This is a PyTorch implementation/tutorial of the paper Distilling the Knowledge in a Neural Network.

It's a way of training a small network using the knowledge in a trained larger network; i.e. distilling the knowledge from the large network.

A large model with regularization or an ensemble of models (using dropout) generalizes better than a small model when trained directly on the data and labels. However, a small model can be trained to generalize better with help of a large model. Smaller models are better in production: faster, less compute, less memory.

The output probabilities of a trained model give more information than the labels because it assigns non-zero probabilities to incorrect classes as well. These probabilities tell us that a sample has a chance of belonging to certain classes. For instance, when classifying digits, when given an image of digit *7*, a generalized model will give a high probability to 7 and a small but non-zero probability to 2, while assigning almost zero probability to other digits. Distillation uses this information to train a small model better.

The probabilities are usually computed with a softmax operation,

$q_{i}=∑_{j}exp(z_{j})exp(z_{i}) $

where $q_{i}$ is the probability for class $i$ and $z_{i}$ is the logit.

We train the small model to minimize the Cross entropy or KL Divergence between its output probability distribution and the large network's output probability distribution (soft targets).

One of the problems here is that the probabilities assigned to incorrect classes by the large network are often very small and don't contribute to the loss. So they soften the probabilities by applying a temperature $T$,

$q_{i}=∑_{j}exp(Tz_{j} )exp(Tz_{i} ) $

where higher values for $T$ will produce softer probabilities.

Paper suggests adding a second loss term for predicting the actual labels when training the small model. We calculate the composite loss as the weighted sum of the two loss terms: soft targets and actual labels.

The dataset for distillation is called *the transfer set*, and the paper suggests using the same training data.

We train on CIFAR-10 dataset. We train a large model that has $14,728,266$ parameters with dropout and it gives an accuracy of 85% on the validation set. A small model with $437,034$ parameters gives an accuracy of 80%.

We then train the small model with distillation from the large model, and it gives an accuracy of 82%; a 2% increase in the accuracy.

```
74import torch
75import torch.nn.functional
76from torch import nn
77
78from labml import experiment, tracker
79from labml.configs import option
80from labml_helpers.train_valid import BatchIndex
81from labml_nn.distillation.large import LargeModel
82from labml_nn.distillation.small import SmallModel
83from labml_nn.experiments.cifar10 import CIFAR10Configs
```

This extends from `CIFAR10Configs`

which defines all the dataset related configurations, optimizer, and a training loop.

`86class Configs(CIFAR10Configs):`

The small model

`94 model: SmallModel`

The large model

`96 large: LargeModel`

KL Divergence loss for soft targets

`98 kl_div_loss = nn.KLDivLoss(log_target=True)`

Cross entropy loss for true label loss

`100 loss_func = nn.CrossEntropyLoss()`

Temperature, $T$

`102 temperature: float = 5.`

Weight for soft targets loss.

The gradients produced by soft targets get scaled by $T_{2}1 $. To compensate for this the paper suggests scaling the soft targets loss by a factor of $T_{2}$

`108 soft_targets_weight: float = 100.`

Weight for true label cross entropy loss

`110 label_loss_weight: float = 0.5`

`112 def step(self, batch: any, batch_idx: BatchIndex):`

Training/Evaluation mode for the small model

`120 self.model.train(self.mode.is_train)`

Large model in evaluation mode

`122 self.large.eval()`

Move data to the device

`125 data, target = batch[0].to(self.device), batch[1].to(self.device)`

Update global step (number of samples processed) when in training mode

```
128 if self.mode.is_train:
129 tracker.add_global_step(len(data))
```

Get the output logits, $v_{i}$, from the large model

```
132 with torch.no_grad():
133 large_logits = self.large(data)
```

Get the output logits, $z_{i}$, from the small model

`136 output = self.model(data)`

Soft targets $p_{i}=∑_{j}exp(Tv_{j} )exp(Tv_{i} ) $

`140 soft_targets = nn.functional.log_softmax(large_logits / self.temperature, dim=-1)`

Temperature adjusted probabilities of the small model $q_{i}=∑_{j}exp(Tz_{j} )exp(Tz_{i} ) $

`143 soft_prob = nn.functional.log_softmax(output / self.temperature, dim=-1)`

Calculate the soft targets loss

`146 soft_targets_loss = self.kl_div_loss(soft_prob, soft_targets)`

Calculate the true label loss

`148 label_loss = self.loss_func(output, target)`

Weighted sum of the two losses

`150 loss = self.soft_targets_weight * soft_targets_loss + self.label_loss_weight * label_loss`

Log the losses

```
152 tracker.add({"loss.kl_div.": soft_targets_loss,
153 "loss.nll": label_loss,
154 "loss.": loss})
```

Calculate and log accuracy

```
157 self.accuracy(output, target)
158 self.accuracy.track()
```

Train the model

`161 if self.mode.is_train:`

Calculate gradients

`163 loss.backward()`

Take optimizer step

`165 self.optimizer.step()`

Log the model parameters and gradients on last batch of every epoch

```
167 if batch_idx.is_last:
168 tracker.add('model', self.model)
```

Clear the gradients

`170 self.optimizer.zero_grad()`

Save the tracked metrics

`173 tracker.save()`

```
176@option(Configs.large)
177def _large_model(c: Configs):
```

`181 return LargeModel().to(c.device)`

```
184@option(Configs.model)
185def _small_student_model(c: Configs):
```

`189 return SmallModel().to(c.device)`

`192def get_saved_model(run_uuid: str, checkpoint: int):`

`197 from labml_nn.distillation.large import Configs as LargeConfigs`

In evaluation mode (no recording)

`200 experiment.evaluate()`

Initialize configs of the large model training experiment

`202 conf = LargeConfigs()`

Load saved configs

`204 experiment.configs(conf, experiment.load_configs(run_uuid))`

Set models for saving/loading

`206 experiment.add_pytorch_models({'model': conf.model})`

Set which run and checkpoint to load

`208 experiment.load(run_uuid, checkpoint)`

Start the experiment - this will load the model, and prepare everything

`210 experiment.start()`

Return the model

`213 return conf.model`

Train a small model with distillation

`216def main(run_uuid: str, checkpoint: int):`

Load saved model

`221 large_model = get_saved_model(run_uuid, checkpoint)`

Create experiment

`223 experiment.create(name='distillation', comment='cifar10')`

Create configurations

`225 conf = Configs()`

Set the loaded large model

`227 conf.large = large_model`

Load configurations

```
229 experiment.configs(conf, {
230 'optimizer.optimizer': 'Adam',
231 'optimizer.learning_rate': 2.5e-4,
232 'model': '_small_student_model',
233 })
```

Set model for saving/loading

`235 experiment.add_pytorch_models({'model': conf.model})`

Start experiment from scratch

`237 experiment.load(None, None)`

Start the experiment and run the training loop

```
239 with experiment.start():
240 conf.run()
```

```
244if __name__ == '__main__':
245 main('d46cd53edaec11eb93c38d6538aee7d6', 1_000_000)
```