{
  "domain": "ai.onnx",
  "name": "SimplifiedLayerNormalization",
  "conformance": "legacy-default-domain",
  "sinceVersion": 1,
  "description": "Implements ONNX Runtime's legacy RMS normalization for models that serialize `SimplifiedLayerNormalization` in the default ONNX domain: `Y = (X / sqrt(mean(X^2) + epsilon)) * scale`. It shares kernels with [ONNX `RMSNormalization`](https://onnx.ai/onnx/operators/onnx__RMSNormalization.html), but retains scale-before-output-cast ordering and optional `inv_std_var`. See the [compatibility discussion](https://github.com/onnx/onnx/issues/6582#issuecomment-3591862327). Supports float16/float32, float32 statistics, and a nonempty normalization suffix.",
  "inputs": [
    {
      "role": "X",
      "dtype": "T",
      "description": "Input tensor; the mean square is taken over the suffix dimensions starting at `axis`."
    },
    {
      "role": "scale",
      "dtype": "V",
      "description": "Scale tensor, unidirectionally broadcastable to `X`; output `Y` has this tensor's dtype."
    }
  ],
  "outputs": [
    {
      "role": "Y",
      "dtype": "V",
      "rank": "ranks.X",
      "shape": "shapes.X",
      "description": "Normalized and scaled output; same shape as `X` and same dtype as `scale`."
    },
    {
      "role": "inv_std_var",
      "dtype": "U",
      "rank": "ranks.X",
      "shape": "prefix(shapes.X, axisNorm) + fill(1, ranks.X - axisNorm)",
      "optional": true,
      "description": "Optional inverse RMS statistic `1 / sqrt(mean(X^2) + epsilon)`; same rank as `X`, with the dimensions from `axis` onward set to one."
    }
  ],
  "attributes": { "axis": -1, "epsilon": 0.00001, "stash_type": 1, "keep_dims": 1 },
  "attributeDescriptions": {
    "axis": "The first dimension of the normalization suffix; negative values count from the end, so the default `-1` normalizes only the last dimension.",
    "epsilon": "Small constant added to the mean square before taking the square root to avoid division by zero.",
    "stash_type": "TensorProto element type of `inv_std_var`; this package implements the legacy float32 value `1`.",
    "keep_dims": "Legacy compatibility attribute accepted and ignored by ONNX Runtime. The supported value `1` records the runtime's fixed behavior: optional statistics retain the input rank with normalized dimensions set to one."
  },
  "attributeConstraints": { "stash_type": { "values": [1] }, "keep_dims": { "values": [1] } },
  "typeConstraints": { "T": ["float32", "float16"], "V": ["float32", "float16"], "U": ["float32"] },
  "args": {
    "x": { "kind": "tensor", "semantic": "X", "role": "input" },
    "scale": { "kind": "tensor", "semantic": "scale", "role": "input" },
    "y": { "kind": "tensor", "semantic": "Y", "role": "output" },
    "invStdVar": { "kind": "tensor", "semantic": "inv_std_var", "role": "output", "required": false }
  },
  "tunables": {
    "WORKGROUP_SIZE": 256,
    "SPLIT_MAX_ROWS": 256,
    "SPLIT_MIN_HIDDEN": 16384,
    "SPLIT_TARGET_ELEMENTS": 4096,
    "MAX_SPLITS": 64
  },
  "derive": {
    "deviceWorkgroupCap": "min(device.limits.maxComputeInvocationsPerWorkgroup, device.limits.maxComputeWorkgroupSizeX)",
    "wave32Adapter": "has(device.adapterInfo, \"subgroupMinSize\") and has(device.adapterInfo, \"subgroupMaxSize\") and device.adapterInfo.subgroupMinSize == 32 and device.adapterInfo.subgroupMaxSize == 32",
    "reportedNonWave32Adapter": "not wave32Adapter and (has(device.adapterInfo, \"subgroupMinSize\") or has(device.adapterInfo, \"subgroupMaxSize\"))",
    "normMaxWorkgroup": "min(tunables.WORKGROUP_SIZE, deviceWorkgroupCap)",
