypes.T == \"f16\"",
              "useSubgroups": "useSubgroups",
              "vectorized": false
            }
          },
          "bindings": "rows",
          "dispatch": { "workgroups": "rowCount" }
        }
      ]
    }
  ]
}