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{
  "op": "ai.onnx.LayerNormalization",
  "fixtureArrays": {
    "onnx_backend_layer_normalization_3d_input_x": [1.764052391052246, 0.40015721321105957, 0.978738009929657, 2.2408931255340576, 1.8675580024719238, -0.9772778749465942, 0.9500884413719177, -0.15135720372200012, -0.10321885347366333, 0.4105985164642334, 0.14404356479644775, 1.4542734622955322, 0.7610377073287964, 0.12167501449584961, 0.44386324286460876, 0.3336743414402008, 1.4940791130065918, -0.2051582634449005, 0.3130677044391632, -0.8540957570075989, -2.5529897212982178, 0.653618574142456, 0.8644362092018127, -0.7421650290489197, 2.269754648208618, -1.4543657302856445, 0.04575851559638977, -0.18718385696411133, 1.5327792167663574, 1.4693588018417358],
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  },
  "cases": [
    {
      "name": "subgroup_vec4_stats_no_bias_2x512",
      "attrs": { "epsilon": 0.00001, "axis": -1 },
      "inputs": {
        "x": {
          "dtype": "float32",
          "shape": [2, 512],
          "data": { "kind": "fillFloat32", "sinStep": 0.13, "cosStep": 0.21 }
        },
        "scale": {
          "dtype": "float32",
          "shape": [512],
          "data": { "kind": "fillFloat32", "sinStep": 0.29, "cosStep": 0.11, "scale": 0.5 }
        }
      },
      "outputs": {
        "y": { "dtype": "float32", "shape": [2, 512], "tolerance": 0.000002 },
        "mean": { "dtype": "float32", "shape": [2, 1], "tolerance": 0.000001 },
        "invStdDev": { "dtype": "float32", "shape": [2, 1], "tolerance": 0.00001 }
      }
    },
    {
      "name": "subgroup_vec4_bias_2x512",
      "attrs": { "epsilon": 0.00001, "axis": -1 },
      "inputs": {
        "x": {
          "dtype": "float32",
          "shape": [2, 512],
          "data": { "kind": "fillFloat32", "sinStep": 0.17, "cosStep": 0.23 }
        },
        "scale": {
          "dtype": "float32",
          "shape": [512],
          "data": { "kind": "fillFloat32", "sinStep": 0.31, "cosStep": 0.07, "scale": 0.4 }
        },
        "b": {
          "dtype": "float32",
          "shape": [512],
          "data": { "kind": "fillFloat32", "sinStep": 0.05, "cosStep": 0.19, "scale": 0.25 }
        }
      },
      "outputs": { "y": { "dtype": "float32", "shape": [2, 512], "tolerance": 0.000002 } }
    },
    {
      "name": "subgroup_vec4_f16_4x32",
      "attrs": { "epsilon": 0.00001, "axis": -1 },
      "inputs": {
        "x": {
          "dtype": "float16",
          "shape": [4, 32],
          "data": { "kind": "fillFloat32", "sinStep": 0.11, "cosStep": 0.27 }
        },
        "scale": {
          "dtype": "float16",
          "shape": [32],
          "data": { "kind": "fillFloat32", "sinStep": 0.21, "cosStep": 0.13, "scale": 0.5 }
        }
      },
      "outputs": { "y": { "dtype": "float16", "shape": [4, 32], "tolerance": 0.005 } }
    },
    {
      "name": "subgroup_vec4_f16_stats_4x32",
      "attrs": { "epsilon": 0.00001, "axis": -1 },
      "inputs": {
        "x": {
          "dtype": "float16",
          "shape": [4, 32],
          "data": { "kind": "fillFloat32", "sinStep": 0.09, "cosStep": 0.19 }
        },
        "scale": {
          "dtype": "float16",
          "shape": [32],
          "data": { "kind": "fillFloat32", "sinStep": 0.23, "cosStep": 0.17, "scale": 0.45 }
        }
      },
      "outputs": {
        "y": { "dtype": "float16", "shape": [4, 32], "tolerance": 0.006 },
