#

Switch Transformer

This is a miniature PyTorch implementation of the paper Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity. Our implementation only has a few million parameters and doesn't do model parallel distributed training. It does single GPU training, but we implement the concept of switching as described in the paper.

The Switch Transformer uses different parameters for each token by switching among parameters based on the token. Therefore, only a fraction of parameters are chosen for each token. So you can have more parameters but less computational cost.

The switching happens at the Position-wise Feedforward network (FFN) of each transformer block. Position-wise feedforward network consists of two sequentially fully connected layers. In switch transformer we have multiple FFNs (multiple experts), and we chose which one to use based on a router. The output is a set of probabilities for picking a FFN, and we pick the one with the highest probability and only evaluate that. So essentially the computational cost is the same as having a single FFN. In our implementation this doesn't parallelize well when you have many or large FFNs since it's all happening on a single GPU. In a distributed setup you would have each FFN (each very large) on a different device.

The paper introduces another loss term to balance load among the experts (FFNs) and discusses dropping tokens when routing is not balanced.

Here's the training code and a notebook for training a switch transformer on Tiny Shakespeare dataset.

40import torch
41from torch import nn
42
43from labml_helpers.module import Module
44from labml_nn.transformers.feed_forward import FeedForward
45from labml_nn.transformers.mha import MultiHeadAttention
46from labml_nn.utils import clone_module_list

#

Routing among multiple FFNs

49class SwitchFeedForward(Module):

#

capacity_factor is the capacity of each expert as a factor relative to ideally balanced load
drop_tokens specifies whether to drop tokens if more tokens are routed to an expert than the capacity
is_scale_prob specifies whether to multiply the input to the FFN by the routing probability
n_experts is the number of experts
expert is the expert layer, a FFN 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 in the FFN

54    def __init__(self, *,
55                 capacity_factor: float,
56                 drop_tokens: bool,
57                 is_scale_prob: bool,
58                 n_experts: int,
59                 expert: FeedForward,
60                 d_model: int):

#

71        super().__init__()
72
73        self.capacity_factor = capacity_factor
74        self.is_scale_prob = is_scale_prob
75        self.n_experts = n_experts
76        self.drop_tokens = drop_tokens

#

make copies of the FFNs

79        self.experts = clone_module_list(expert, n_experts)

#

Routing layer and softmax

81        self.switch = nn.Linear(d_model, n_experts)
82        self.softmax = nn.Softmax(dim=-1)

#

x is the input to the switching module with shape [seq_len, batch_size, d_model]

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

#

Capture the shape to change shapes later

90        seq_len, batch_size, d_model = x.shape

#

Flatten the sequence and batch dimensions

92        x = x.view(-1, d_model)

#

Get routing probabilities for each of the tokens. $p_{i} (x) = \frac{e ^{h (x)_{i}}}{\sum _{j}^{N} e ^{h (x)_{j}}}$ where $N$ is the number of experts n_experts and $h (\cdot)$ is the linear transformation of token embeddings.

98        route_prob = self.softmax(self.switch(x))

#

Get the maximum routing probabilities and the routes. We route to the expert with highest probability

102        route_prob_max, routes = torch.max(route_prob, dim=-1)

#

Get indexes of tokens going to each expert

105        indexes_list = [torch.eq(routes, i).nonzero(as_tuple=True)[0] for i in range(self.n_experts)]

#

Initialize an empty tensor to store outputs

108        final_output = x.new_zeros(x.shape)

#

Capacity of each expert. $expert capacity = \frac{tokens per batch}{number of experts} \times capacity factor$

114        capacity = int(self.capacity_factor * len(x) / self.n_experts)

#

Number of tokens routed to each expert.

116        counts = x.new_tensor([len(indexes_list[i]) for i in range(self.n_experts)])

#

Initialize an empty list of dropped tokens

119        dropped = []

#

Only drop tokens if drop_tokens is True .

