LpNormalization#

Domain: ai.onnx
Since version: 22

Given a matrix, apply Lp-normalization along the provided axis. The output is computed as: output = input / Lp_norm(input, axis). When the Lp norm is zero (i.e., all elements along the axis are zero), the output is defined to be zero to avoid division by zero.

Inputs

input (T): Input matrix

Outputs

output (T): Matrix after normalization

Attributes

axis (int): The axis on which to apply normalization, -1 mean last axis.
p (int): The order of the normalization, only 1 or 2 are supported.

Type Constraints

T: Constrain input and output types to float tensors. Allowed types: tensor(bfloat16), tensor(double), tensor(float), tensor(float16).

Examples#

test_cc_lpnormalization_axis0_p1

Node:
  LpNormalization(x) -> (y)
  Attributes:
    axis = 0
    p = 1

Inputs:
  x: shape=(2, 2, 3), dtype=float32
    [[[1., 2., 2.],
      [3., 4., 0.]],

     [[0., 5., 5.],
      [6., 8., 0.]]]

Outputs:
  y: shape=(2, 2, 3), dtype=float32
    [[[1.        , 0.2857143 , 0.2857143 ],
      [0.33333334, 0.33333334, 0.        ]],

     [[0.        , 0.71428573, 0.71428573],
      [0.6666667 , 0.6666667 , 0.        ]]]

test_cc_lpnormalization_default

Node:
  LpNormalization(x) -> (y)

Inputs:
  x: shape=(2, 2, 3), dtype=float32
    [[[1., 2., 2.],
      [3., 4., 0.]],

     [[0., 5., 5.],
      [6., 8., 0.]]]

Outputs:
  y: shape=(2, 2, 3), dtype=float32
    [[[0.33333334, 0.6666667 , 0.6666667 ],
      [0.6       , 0.8       , 0.        ]],

     [[0.        , 0.70710677, 0.70710677],
      [0.6       , 0.8       , 0.        ]]]

test_l1normalization_axis_0

Node:
  LpNormalization(x) -> (y)
  Attributes:
    axis = 0
    p = 1

Inputs:
  x: shape=(2,), dtype=float32
    [3., 4.]

Outputs:
  y: shape=(2,), dtype=float32
    [0.42857143, 0.5714286 ]

test_l1normalization_axis_1

Node:
  LpNormalization(x) -> (y)
  Attributes:
    axis = 1
    p = 1

Inputs:
  x: shape=(2, 2), dtype=float32
    [[3., 4.],
     [6., 8.]]

Outputs:
  y: shape=(2, 2), dtype=float32
    [[0.42857143, 0.5714286 ],
     [0.42857143, 0.5714286 ]]

test_l1normalization_axis_last

Node:
  LpNormalization(x) -> (y)
  Attributes:
    axis = -1
    p = 1

Inputs:
  x: shape=(2, 2, 3), dtype=float32
    [[[1., 2., 2.],
      [3., 4., 0.]],

     [[0., 5., 5.],
      [6., 8., 0.]]]

Outputs:
  y: shape=(2, 2, 3), dtype=float32
    [[[0.2       , 0.4       , 0.4       ],
      [0.42857143, 0.5714286 , 0.        ]],

     [[0.        , 0.5       , 0.5       ],
      [0.42857143, 0.5714286 , 0.        ]]]

test_l2normalization_axis_0

Node:
  LpNormalization(x) -> (y)
  Attributes:
    axis = 0
    p = 2

Inputs:
  x: shape=(2, 2, 3), dtype=float32
    [[[1., 2., 2.],
      [3., 4., 0.]],

     [[0., 5., 5.],
      [6., 8., 0.]]]

Outputs:
  y: shape=(2, 2, 3), dtype=float32
    [[[1.        , 0.37139067, 0.37139067],
      [0.4472136 , 0.4472136 , 0.        ]],

     [[0.        , 0.9284767 , 0.9284767 ],
      [0.8944272 , 0.8944272 , 0.        ]]]

test_l2normalization_axis_1

Node:
  LpNormalization(x) -> (y)
  Attributes:
    axis = 1
    p = 2

Inputs:
  x: shape=(2, 2), dtype=float32
    [[3., 4.],
     [6., 8.]]

Outputs:
  y: shape=(2, 2), dtype=float32
    [[0.6, 0.8],
     [0.6, 0.8]]

Differences with previous version (1)#

SchemaDiff: LpNormalization (domain 'ai.onnx')

old version: 1
new version: 22
breaking: no

Type constraints:

changed ‘T’: added types: [‘tensor(bfloat16)’]

Version History#

Version 1