This is a PyTorch implementation of the DeepNorm from the paper DeepNet: Scaling Transformers to 1,000 Layers.

The paper proposes a method to stabilize extremely deep transformers through a new normalizing function to replace LayerNorm and a weight initialization scheme. This combines the performance of Post-LayerNorm and the stability of Pre-LayerNorm. Transformers with DeepNorms are supposed to be stable even without a learning rate warm-up.

The paper first shows that the changes to layer outputs (for the same input) change gradually during stable training; when unstable it changes rapidly during the initial training steps. This happens with initializing weights to small values, and learning rate warm-ups where the training is stable. They use the idea of keeping the changes to layer outputs small to derive the new normalization and weight initialization mechanism.

Usually, the weights are initialized with Xavier or Kaiming initializations. This paper scales (sets the gain) the weights by a constant $β$ depending on the size of the transformer.

DeepNorm suggests scaling the weights of the two linear transforms in the Feed-Forward Network, the value projection transform, and the output projection transform of the attention layer. Weights of these transforms are scaled by (has a gain equal to) $β$.

The scaling is implemented in the

$x_{l+1}=LN(αx_{l}+G_{l}(x_{l},θ_{l}))$

where $α$ is a constant that depends on the depth of the transformer, $LN$ is Layer Normalization, and $G_{l}(x_{l},θ_{l})$ is the function of the $l$-th transformer sub-layer (FFN or attention).

This function is used to replace Post-LayerNorm.

Where $N$ is the number of layers in the encoder and $M$ is the number of layers in the decoder.

Refer to the paper for derivation.

Here is an experiment implementation that uses DeepNorm.

```
73from typing import Union, List
74
75import torch
76from torch import nn, Size
77
78from labml_nn.normalization.layer_norm import LayerNorm
79from labml_nn.transformers import MultiHeadAttention
80from labml_nn.transformers.feed_forward import FeedForward
81from labml_nn.transformers.utils import subsequent_mask
```

`84class DeepNorm(nn.Module):`

`alpha`

is $α$`normalized_shape`

is the shape for LayerNorm $LN$`eps`

is $ϵ$ for LayerNorm`elementwise_affine`

is a flag indicating whether to do an elementwise transformation in LayerNorm

```
91 def __init__(self, alpha: float, normalized_shape: Union[int, List[int], Size], *,
92 eps: float = 1e-5,
93 elementwise_affine: bool = True):
```

```
100 super().__init__()
101
102 self.alpha = alpha
```

Initialize $LN$

`104 self.layer_norm = LayerNorm(normalized_shape, eps=eps, elementwise_affine=elementwise_affine)`

`x`

is the output from the previous layer $x_{l}$`gx`

is the output of the current sub-layer $G_{l}(x_{l},θ_{l})$

`106 def forward(self, x: torch.Tensor, gx: torch.Tensor):`

$x_{l+1}=LN(αx_{l}+G_{l}(x_{l},θ_{l}))$

`112 return self.layer_norm(x + self.alpha * gx)`

This implements a transformer decoder layer with DeepNorm. Encoder layers will have a similar form.

`115class DeepNormTransformerLayer(nn.Module):`

`d_model`

is the token embedding size`self_attn`

is the self attention module`feed_forward`

is the feed forward module`deep_norm_alpha`

is $α$ coefficient in DeepNorm`deep_norm_beta`

is $β$ constant for scaling weights initialization

```
122 def __init__(self, *,
123 d_model: int,
124 self_attn: MultiHeadAttention,
125 feed_forward: FeedForward,
126 deep_norm_alpha: float,
127 deep_norm_beta: float,
128 ):
```

```
136 super().__init__()
137
138 self.self_attn = self_attn
139 self.feed_forward = feed_forward
```

DeepNorms after attention and feed forward network

```
141 self.self_attn_norm = DeepNorm(deep_norm_alpha, [d_model])
142 self.feed_forward_norm = DeepNorm(deep_norm_alpha, [d_model])
```

Scale weights after initialization

`145 with torch.no_grad():`

Feed forward network linear transformations

```
147 feed_forward.layer1.weight *= deep_norm_beta
148 feed_forward.layer2.weight *= deep_norm_beta
```

Attention value projection

`151 self_attn.value.linear.weight *= deep_norm_beta`

Attention output project

`153 self_attn.output.weight *= deep_norm_beta`

The mask will be initialized on the first call

`156 self.mask = None`

`x`

are the embeddings of shape`[seq_len, batch_size, d_model]`

`158 def forward(self, x: torch.Tensor):`

Create causal mask

`163 if self.mask is None or self.mask.size(0) != len(x):`

Subsequent mask, will mask out tokens from seeing future tokens

`165 self.mask = subsequent_mask(len(x)).to(x.device)`

Run through self attention, i.e. keys and values are from self

`168 x = self.self_attn_norm(x, self.self_attn(query=x, key=x, value=x, mask=self.mask))`

Pass through the feed-forward network

`170 x = self.feed_forward_norm(x, self.feed_forward(x))`

`173 return x`