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89 lines
3.3 KiB
Python
89 lines
3.3 KiB
Python
"""
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---
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title: Noam optimizer from Attention is All You Need paper
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summary: >
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This is a tutorial/implementation of Noam optimizer.
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Noam optimizer has a warm-up period and then an exponentially decaying learning rate.
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---
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# Noam Optimizer
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This is the [PyTorch](https://pytorch.org) implementation of optimizer introduced in the paper
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[Attention Is All You Need](https://arxiv.org/abs/1706.03762).
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"""
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from typing import Dict
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from labml_nn.optimizers import WeightDecay
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from labml_nn.optimizers.amsgrad import AMSGrad
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class Noam(AMSGrad):
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"""
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## Noam Optimizer
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This class extends from Adam optimizer defined in [`adam.py`](adam.html).
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"""
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def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-16,
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weight_decay: WeightDecay = WeightDecay(),
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optimized_update: bool = True,
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amsgrad=False,
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warmup=0, d_model=512, defaults=None):
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"""
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### Initialize the optimizer
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* `params` is the list of parameters
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* `lr` is the learning rate $\alpha$
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* `betas` is a tuple of ($\beta_1$, $\beta_2$)
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* `eps` is $\hat{\epsilon}$ or $\epsilon$ based on `optimized_update`
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* `weight_decay` is an instance of class `WeightDecay` defined in [`__init__.py`](index.html)
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* 'optimized_update' is a flag whether to optimize the bias correction of the second moment
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by doing it after adding $\epsilon$
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* `amsgrad` is a flag indicating whether to use AMSGrad or fallback to plain Adam
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* `warmup` number of warmup steps
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* `d_model` model size; i.e. number of dimensions in the transformer
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* `defaults` is a dictionary of default for group values.
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This is useful when you want to extend the class `AdamWarmup`.
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"""
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defaults = {} if defaults is None else defaults
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defaults.update(dict(warmup=warmup))
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super().__init__(params, lr, betas, eps, weight_decay, optimized_update, amsgrad, defaults)
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self.d_model = d_model
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def get_lr(self, state: Dict[str, any], group: Dict[str, any]):
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"""
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### Get learning-rate
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$$\alpha \frac{1}{\sqrt{d_{model}}} \min \bigg(\frac{1}{\sqrt{t}}, \frac{t}{w^{3/2}}\bigg)$$
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where $w$ is the number of warmup steps.
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"""
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# $$\min \bigg(\frac{1}{\sqrt{t}}, \frac{t}{w^{3/2}}\bigg)$$
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factor = min(state['step'] ** (-0.5), state['step'] * group['warmup'] ** (-1.5))
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# $$\alpha \frac{1}{\sqrt{d_{model}}} \min \bigg(\frac{1}{\sqrt{t}}, \frac{t}{w^{3/2}}\bigg)$$
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return group['lr'] * self.d_model ** (-0.5) * factor
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def _test_noam_lr():
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"""
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### Plot learning rate for different warmups and model sizes
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"""
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import matplotlib.pyplot as plt
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import numpy as np
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from torch import nn
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model = nn.Linear(10, 10)
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opts = [Noam(model.parameters(), d_model=512, warmup=4000, lr=1),
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Noam(model.parameters(), d_model=512, warmup=8000, lr=1),
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Noam(model.parameters(), d_model=2048, warmup=2000, lr=1)]
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plt.plot(np.arange(1, 20000), [[opt.get_lr({'step': i}, opt.defaults) for opt in opts] for i in range(1, 20000)])
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plt.legend(["512:4000", "512:8000", "2048:2000"])
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plt.title("Learning Rate")
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plt.show()
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if __name__ == '__main__':
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_test_noam_lr()
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