    "hasSubgroupId": "device.features.has(\"subgroups\") and device.wgslLanguageFeatures.has(\"subgroup_id\")",
    "axisNorm": "attrs.axis if attrs.axis >= 0 else attrs.axis + ranks.X",
    "normRows": "outer(shapes.X, axisNorm)",
    "normHidden": "dim(shapes.X, axisNorm) * inner(shapes.X, axisNorm)",
    "normRowStride": "max(1, min(normRows, device.limits.maxComputeWorkgroupsPerDimension))",
    "rowWg": "min(normMaxWorkgroup, pow2ceil(max(1, normHidden)))",
    "baseOk": "ranks.X >= 1 and sameShape(shapes.Y, shapes.X) and ranks.scale >= 0 and ranks.scale <= ranks.X and broadcastable(shapes.scale, shapes.X) and attrs.axis + ranks.X >= 0 and attrs.axis < ranks.X and normHidden > 0 and attrs.stash_type == onnxDtypeCode(\"float32\") and f16Ok(dtypes.T) and f16Ok(dtypes.V)",
    "lastAxisOk": "baseOk and (attrs.axis == -1 or attrs.axis == ranks.X - 1)",
    "suffixAxisOk": "baseOk and ranks.X >= 2 and not (attrs.axis == -1 or attrs.axis == ranks.X - 1)",
    "noStats": "not present.invStdVar",
    "statsOk": "present.invStdVar and ranks.inv_std_var == ranks.X and sameShape(prefix(shapes.inv_std_var, axisNorm), prefix(shapes.X, axisNorm)) and numel(suffix(shapes.inv_std_var, axisNorm)) == 1",
    "sameDtype": "dtypes.T == dtypes.V",
    "splitCount": "min(tunables.MAX_SPLITS, pow2ceil(ceilDiv(normHidden, tunables.SPLIT_TARGET_ELEMENTS)))",
    "splitScratchBytes": "normRows * splitCount * 4",
    "splitFits": "normRows <= tunables.SPLIT_MAX_ROWS and splitCount <= device.limits.maxComputeWorkgroupsPerDimension and splitScratchBytes <= device.limits.maxStorageBufferBindingSize and splitScratchBytes <= device.limits.maxBufferSize"
  },
  "bindingSets": {
    "rows": [
      {
        "name": "x",
        "arg": "x",
        "semantic": "X",
        "buffer": { "type": "read-only-storage" },
        "elementType": "$xElement"
      },
      {
        "name": "scale",
        "arg": "scale",
        "semantic": "scale",
        "buffer": { "type": "read-only-storage" },
        "elementType": "$ioElement"
      },
      { "name": "y", "arg": "y", "semantic": "Y", "buffer": { "type": "storage" }, "elementType": "$ioElement" },
      {
        "name": "params",
        "semantic": "kernel.params",
        "buffer": { "type": "uniform" },
        "struct": {
          "name": "Params",
          "fields": [
            { "name": "rows", "type": "u32", "value": "normRows" },
            { "name": "rowStride", "type": "u32", "value": "normRowStride" }
          ]
        }
      }
    ],
    "rowsStats": [
      {
        "name": "x",
        "arg": "x",
        "semantic": "X",
        "buffer": { "type": "read-only-storage" },
        "elementType": "$xElement"
      },
      {
        "name": "scale",
        "arg": "scale",
        "semantic": "scale",
        "buffer": { "type": "read-only-storage" },
        "elementType": "$ioElement"
      },
      { "name": "y", "arg": "y", "semantic": "Y", "buffer": { "type": "storage" }, "elementType": "$ioElement" },
      {
        "name": "inv_std_out",
        "arg": "invStdVar",
        "semantic": "inv_std_var",
        "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" }
          ]
        }
      }
    ],
    "splitPartials": [
      {
        "name": "x",
        "arg": "x",
        "semantic": "X",
        "buffer": { "type": "read-only-storage" },
        "elementType": "$xElement"
      },
      { "name": "partials", "semantic": "partials", "buffer": { "type": "storage" }, "elementType": "f32" },
      {
        "name": "params",