        "mean": { "dtype": "float32", "shape": [4, 1], "tolerance": 0.002 },
        "invStdDev": { "dtype": "float32", "shape": [4, 1], "tolerance": 0.02 }
      }
    },
    {
      "name": "subgroup_vec4_f16_bias_4x32",
      "attrs": { "epsilon": 0.00001, "axis": -1 },
      "inputs": {
        "x": {
          "dtype": "float16",
          "shape": [4, 32],
          "data": { "kind": "fillFloat32", "sinStep": 0.15, "cosStep": 0.25 }
        },
        "scale": {
          "dtype": "float16",
          "shape": [32],
          "data": { "kind": "fillFloat32", "sinStep": 0.27, "cosStep": 0.09, "scale": 0.45 }
        },
        "b": {
          "dtype": "float16",
          "shape": [32],
          "data": { "kind": "fillFloat32", "sinStep": 0.07, "cosStep": 0.21, "scale": 0.2 }
        }
      },
      "outputs": { "y": { "dtype": "float16", "shape": [4, 32], "tolerance": 0.006 } }
    },
    {
      "name": "subgroup_vec4_f16_bias_stats_4x32",
      "attrs": { "epsilon": 0.00001, "axis": -1 },
      "inputs": {
        "x": {
          "dtype": "float16",
          "shape": [4, 32],
          "data": { "kind": "fillFloat32", "sinStep": 0.12, "cosStep": 0.29 }
        },
        "scale": {
          "dtype": "float16",
          "shape": [32],
          "data": { "kind": "fillFloat32", "sinStep": 0.25, "cosStep": 0.11, "scale": 0.4 }
        },
        "b": {
          "dtype": "float16",
          "shape": [32],
          "data": { "kind": "fillFloat32", "sinStep": 0.05, "cosStep": 0.17, "scale": 0.25 }
        }
      },
      "outputs": {
        "y": { "dtype": "float16", "shape": [4, 32], "tolerance": 0.006 },
        "mean": { "dtype": "float32", "shape": [4, 1], "tolerance": 0.002 },
        "invStdDev": { "dtype": "float32", "shape": [4, 1], "tolerance": 0.02 }
      }
    },
    {
      "name": "f32_subnormal_scale_preserves_tiny_outputs_gpu_gap",
      "skipGpu": {
        "category": "permanent",
        "reason": "Portable WGSL floating-point semantics do not guarantee preservation of the subnormal values required by this fixture. Backend evidence: WebGPU/Metal flushes subnormals to zero in f32; the subnormal per-element scale collapses so tiny normalized outputs cannot be preserved."
      },
      "provenance": {
        "source": "onnxruntime/test/contrib_ops/layer_norm_op_test.cc",
        "test": "LayerNormalization",
        "notes": "A valid subnormal scale should produce finite subnormal normalized outputs rather than being flushed to zero."
      },
      "attrs": { "epsilon": 0.00001, "axis": -1 },
      "inputs": {
        "x": { "dtype": "float32", "shape": [1, 4], "data": { "kind": "values", "values": [-1.0, 0.0, 1.0, 2.0] } },
        "scale": {
          "dtype": "float32",
          "shape": [4],
          "data": { "kind": "values", "values": [1e-40, 2e-40, -3e-40, 4e-40] }
        }
      },
      "outputs": { "y": { "dtype": "float32", "shape": [1, 4], "tolerance": 1e-44 } }
    },
    {
      "name": "f32_subnormal_scale_preserves_tiny_outputs_odd_hidden_gpu_gap",
      "skipGpu": {
        "category": "permanent",
        "reason": "Portable WGSL floating-point semantics do not guarantee preservation of the subnormal values required by this fixture. Backend evidence: WebGPU/Metal flushes subnormals to zero in f32; the subnormal per-element scale collapses so tiny normalized outputs cannot be preserved (odd hidden size)."
