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<!DOCTYPE html>
<html>
<head>
<title>14.4 - BatchNorm [Andrei Bursuc]</title>
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layout: true
.center.footer[Marc LELARGE and Andrei BURSUC | Deep Learning Do It Yourself | 14.4 BatchNorm]
---
class: center, middle, title-slide
count: false
## Going Deeper
# 14.4 BatchNorm
<br/>
<br/>
.bold[Andrei Bursuc ]
<br/>
url: https://dataflowr.github.io/website/
.citation[
With slides from A. Karpathy, F. Fleuret, G. Louppe, C. Ollion, O. Grisel, Y. Avrithis ...]
---
class: middle
.bigger[Previously we saw that maintaining proper statistics of the activations and derivatives was a critical issue to allow the training of deep architectures.]
.hidden.bigger[We can addres this by:
($1$) crafting smarter _weight initialization_ techniques
]
.hidden.bigger[
($2$) explicitly _forcing the activation statistics_ during the forward pass by re-normalizing them.
]
.hidden.center.bigger[__Batch normalization__ .cites[(Ioffe and Szegedy, 2015)] was the first method introducing this idea.]
---
count: false
class: middle
.bigger[Previously we saw that maintaining proper statistics of the activations and derivatives was a critical issue to allow the training of deep architectures.]
.bigger[We can addres this by:
($1$) crafting smarter _weight initialization_ techniques
]
.hidden.bigger[
($2$)explicitly _forcing the activation statistics_ during the forward pass by re-normalizing them.
]
.hidden.center.bigger[__Batch normalization__ .cites[(Ioffe and Szegedy, 2015)] was the first method introducing this idea.]
---
count: false
class: middle
.bigger[Previously we saw that maintaining proper statistics of the activations and derivatives was a critical issue to allow the training of deep architectures.]
.bigger[We can addres this by:
($1$) crafting smarter _weight initialization_ techniques
]
.bigger[
($2$) explicitly _forcing the activation statistics_ during the forward pass by re-normalizing them.
]
.hidden.center.bigger[__Batch normalization__ .cites[(Ioffe and Szegedy, 2015)] was the first method introducing this idea.]
---
count: false
class: middle
.bigger[Previously we saw that maintaining proper statistics of the activations and derivatives was a critical issue to allow the training of deep architectures.]
.bigger[We can addres this by:
($1$) crafting smarter _weight initialization_ techniques
]
.bigger[
($2$) explicitly _forcing the activation statistics_ during the forward pass by re-normalizing them.
]
.center.bigger[__Batch normalization__ .cites[(Ioffe and Szegedy, 2015)] was the first method introducing this idea.]
---
class: middle
.bigger.italic["Training Deep Neural Networks is complicated by the fact that the _distribution of each layer's inputs changes during training, as the parameters of the previous layers change_. This slows down the training by requiring lower learning rates and careful parameter initialization ..."]
.pull-right[(Ioffe and Szegedy, 2015)]
.reset-column[
]
.hidden.center.width-60[]
.citation[S. Ioffe and C. Szegedy, Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift; arXiv 2015]
---
count: false
class: middle
.bigger.italic["Training Deep Neural Networks is complicated by the fact that the _distribution of each layer's inputs changes during training, as the parameters of the previous layers change_. This slows down the training by requiring lower learning rates and careful parameter initialization ..."]
.pull-right[(Ioffe and Szegedy, 2015)]
.reset-column[
]
.center.width-60[]
.citation[S. Ioffe and C. Szegedy, Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift; arXiv 2015]
---
<br/>
Consider a simplified 3-layer MLP, with $x, w\_1, w\_2, w\_3 \in\mathbb{R}$, such that
$$f(x; w\_1, w\_2, w\_3) = \sigma\left(w\_3\sigma\left( w\_2 \sigma\left( w\_1 x \right)\right)\right). $$
Under the hood, this would be evaluated as
$$\begin{aligned}
u\_1 &= w\_1 x \\\\
u\_2 &= \sigma(u\_1) \\\\
u\_3 &= w\_2 u\_2 \\\\
u\_4 &= \sigma(u\_3) \\\\
u\_5 &= w\_3 u\_4 \\\\
\hat{y} &= \sigma(u\_5)
\end{aligned}$$
.citation[S. Ioffe and C. Szegedy, Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift; arXiv 2015]
--
count: false
Batch normalization can be done anywhere in a deep architecture, and forces the activations' first and second order moments, so that the following layers do not need to adapt to their drift.
---
# Batch normalization
Normalize activations in each **mini-batch** before activation function:
*speeds up* and *stabilizes* training
.citation[S. Ioffe and C. Szegedy, Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift; arXiv 2015]
--
count: false
.center.width-50[]
<br/>
---
# Batch normalization
During training batch normalization _shifts and rescales according to the mean and variance estimated on the batch_.
