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DeepNorm

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.

Weight Initializations

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

Normalization Function

$x_{l + 1} = L N (α x_{l} + G_{l} (x_{l}, θ_{l}))$

where $α$ is a constant that depends on the depth of the transformer, $L N$ 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.

$α$ and $β$ constants

Type Encoder on l y Decoder on l y Enc-Dec Enc- α (2 N)^{\frac{1}{4}} - 0.81 (N^{4} M)^{\frac{1}{16}} Enc- β (8 N)^{- \frac{1}{4}} - 0.87 (N^{4} M)^{- \frac{1}{16}} Dec- α - (2 M)^{\frac{1}{4}} (3 M)^{\frac{1}{4}} Dec- β - (8 M)^{- \frac{1}{4}} (12 M)^{- \frac{1}{4}}

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.

75from typing import Union, List
76
77import torch
78from torch import nn, Size
79
80from labml_nn.normalization.layer_norm import LayerNorm
81from labml_nn.transformers import MultiHeadAttention
82from labml_nn.transformers.feed_forward import FeedForward
83from labml_nn.transformers.utils import subsequent_mask

#

DeepNorm Normalization

$x_{l + 1} = L N (α x_{l} + G_{l} (x_{l}, θ_{l}))$

86class DeepNorm(nn.Module):

#

alpha is $α$
normalized_shape is the shape for LayerNorm $L N$
eps is $ϵ$ for LayerNorm
elementwise_affine is a flag indicating whether to do an elementwise transformation in LayerNorm

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

#

102        super().__init__()
103
104        self.alpha = alpha

#

Initialize $L N$

106        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 $G_{l} (x_{l}, θ_{l})$

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

#

$x_{l + 1} = L N (α x_{l} + G_{l} (x_{l}, θ_{l}))$

114        return x + self.alpha * gx

#

Transformer Decoder Layer with DeepNorm

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

117class 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

124    def __init__(self, *,
125                 d_model: int,
126                 self_attn: MultiHeadAttention,
127                 feed_forward: FeedForward,
128                 deep_norm_alpha: float,
129                 deep_norm_beta: float,
130                 ):

#

138        super().__init__()
139
140        self.self_attn = self_attn
141        self.feed_forward = feed_forward

#

DeepNorms after attention and feed forward network

143        self.self_attn_norm = DeepNorm(deep_norm_alpha, [d_model])
144        self.feed_forward_norm = DeepNorm(deep_norm_alpha, [d_model])

#

Scale weights after initialization

147        with torch.no_grad():

#

Feed forward network linear transformations

149            feed_forward.layer1.weight *= deep_norm_beta
150            feed_forward.layer2.weight *= deep_norm_beta

#

Attention value projection

153            self_attn.value.linear.weight *= deep_norm_beta

#

Attention output project

155            self_attn.output.weight *= deep_norm_beta

#

The mask will be initialized on the first call

158        self.mask = None

#

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

160    def forward(self, x: torch.Tensor):

#

Create causal mask

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

#

Subsequent mask, will mask out tokens from seeing future tokens

167            self.mask = subsequent_mask(len(x)).to(x.device)

#

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

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

#

Pass through the feed-forward network

172        x = self.feed_forward_norm(x, self.feed_forward(x))

#

175        return x

DeepNorm

Weight Initializations

Normalization Function

α and β constants

DeepNorm Normalization

Transformer Decoder Layer with DeepNorm

$α$ and $β$ constants