      },
      "provenance": {
        "source": "onnxruntime/test/contrib_ops/layer_norm_op_test.cc",
        "test": "LayerNormalization",
        "notes": "Odd hidden-size companion for subnormal scale values; this exercises the non-vec4 last-axis path."
      },
      "attrs": { "epsilon": 0.00001, "axis": -1 },
      "inputs": {
        "x": { "dtype": "float32", "shape": [1, 3], "data": { "kind": "values", "values": [-1.0, 0.0, 2.0] } },
        "scale": { "dtype": "float32", "shape": [3], "data": { "kind": "values", "values": [1e-40, -2e-40, 3e-40] } }
      },
      "outputs": { "y": { "dtype": "float32", "shape": [1, 3], "tolerance": 1e-44 } }
    },
    {
      "name": "last_axis_y_only",
      "attrs": { "epsilon": 0.00001, "axis": -1 },
      "inputs": {
        "x": {
          "dtype": "float32",
          "shape": [3, 8],
          "data": { "kind": "fillFloat32", "sinStep": 0.17, "cosStep": 0.29 }
        },
        "scale": {
          "dtype": "float32",
          "shape": [8],
          "data": { "kind": "fillFloat32", "sinStep": 0.31, "cosStep": 0.07, "scale": 0.4 }
        }
      },
      "outputs": { "y": { "dtype": "float32", "shape": [3, 8], "tolerance": 0.000001 } }
    },
    {
      "name": "last_axis_bias_and_stats",
      "attrs": { "epsilon": 0.00001, "axis": -1 },
      "inputs": {
        "x": {
          "dtype": "float32",
          "shape": [2, 3, 7],
          "data": { "kind": "fillFloat32", "sinStep": 0.11, "cosStep": 0.23 }
        },
        "scale": {
          "dtype": "float32",
          "shape": [7],
          "data": { "kind": "fillFloat32", "sinStep": 0.19, "cosStep": 0.13, "scale": 0.35 }
        },
        "b": {
          "dtype": "float32",
          "shape": [7],
          "data": { "kind": "fillFloat32", "sinStep": 0.07, "cosStep": 0.17, "scale": 0.2 }
        }
      },
      "outputs": {
        "y": { "dtype": "float32", "shape": [2, 3, 7], "tolerance": 0.00002 },
        "mean": { "dtype": "float32", "shape": [2, 3, 1], "tolerance": 0.000001 },
        "invStdDev": { "dtype": "float32", "shape": [2, 3, 1], "tolerance": 0.001 }
      }
    },
    {
      "name": "f32_tiny_variance_epsilon_zero_gpu_gap",
      "skipGpu": {
        "category": "permanent",
        "reason": "Portable WGSL floating-point semantics do not guarantee preservation of the subnormal values required by this fixture. Backend evidence: WebGPU/Metal flushes subnormals to zero in f32; the subnormal variance collapses to zero so inverseSqrt produces Infinity instead of a finite large InvStdDev."
      },
      "provenance": {
        "source": "onnxruntime/test/contrib_ops/layer_norm_op_test.cc",
        "test": "LayerNormTest.LayerNorm17_opset",
        "notes": "Valid epsilon=0 edge: normal inputs produce subnormal variance but finite order-one normalized outputs and finite large InvStdDev."
      },
      "attrs": { "epsilon": 0, "axis": -1 },
      "inputs": {
        "x": {
          "dtype": "float32",
          "shape": [2, 2],
          "data": { "kind": "values", "values": [1e-20, -1e-20, 2e-20, -2e-20] }
        },
        "scale": { "dtype": "float32", "shape": [2], "data": { "kind": "values", "values": [1.0, 1.0] } },
        "b": { "dtype": "float32", "shape": [2], "data": { "kind": "values", "values": [0.0, 0.0] } }
      },
      "outputs": {
        "y": { "dtype": "float32", "shape": [2, 2], "tolerance": 0.00001 },
        "mean": { "dtype": "float32", "shape": [2, 1], "tolerance": 0 },
        "invStdDev": { "dtype": "float32", "shape": [2, 1], "tolerance": 1000000000000000, "relTolerance": 0.00001 }
      }
    },
    {
      "name": "last_axis_mean_only_no_bias",
      "provenance": {
        "source": "ONNX LayerNormalization-17 optional-output contract",
        "notes": "Requests Mean while independently omitting both B and InvStdDev."
