### Add & Norm in IT Context In the field of information technology, particularly within deep learning and neural networks, **Add & Norm** refers to a specific operation commonly found in transformer-based models such as the Transformer architecture introduced by Vaswani et al.[^1]. This process involves two primary steps: 1. **Residual Connection (Add)**: In this step, the input to a sub-layer is added element-wise to its output. The purpose of residual connections is to mitigate the vanishing gradient problem during training, allowing gradients to flow directly through the network without significant degradation over many layers. For example, given an input \(X\) and the output from some transformation function \(F(X)\), the result after adding would be: ```python Y = X + F(X) ``` 2. **Layer Normalization (Norm)**: After performing addition with residuals, layer normalization standardizes the outputs across features for each individual sample independently. Layer normalization adjusts activations so they have zero mean and unit variance per feature dimension. Mathematically, it can be represented as follows where \(\mu_L\) represents the mean value computed along all dimensions except batch size while \(\sigma_L\) denotes corresponding standard deviation: \[ LN(x_i) =\frac{x_i-\mu_{L}}{\sqrt{{\sigma}_{L}^{2}+\epsilon}} \] Together these operations form what’s known as “addition followed by normalization,” which enhances performance stability when scaling up complex architectures like transformers or other multi-head attention mechanisms[^2]. ```python import torch.nn as nn class AddAndNorm(nn.Module): def __init__(self, eps=1e-6): super(AddAndNorm, self).__init__() self.norm = nn.LayerNorm(normalized_shape=(d_model,), eps=eps) def forward(self, x, sublayer_output): out = x + sublayer_output # Residual connection return self.norm(out) # Normalization ```