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LayerNormalization

Description

This is layer normalization defined in ONNX as function. The overall computation can be split into two stages. The first stage is standardization, which makes the normalized elements have zero mean and unit variances. 

 

 

The computation required by standardization can be described by the following equations.

Mean = ReduceMean<axes=normalized_axes>(X)
D = Sub(X, Mean)
DD = Mul(D, D)
Var = ReduceMean<axes=normalized_axes>(DD)
VarEps = Add(Var, epsilon)
StdDev = Sqrt(VarEps)
InvStdDev = Reciprocal(StdDev)
Normalized = Mul(D, InvStdDev)

 

where normalized_axes is [axis, ..., rank of X - 1]. The variables Var and StdDev stand for variance and standard deviation, respectively. The second output is Mean and the last one is InvStdDev. Depending on stash_type attribute, the actual computation must happen in different floating-point precision. For example, if stash_type is 1, this operator casts all input variables to 32-bit float, perform the computation, and finally cast Normalized back to the original type of X. The second stage then scales and shifts the outcome of the first stage using

NormalizedScaled = Mul(Normalized, Scale)
Y = Add(NormalizedScaled, B)

 

The second stage doesn’t depends on stash_type. All equations are in this syntax. The same variable (i.e., input, output, and attribute) uses the same name in the equations above and this operator’s definition. Let d[i] indicate the i-th dimension of X. If X’s shape is [d[0], ..., d[axis-1], d[axis], ..., d[rank-1]], the shape of Mean and InvStdDev is [d[0], ..., d[axis-1], 1, ..., 1]. Y and X have the same shape. This operator supports unidirectional broadcasting (tensors Scale and B should be unidirectional broadcastable to tensor X); for more details please check Broadcasting in ONNX.

 

 

 

Input parameters

 

specified_outputs_name : array, this parameter lets you manually assign custom names to the output tensors of a node.

 Graphs in : cluster, ONNX model architecture.

X (heterogeneous) – T : object, tensor to be normalized.
 Scale (heterogeneous) – T : object, scale tensor.
B (optional, heterogeneous) – T : object, bias tensor.

 Parameters : cluster,

axis : integer, the first normalization dimension. If rank(X) is r, axis’ allowed range is [-r, r). Negative value means counting dimensions from the back.
Default value “-1”.
epsilon : float, the epsilon value to use to avoid division by zero.
Default value “1e-05”.
stash_type : integer, type of Mean and InvStdDev. This also specifies stage one’s computation precision.
Default value “1”.
 training_mode : boolean, whether the layer is in training mode (can store data for backward).
Default value “False”.
 lda coeff : float, defines the coefficient by which the loss derivative will be multiplied before being sent to the previous layer (since during the backward run we go backwards).
Default value “1”.

 name (optional) : string, name of the node.

Output parameters

 Graphs out : cluster, ONNX model architecture.

Y (heterogeneous) – T : object, normalized tensor.
Mean (optional, heterogeneous) – U : object, saved mean used during training to speed up gradient computation.
InvStdDev (optional, heterogeneous) – U : object, saved inverse standard deviation used during training to speed up gradient computation.

Type Constraints

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

U in (tensor(bfloat16), tensor(float)) : Type of Mean and InvStdDev tensors.

Example

All these exemples are snippets PNG, you can drop these Snippet onto the block diagram and get the depicted code added to your VI (Do not forget to install Deep Learning library to run it).
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