      },
      "attrs": { "epsilon": 0.00001, "axis": -1 },
      "inputs": {
        "x": {
          "dtype": "float32",
          "shape": [2, 4],
          "data": { "kind": "values", "values": [1.5, -2.0, 0.25, 4.0, 10.0, 10.5, 9.75, 10.25] }
        },
        "scale": { "dtype": "float32", "shape": [4], "data": { "kind": "values", "values": [1.0, -0.5, 2.0, 0.25] } }
      },
      "outputs": {
        "y": { "dtype": "float32", "shape": [2, 4], "tolerance": 0.000002 },
        "mean": { "dtype": "float32", "shape": [2, 1], "tolerance": 0.000001 }
      }
    },
    {
      "name": "suffix_axis_inv_std_dev_only_no_bias",
      "provenance": {
        "source": "ONNX LayerNormalization-17 optional-output contract",
        "notes": "Requests InvStdDev while independently omitting the earlier optional Mean output and B."
      },
      "attrs": { "epsilon": 0.00001, "axis": 1 },
      "inputs": {
        "x": {
          "dtype": "float32",
          "shape": [2, 2, 3],
          "data": { "kind": "values", "values": [-3.0, -1.0, 2.0, 4.0, 5.0, 8.0, 10.0, 8.0, 7.0, 3.0, 1.0, -2.0] }
        },
        "scale": {
          "dtype": "float32",
          "shape": [2, 3],
          "data": { "kind": "values", "values": [1.0, 0.5, -1.0, 2.0, -0.25, 0.75] }
        }
      },
      "outputs": {
        "y": { "dtype": "float32", "shape": [2, 2, 3], "tolerance": 0.000002 },
        "invStdDev": { "dtype": "float32", "shape": [2, 1, 1], "tolerance": 0.000001 }
      }
    },
    {
      "name": "suffix_axis_bias_inv_std_dev_only",
      "provenance": {
        "source": "ONNX LayerNormalization-17 optional-output contract",
        "notes": "Requests B and InvStdDev while independently omitting the earlier optional Mean output."
      },
      "attrs": { "epsilon": 0.00001, "axis": 1 },
      "inputs": {
        "x": {
          "dtype": "float32",
          "shape": [2, 2, 3],
          "data": { "kind": "values", "values": [-2.0, 0.0, 1.0, 3.0, 7.0, 9.0, 12.0, 9.0, 6.0, 4.0, 2.0, -1.0] }
        },
        "scale": {
          "dtype": "float32",
          "shape": [2, 3],
          "data": { "kind": "values", "values": [0.5, -1.0, 1.5, 0.25, 2.0, -0.75] }
        },
        "b": {
          "dtype": "float32",
          "shape": [2, 3],
          "data": { "kind": "values", "values": [0.1, -0.2, 0.3, -0.4, 0.5, -0.6] }
        }
      },
      "outputs": {
        "y": { "dtype": "float32", "shape": [2, 2, 3], "tolerance": 0.000002 },
        "invStdDev": { "dtype": "float32", "shape": [2, 1, 1], "tolerance": 0.000001 }
      }
    },
    {
      "name": "last_axis_mean_only_output",
      "provenance": {
        "source": "cmake/external/onnx/onnx/backend/test/data/node/test_layer_normalization_default_axis",
        "notes": "ONNX optional outputs may be requested as a prefix; this asks for Y and Mean without InvStdDev."