        "semantic": "kernel.params",
        "buffer": { "type": "uniform" },
        "struct": {
          "name": "Params",
          "fields": [
            { "name": "rows", "type": "u32", "value": "normRows" },
            { "name": "rowStride", "type": "u32", "value": "normRowStride" }
          ]
        }
      }
    ],
    "splitNormalize": [
      {
        "name": "x",
        "arg": "x",
        "semantic": "X",
        "buffer": { "type": "read-only-storage" },
        "elementType": "$xElement"
      },
      {
        "name": "scale",
        "arg": "scale",
        "semantic": "scale",
        "buffer": { "type": "read-only-storage" },
        "elementType": "$ioElement"
      },
      { "name": "partials", "semantic": "partials", "buffer": { "type": "read-only-storage" }, "elementType": "f32" },
      { "name": "y", "arg": "y", "semantic": "Y", "buffer": { "type": "storage" }, "elementType": "$ioElement" },
      {
        "name": "params",
        "semantic": "kernel.params",
        "buffer": { "type": "uniform" },
        "struct": {
          "name": "Params",
          "fields": [
            { "name": "rows", "type": "u32", "value": "normRows" },
            { "name": "rowStride", "type": "u32", "value": "normRowStride" }
          ]
        }
      }
    ],
    "splitNormalizeStats": [
      {
        "name": "x",
        "arg": "x",
        "semantic": "X",
        "buffer": { "type": "read-only-storage" },
        "elementType": "$xElement"
      },
      {
        "name": "scale",
        "arg": "scale",
        "semantic": "scale",
        "buffer": { "type": "read-only-storage" },
        "elementType": "$ioElement"
      },
      { "name": "partials", "semantic": "partials", "buffer": { "type": "read-only-storage" }, "elementType": "f32" },
      { "name": "y", "arg": "y", "semantic": "Y", "buffer": { "type": "storage" }, "elementType": "$ioElement" },
      {
        "name": "inv_std_out",
        "arg": "invStdVar",
        "semantic": "inv_std_var",
        "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",
      "priority": 1,
      "when": ["lastAxisOk", "noStats"],
      "constants": {
        "scalar": "dtypes.V",
        "xElement": "dtypes.T",
        "ioElement": "dtypes.V",
        "usesF16": "dtypes.T == \"f16\" or dtypes.V == \"f16\"",
        "hiddenSize": "normHidden",
        "workgroupSize": "rowWg",
        "epsilon": "attrs.epsilon"
      },
      "passes": [
        {
          "id": "main",
          "name": "SimplifiedLayerNormalization.Row",
          "source": {
            "shader": "rms-normalization.wgsl.jinja",
            "inputs": {
              "xShape": "shapes.X",
              "scaleShape": "shapes.scale",
              "xRank": "ranks.X",
              "scaleRank": "ranks.scale",
              "writeStats": false,
              "rmsScaleAfterCast": false
            }
          },
          "bindings": "rows",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
    },
    {
      "id": "last_axis_stats",
      "priority": 2,
      "when": ["lastAxisOk", "statsOk"],
      "constants": {
        "scalar": "dtypes.V",
        "xElement": "dtypes.T",
        "ioElement": "dtypes.V",
        "usesF16": "dtypes.T == \"f16\" or dtypes.V == \"f16\"",
        "hiddenSize": "normHidden",
        "workgroupSize": "rowWg",
        "epsilon": "attrs.epsilon"
      },
      "passes": [
        {
          "id": "main",
          "name": "SimplifiedLayerNormalization.Row",
          "source": {
            "shader": "rms-normalization.wgsl.jinja",