121        if self.drop_tokens:

#

Drop tokens in each of the experts

123            for i in range(self.n_experts):

#

Ignore if the expert is not over capacity

125                if len(indexes_list[i]) <= capacity:
126                    continue

#

Shuffle indexes before dropping

128                indexes_list[i] = indexes_list[i][torch.randperm(len(indexes_list[i]))]

#

Collect the tokens over capacity as dropped tokens

130                dropped.append(indexes_list[i][capacity:])

#

Keep only the tokens upto the capacity of the expert

132                indexes_list[i] = indexes_list[i][:capacity]

#

Get outputs of the expert FFNs

135        expert_output = [self.experts[i](x[indexes_list[i], :]) for i in range(self.n_experts)]

#

Assign to final output

138        for i in range(self.n_experts):
139            final_output[indexes_list[i], :] = expert_output[i]

#

Pass through the dropped tokens

142        if dropped:
143            dropped = torch.cat(dropped)
144            final_output[dropped, :] = x[dropped, :]
145
146        if self.is_scale_prob:

#

Multiply by the expert outputs by the probabilities $y = p_{i} (x) E_{i} (x)$

148            final_output = final_output * route_prob_max.view(-1, 1)
149        else:

#

Don't scale the values but multiply by $\frac{p}{p ^} = 1$ so that the gradients flow (this is something we experimented with).

152            final_output = final_output * (route_prob_max / route_prob_max.detach()).view(-1, 1)

#

Change the shape of the final output back to [seq_len, batch_size, d_model]

155        final_output = final_output.view(seq_len, batch_size, d_model)

#

Return

the final output
number of tokens routed to each expert
sum of probabilities for each expert
number of tokens dropped.
routing probabilities of the selected experts

These are used for the load balancing loss and logging

166        return final_output, counts, route_prob.sum(0), len(dropped), route_prob_max

#

Switch Transformer Block

This is the same as normal transformer block with handling extra outputs of switch feedforward module.

169class SwitchTransformerLayer(Module):

#

d_model is the token embedding size
attn is the attention module
feed_forward is the feed forward module (which is the switching module in this case)
dropout_prob is the probability of dropping out after self attention and FFN

177    def __init__(self, *,
178                 d_model: int,
179                 attn: MultiHeadAttention,
180                 feed_forward: SwitchFeedForward,
181                 dropout_prob: float):

#

188        super().__init__()
189        self.size = d_model
190        self.attn = attn
191        self.feed_forward = feed_forward
192        self.dropout = nn.Dropout(dropout_prob)
193        self.norm_self_attn = nn.LayerNorm([d_model])
194        self.norm_ff = nn.LayerNorm([d_model])

#

196    def forward(self, *,
197                x: torch.Tensor,
198                mask: torch.Tensor):

#

Normalize the vectors before doing self attention

200        z = self.norm_self_attn(x)

#

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

202        self_attn = self.attn(query=z, key=z, value=z, mask=mask)

#

Add the self attention results

204        x = x + self.dropout(self_attn)

#

Normalize for feed-forward

207        z = self.norm_ff(x)

#

Pass through the switching feed-forward network

209        ff, counts, route_prob, n_dropped, route_prob_max = self.feed_forward(z)

#

Add the feed-forward results back

211        x = x + self.dropout(ff)
212
213        return x, counts, route_prob, n_dropped, route_prob_max

#

Switch Transformer

216class SwitchTransformer(Module):

#

221    def __init__(self, layer: SwitchTransformerLayer, n_layers: int):
222        super().__init__()

#

Make copies of the transformer layer

224        self.layers = clone_module_list(layer, n_layers)

#

Final normalization layer

226        self.norm = nn.LayerNorm([layer.size])

#

228    def forward(self, x: torch.Tensor, mask: torch.Tensor):

#

Run through each transformer layer

230        counts, route_prob, n_dropped, route_prob_max = [], [], [], []
231        for layer in self.layers:
232            x, f, p, n_d, p_max = layer(x=x, mask=mask)
233            counts.append(f)
234            route_prob.append(p)
235            n_dropped.append(n_d)
236            route_prob_max.append(p_max)

#

Finally, normalize the vectors

238        x = self.norm(x)

#

240        return x, torch.stack(counts), torch.stack(route_prob), n_dropped, torch.stack(route_prob_max)