# Position-wise Feed-Forward Network (FFN)

This is a PyTorch implementation of position-wise feedforward network used in transformer.

FFN consists of two fully connected layers. Number of dimensions in the hidden layer $d_{ff}$, is generally set to around four times that of the token embedding $d_{model}$. So it is sometime also called the expand-and-contract network.

There is an activation at the hidden layer, which is usually set to ReLU (Rectified Linear Unit) activation,

That is, the FFN function is, where $W_1$, $W_2$, $b_1$ and $b_2$ are learnable parameters.

Sometimes the GELU (Gaussian Error Linear Unit) activation is also used instead of ReLU. where $\Phi(x) = P(X \le x), X \sim \mathcal{N}(0,1)$

### Gated Linear Units

This is a generic implementation that supports different variants including Gated Linear Units (GLU). We have also implemented experiments on these:

38import torch
39from torch import nn as nn
40
41from labml_helpers.module import Module

## FFN module

44class FeedForward(Module):
• d_model is the number of features in a token embedding
• d_ff is the number of features in the hidden layer of the FFN
• dropout is dropout probability for the hidden layer
• is_gated specifies whether the hidden layer is gated
• bias1 specified whether the first fully connected layer should have a learnable bias
• bias2 specified whether the second fully connected layer should have a learnable bias
• bias_gate specified whether the fully connected layer for the gate should have a learnable bias
49    def __init__(self, d_model: int, d_ff: int,
50                 dropout: float = 0.1,
51                 activation=nn.ReLU(),
52                 is_gated: bool = False,
53                 bias1: bool = True,
54                 bias2: bool = True,
55                 bias_gate: bool = True):
65        super().__init__()

Layer one parameterized by weight $W_1$ and bias $b_1$

67        self.layer1 = nn.Linear(d_model, d_ff, bias=bias1)

Layer one parameterized by weight $W_1$ and bias $b_1$

69        self.layer2 = nn.Linear(d_ff, d_model, bias=bias2)

Hidden layer dropout

71        self.dropout = nn.Dropout(dropout)

Activation function $f$

73        self.activation = activation

Whether there is a gate

75        self.is_gated = is_gated
76        if is_gated:

If there is a gate the linear layer to transform inputs to be multiplied by the gate, parameterized by weight $V$ and bias $c$

79            self.linear_v = nn.Linear(d_model, d_ff, bias=bias_gate)
81    def forward(self, x: torch.Tensor):

$f(x W_1 + b_1)$

83        g = self.activation(self.layer1(x))

If gated, $f(x W_1 + b_1) \otimes (x V + b)$

85        if self.is_gated:
86            x = g * self.linear_v(x)

Otherwise

88        else:
89            x = g

Apply dropout

91        x = self.dropout(x)

$(f(x W_1 + b_1) \otimes (x V + b)) W_2 + b_2$ or $f(x W_1 + b_1) W_2 + b_2$ depending on whether it is gated

94        return self.layer2(x)