The Affine Operator is an affine transformation layer introduced in the ResMLP architecture. This replaces layer normalization, as in Transformer based networks, which is possible since in the ResMLP, there are no selfattention layers which makes training more stable  hence allowing a more simple affine transformation.
The affine operator is defined as:
$$ \operatorname{Aff}_{\mathbf{\alpha}, \mathbf{\beta}}(\mathbf{x})=\operatorname{Diag}(\mathbf{\alpha}) \mathbf{x}+\mathbf{\beta} $$
where $\alpha$ and $\beta$ are learnable weight vectors. This operation only rescales and shifts the input elementwise. This operation has several advantages over other normalization operations: first, as opposed to Layer Normalization, it has no cost at inference time, since it can absorbed in the adjacent linear layer. Second, as opposed to BatchNorm and Layer Normalization, the Aff operator does not depend on batch statistics.
Source: ResMLP: Feedforward networks for image classification with dataefficient trainingPaper  Code  Results  Date  Stars 

Task  Papers  Share 

Image Classification  3  21.43% 
Object Detection  2  14.29% 
Semantic Segmentation  2  14.29% 
OutofDistribution Detection  1  7.14% 
Adversarial Attack  1  7.14% 
Instance Segmentation  1  7.14% 
FineGrained Image Classification  1  7.14% 
General Classification  1  7.14% 
Machine Translation  1  7.14% 
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