            "inputs": {
              "xShape": "shapes.X",
              "scaleShape": "shapes.scale",
              "xRank": "ranks.X",
              "scaleRank": "ranks.scale",
              "writeStats": true,
              "rmsScaleAfterCast": false
            }
          },
          "bindings": "rowsStats",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
    },
    {
      "id": "suffix_axis",
      "priority": 10,
      "when": ["suffixAxisOk", "noStats"],
      "constants": {
        "scalar": "dtypes.V",
        "xElement": "dtypes.T",
        "ioElement": "dtypes.V",
        "usesF16": "dtypes.T == \"f16\" or dtypes.V == \"f16\"",
        "hiddenSize": "normHidden",
        "workgroupSize": "rowWg",
        "epsilon": "attrs.epsilon"
      },
      "passes": [
        {
          "id": "main",
          "name": "SimplifiedLayerNormalization.Row",
          "source": {
            "shader": "rms-normalization.wgsl.jinja",
            "inputs": {
              "xShape": "shapes.X",
              "scaleShape": "shapes.scale",
              "xRank": "ranks.X",
              "scaleRank": "ranks.scale",
              "writeStats": false,
              "rmsScaleAfterCast": false
            }
          },
          "bindings": "rows",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
    },
    {
      "id": "suffix_axis_stats",
      "priority": 11,
      "when": ["suffixAxisOk", "statsOk"],
      "constants": {
        "scalar": "dtypes.V",
        "xElement": "dtypes.T",
        "ioElement": "dtypes.V",
        "usesF16": "dtypes.T == \"f16\" or dtypes.V == \"f16\"",
        "hiddenSize": "normHidden",
        "workgroupSize": "rowWg",
        "epsilon": "attrs.epsilon"
      },
      "passes": [
        {
          "id": "main",
          "name": "SimplifiedLayerNormalization.Row",
          "source": {
            "shader": "rms-normalization.wgsl.jinja",
            "inputs": {
              "xShape": "shapes.X",
              "scaleShape": "shapes.scale",
              "xRank": "ranks.X",
              "scaleRank": "ranks.scale",
              "writeStats": true,
              "rmsScaleAfterCast": false
            }
          },
          "bindings": "rowsStats",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
    },
    {
      "id": "suffix_axis_splitk",
      "priority": 15,
      "when": ["baseOk", "ranks.X >= 2", "noStats", "splitFits"],
      "demoteWhen": ["reportedNonWave32Adapter", "normHidden < tunables.SPLIT_MIN_HIDDEN"],
      "constants": {
        "scalar": "dtypes.V",
        "xElement": "dtypes.T",
        "ioElement": "dtypes.V",
        "usesF16": "dtypes.T == \"f16\" or dtypes.V == \"f16\"",
        "hiddenSize": "normHidden",
        "workgroupSize": "normMaxWorkgroup",
        "split": "splitCount",
        "epsilon": "attrs.epsilon"
      },
      "intermediates": [{ "id": "partials", "dtype": "float32", "shape": "[normRows * splitCount]" }],
      "passes": [
        {
          "id": "partials",
          "name": "SimplifiedLayerNormalization.SplitKPartials",
          "source": { "shader": "rms-normalization-splitk-partials.wgsl.jinja", "inputs": {} },
          "bindings": "splitPartials",
          "dispatch": { "workgroups": "normRows", "z": "splitCount" }
        },
        {
          "id": "normalize",
          "name": "SimplifiedLayerNormalization.SplitKNormalize",
          "source": {
            "shader": "rms-normalization-splitk-normalize.wgsl.jinja",
            "inputs": {
              "xShape": "shapes.X",
              "scaleShape": "shapes.scale",