.center.width-50[]
<br/>
.citation[S. Ioffe and C. Szegedy, Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift; arXiv 2015]
---
# Batch normalization
As for dropout, the model behaves differently during __train__ and __test__.
At **test time**, use average and standard deviation computed on
*the whole dataset* instead of batch
Widely used in CNNs, but requires the mini-batch to be large
enough to compute statistics in the minibatch.
---
# Batch normalization
As dropout, batch normalization is implemented as a separate module .highlight[`torch.BatchNorm1d`] / .highlight[`torch.BatchNorm2d`] / .highlight[`torch.BatchNorm3d`] that processes the input components separately.
--
count: false
```py
>>> x = torch.randn(16, 100, 7, 7)
>>> bn2d = nn.BatchNorm2d(100)
>>> y = bn2d(x)
>>> x.size()
torch.Size([16, 100, 7, 7])
>>> y.size()
torch.Size([16, 100, 7, 7])
>>> bn2d.weight.data.size()
torch.Size([100])
>>> bn2d.bias.data.size()
torch.Size([100])
>>> bn2d.running_mean.size()
torch.Size([100])
>>> bn2d.running_var.size()
torch.Size([100])
```
---
count: false
# Batch normalization
As dropout, batch normalization is implemented as a separate module .highlight[`torch.BatchNorm1d`] / .highlight[`torch.BatchNorm2d`] / .highlight[`torch.BatchNorm3d`] that processes the input components separately.
```py
*>>> x = torch.randn(16, 100, 7, 7)
>>> bn2d = nn.BatchNorm2d(100)
>>> y = bn2d(x)
*>>> x.size()
*torch.Size([16, 100, 7, 7])
*>>> y.size()
*torch.Size([16, 100, 7, 7])
>>> bn2d.weight.data.size()
torch.Size([100])
>>> bn2d.bias.data.size()
torch.Size([100])
>>> bn2d.running_mean.size()
torch.Size([100])
>>> bn2d.running_var.size()
torch.Size([100])
```
---
count: false
# Batch normalization
As dropout, batch normalization is implemented as a separate module .highlight[`torch.BatchNorm1d`] / .highlight[`torch.BatchNorm2d`] / .highlight[`torch.BatchNorm3d`] that processes the input components separately.
```py
>>> x = torch.randn(16, 100, 7, 7)
*>>> bn2d = nn.BatchNorm2d(100)
>>> y = bn2d(x)
>>> x.size()
torch.Size([16, 100, 7, 7])
>>> y.size()
torch.Size([16, 100, 7, 7])
*>>> bn2d.weight.data.size()
*torch.Size([100])
*>>> bn2d.bias.data.size()
*torch.Size([100])
>>> bn2d.running_mean.size()
torch.Size([100])
>>> bn2d.running_var.size()
torch.Size([100])
```
---
count: false
# Batch normalization
As dropout, batch normalization is implemented as a separate module .highlight[`torch.BatchNorm1d`] / .highlight[`torch.BatchNorm2d`] / .highlight[`torch.BatchNorm3d`] that processes the input components separately.
```py
>>> x = torch.randn(16, 100, 7, 7)
*>>> bn2d = nn.BatchNorm2d(100)
>>> y = bn2d(x)
>>> x.size()
torch.Size([16, 100, 7, 7])
>>> y.size()
torch.Size([16, 100, 7, 7])
>>> bn2d.weight.data.size()
torch.Size([100])
>>> bn2d.bias.data.size()
torch.Size([100])
*>>> bn2d.running_mean.size()
*torch.Size([100])
*>>> bn2d.running_var.size()
*torch.Size([100])
```
---
# Batch normalization
Results on ImageNet LSVRC 2012:
.center.width-70[]
.citation[S. Ioffe and C. Szegedy, Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift; arXiv 2015]
--
count: false
- learning rate can be greater
- dropout and local normalization are not necessary
- $L\_2$ regularization influence should be reduced
---
# Multiple variants
.center.width-90[]
.citation[Y. Wu and K. He, Group Normalization, ECCV 2018]
---
# Weight Standardization
- recent approach for *micro-batch training* (i.e. 1-2 images per GPU): object detection, semantic segmentation
- .italic[standardizes]/normalizes weights in convolutional layers
.center.width-60[]
.citation[S. Qiao et al., Weight Standardization, arXiv 2019]
---
# Weight Standardization
.center.width-50[]
.citation[S. Qiao et al., Weight Standardization, arXiv 2019]
---
class: end-slide, center
count: false
The end.
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