      },
      "attrs": { "epsilon": 0.00001, "axis": -1 },
      "inputs": {
        "x": {
          "dtype": "float32",
          "shape": [2, 4],
          "data": { "kind": "values", "values": [1.5, -2.0, 0.25, 4.0, 10.0, 10.5, 9.75, 10.25] }
        },
        "scale": { "dtype": "float32", "shape": [4], "data": { "kind": "values", "values": [1.0, -0.5, 2.0, 0.25] } },
        "b": { "dtype": "float32", "shape": [4], "data": { "kind": "values", "values": [0.0, 0.1, -0.2, 0.5] } }
      },
      "outputs": {
        "y": { "dtype": "float32", "shape": [2, 4], "tolerance": 0.000002 },
        "mean": { "dtype": "float32", "shape": [2, 1], "tolerance": 0.000001 }
      }
    },
    {
      "name": "large_values_centered_variance_regression",
      "attrs": { "epsilon": 0.00001, "axis": -1 },
      "provenance": {
        "source": "onnxruntime/test/contrib_ops/layer_norm_op_test.cc",
        "test": "LayerNormTest.LayerNorm_LargeValues_NoNaN"
      },
      "inputs": {
        "x": {
          "dtype": "float32",
          "shape": [1, 4],
          "data": { "kind": "values", "values": [40000.0, 40001.0, 40002.0, 40003.0] }
        },
        "scale": { "dtype": "float32", "shape": [4], "data": { "kind": "values", "values": [1.0, 1.0, 1.0, 1.0] } },
        "b": { "dtype": "float32", "shape": [4], "data": { "kind": "constant", "value": 0.0 } }
      },
      "outputs": {
        "y": {
          "dtype": "float32",
          "shape": [1, 4],
          "tolerance": 0.00001,
          "data": {
            "kind": "values",
            "values": [-1.3416354656219482, -0.4472118020057678, 0.4472118020057678, 1.3416354656219482]
          }
        },
        "mean": {
          "dtype": "float32",
          "shape": [1, 1],
          "tolerance": 0.0001,
          "data": { "kind": "values", "values": [40001.5] }
        },
        "invStdDev": {
          "dtype": "float32",
          "shape": [1, 1],
          "tolerance": 0.00001,
          "data": { "kind": "values", "values": [0.8944236040115356] }
        }
      }
    },
    {
      "name": "ort_very_large_values_no_nan",
      "attrs": { "epsilon": 0.00001, "axis": -1 },
      "provenance": {
        "source": "onnxruntime/test/contrib_ops/layer_norm_op_test.cc",
        "test": "LayerNormTest.LayerNorm_VeryLargeValues_NoNaN"
      },
      "inputs": {
        "x": {
          "dtype": "float32",
          "shape": [1, 4],
          "data": { "kind": "values", "values": [80000.0, 80001.0, 80002.0, 80003.0] }
        },
        "scale": { "dtype": "float32", "shape": [4], "data": { "kind": "values", "values": [1.0, 1.0, 1.0, 1.0] } },
        "b": { "dtype": "float32", "shape": [4], "data": { "kind": "constant", "value": 0.0 } }
      },
      "outputs": {
        "y": {
          "dtype": "float32",
          "shape": [1, 4],
          "tolerance": 0.00001,
          "data": {
            "kind": "values",
            "values": [-1.3416354656219482, -0.4472118020057678, 0.4472118020057678, 1.3416354656219482]
          }
        },
        "mean": {
          "dtype": "float32",
          "shape": [1, 1],
          "tolerance": 0.0001,
          "data": { "kind": "values", "values": [80001.5] }
        },
        "invStdDev": {
          "dtype": "float32",
          "shape": [1, 1],
          "tolerance": 0.00001,
          "data": { "kind": "values", "values": [0.8944236040115356] }
        }
      }
    },
    {
      "name": "zero_variance_bias",
      "attrs": { "epsilon": 0.00001, "axis": -1 },
      "inputs": {
        "x": { "dtype": "float32", "shape": [2, 4], "data": { "kind": "constant", "value": 5.0 } },
        "scale": { "dtype": "float32", "shape": [4], "data": { "kind": "values", "values": [1.0, 2.0, 3.0, 4.0] } },
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