              "xRank": "ranks.X",
              "scaleRank": "ranks.scale",
              "writeStats": false,
              "rmsScaleAfterCast": false
            }
          },
          "bindings": "splitNormalize",
          "dispatch": { "workgroups": "normRows", "z": "splitCount" }
        }
      ]
    },
    {
      "id": "suffix_axis_splitk_stats",
      "priority": 16,
      "when": ["baseOk", "ranks.X >= 2", "statsOk", "splitFits"],
      "demoteWhen": ["reportedNonWave32Adapter", "normHidden < tunables.SPLIT_MIN_HIDDEN"],
      "constants": {
        "scalar": "dtypes.V",
        "xElement": "dtypes.T",
        "ioElement": "dtypes.V",
        "usesF16": "dtypes.T == \"f16\" or dtypes.V == \"f16\"",
        "hiddenSize": "normHidden",
        "workgroupSize": "normMaxWorkgroup",
        "split": "splitCount",
        "epsilon": "attrs.epsilon"
      },
      "intermediates": [{ "id": "partials", "dtype": "float32", "shape": "[normRows * splitCount]" }],
      "passes": [
        {
          "id": "partials",
          "name": "SimplifiedLayerNormalization.SplitKPartials",
          "source": { "shader": "rms-normalization-splitk-partials.wgsl.jinja", "inputs": {} },
          "bindings": "splitPartials",
          "dispatch": { "workgroups": "normRows", "z": "splitCount" }
        },
        {
          "id": "normalize",
          "name": "SimplifiedLayerNormalization.SplitKNormalize",
          "source": {
            "shader": "rms-normalization-splitk-normalize.wgsl.jinja",
            "inputs": {
              "xShape": "shapes.X",
              "scaleShape": "shapes.scale",
              "xRank": "ranks.X",
              "scaleRank": "ranks.scale",
              "writeStats": true,
              "rmsScaleAfterCast": false
            }
          },
          "bindings": "splitNormalizeStats",
          "dispatch": { "workgroups": "normRows", "z": "splitCount" }
        }
      ]
    },
    {
      "id": "last_axis_row_vec4",
      "priority": 110,
      "when": ["lastAxisOk", "sameDtype", "noStats", "ranks.scale >= 1", "numel(shapes.scale) == dim(shapes.X, -1)", "dim(shapes.scale, -1) == dim(shapes.X, -1)", "dim(shapes.X, -1) % 4 == 0"],
      "constants": {
        "scalar": "dtypes.T",
        "xElement": "\"vec4<\" ~ dtypes.T ~ \">\"",
        "ioElement": "\"vec4<\" ~ dtypes.T ~ \">\""
      },
      "passes": [
        {
          "id": "main",
          "name": "SimplifiedLayerNormalization.LastAxisRow",
          "source": {
            "shader": "norm-row-stats.wgsl.jinja",
            "inputs": {
              "mode": "\"rms\"",
              "vec4": true,
              "writeStats": false,
              "rmsScaleAfterCast": false,
              "scalar": "dtypes.T",
              "usesF16": "dtypes.T == \"f16\"",
              "hidden": "dim(shapes.X, -1)",
              "wg": "min(normMaxWorkgroup, pow2ceil(max(1, dim(shapes.X, -1) / 4)))",
              "epsilon": "attrs.epsilon",
              "hiddenVec": "dim(shapes.X, -1) / 4",
              "vecType": "\"vec4<\" ~ dtypes.T ~ \">\"",
              "combineSubgroups": "hasSubgroupId"
            }
          },
          "subgroupCollectivesWidth": "portable",
          "bindings": "rows",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
    },
    {
      "id": "last_axis_row",
      "priority": 100,
      "when": ["lastAxisOk", "sameDtype", "noStats", "ranks.scale >= 1", "numel(shapes.scale) == dim(shapes.X, -1)", "dim(shapes.scale, -1) == dim(shapes.X, -1)"],
