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
```

`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)=∑_{j}e_{h(x)_{j}}e_{h(x)_{i}} $ where $N$ is the number of experts `n_experts`

and $h(⋅)$ 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. $expertcapacity=numberofexpertstokensperbatch ×capacityfactor$

`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 $p^ p =1$ 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`

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
```

`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)`