#

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.

39import torch
40from torch import nn
41
42from labml_helpers.module import Module
43from labml_nn.transformers.feed_forward import FeedForward
44from labml_nn.transformers.mha import MultiHeadAttention
45from labml_nn.utils import clone_module_list

#

Routing among multiple FFNs

48class 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

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

#

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

#

make copies of the FFNs

78        self.experts = clone_module_list(expert, n_experts)

#

Routing layer and softmax

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

#

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

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

#

Capture the shape to change shapes later

89        seq_len, batch_size, d_model = x.shape

#

Flatten the sequence and batch dimensions

91        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.

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

#

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

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

#

Get indexes of tokens going to each expert

104        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

107        final_output = x.new_zeros(x.shape)

#

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

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

#

Number of tokens routed to each expert.

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

#

Initialize an empty list of dropped tokens

118        dropped = []

#

Only drop tokens if drop_tokens is True .

120        if self.drop_tokens:

#

Drop tokens in each of the experts

122            for i in range(self.n_experts):

#

Ignore if the expert is not over capacity

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

#

Shuffle indexes before dropping

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

#

Collect the tokens over capacity as dropped tokens

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

#

Keep only the tokens upto the capacity of the expert

131                indexes_list[i] = indexes_list[i][:capacity]

#

Get outputs of the expert FFNs

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

#

Assign to final output

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

#

Pass through the dropped tokens

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

#

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

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

#

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

151            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]

154        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

165        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.

168class 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

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

#

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

#

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

#

Normalize the vectors before doing self attention

199        z = self.norm_self_attn(x)

#

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

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

#

Add the self attention results

203        x = x + self.dropout(self_attn)

#

Normalize for feed-forward

206        z = self.norm_ff(x)

#

Pass through the switching feed-forward network

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

#

Add the feed-forward results back

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

#

Switch Transformer

215class SwitchTransformer(Module):

#

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

#

Make copies of the transformer layer

223        self.layers = clone_module_list(layer, n_layers)

#

Final normalization layer

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

#

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

#

Run through each transformer layer

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

#

Finally, normalize the vectors

237        x = self.norm(x)

#

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