      "constants": { "scalar": "dtypes.T", "xElement": "dtypes.T", "ioElement": "dtypes.T" },
      "passes": [
        {
          "id": "main",
          "name": "SimplifiedLayerNormalization.LastAxisRow",
          "source": {
            "shader": "norm-row-stats.wgsl.jinja",
            "inputs": {
              "mode": "\"rms\"",
              "vec4": false,
              "writeStats": false,
              "rmsScaleAfterCast": false,
              "scalar": "dtypes.T",
              "usesF16": "dtypes.T == \"f16\"",
              "hidden": "dim(shapes.X, -1)",
              "wg": "min(normMaxWorkgroup, pow2ceil(max(1, dim(shapes.X, -1))))",
              "epsilon": "attrs.epsilon",
              "hiddenVec": 1,
              "vecType": "\"vec4<\" ~ dtypes.T ~ \">\"",
              "combineSubgroups": "hasSubgroupId"
            }
          },
          "subgroupCollectivesWidth": "portable",
          "bindings": "rows",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
    },
    {
      "id": "last_axis_row_vec4_stats",
      "priority": 112,
      "when": ["lastAxisOk", "sameDtype", "statsOk", "ranks.scale >= 1", "numel(shapes.scale) == dim(shapes.X, -1)", "dim(shapes.scale, -1) == dim(shapes.X, -1)", "dim(shapes.X, -1) % 4 == 0"],
      "constants": {
        "scalar": "dtypes.T",
        "xElement": "\"vec4<\" ~ dtypes.T ~ \">\"",
        "ioElement": "\"vec4<\" ~ dtypes.T ~ \">\""
      },
      "passes": [
        {
          "id": "main",
          "name": "SimplifiedLayerNormalization.LastAxisRow",
          "source": {
            "shader": "norm-row-stats.wgsl.jinja",
            "inputs": {
              "mode": "\"rms\"",
              "vec4": true,
              "writeStats": true,
              "rmsScaleAfterCast": false,
              "scalar": "dtypes.T",
              "usesF16": "dtypes.T == \"f16\"",
              "hidden": "dim(shapes.X, -1)",
              "wg": "min(normMaxWorkgroup, pow2ceil(max(1, dim(shapes.X, -1) / 4)))",
              "epsilon": "attrs.epsilon",
              "hiddenVec": "dim(shapes.X, -1) / 4",
              "vecType": "\"vec4<\" ~ dtypes.T ~ \">\"",
              "combineSubgroups": "hasSubgroupId"
            }
          },
          "subgroupCollectivesWidth": "portable",
          "bindings": "rowsStats",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
    },
    {
      "id": "last_axis_row_stats",
      "priority": 102,
      "when": ["lastAxisOk", "sameDtype", "statsOk", "ranks.scale >= 1", "numel(shapes.scale) == dim(shapes.X, -1)", "dim(shapes.scale, -1) == dim(shapes.X, -1)"],
      "constants": { "scalar": "dtypes.T", "xElement": "dtypes.T", "ioElement": "dtypes.T" },
      "passes": [
        {
          "id": "main",
          "name": "SimplifiedLayerNormalization.LastAxisRow",
          "source": {
            "shader": "norm-row-stats.wgsl.jinja",
            "inputs": {
              "mode": "\"rms\"",
              "vec4": false,
              "writeStats": true,
              "rmsScaleAfterCast": false,
              "scalar": "dtypes.T",
              "usesF16": "dtypes.T == \"f16\"",
              "hidden": "dim(shapes.X, -1)",
              "wg": "min(normMaxWorkgroup, pow2ceil(max(1, dim(shapes.X, -1))))",
              "epsilon": "attrs.epsilon",
              "hiddenVec": 1,
              "vecType": "\"vec4<\" ~ dtypes.T ~ \">\"",
              "combineSubgroups": "hasSubgroupId"
            }
          },
          "subgroupCollectivesWidth": "portable",
          "bindings": "rowsStats",
          "dispatch": { "workgroups": "normRows" }
        }
      ]
    }
  ]
}