pytorch關(guān)于卷積操作的初始化方式(kaiming_uniform_詳解)
摘要:
最近寫(xiě)了一篇文章,reviewers給了幾個(gè)意見(jiàn),其中之一就是:不同配置下的網(wǎng)絡(luò)初始化條件是否相同,是怎樣初始化的?
之前竟然沒(méi)有關(guān)注過(guò)這個(gè)問(wèn)題,應(yīng)該是torch默認(rèn)情況下會(huì)初始化卷積核參數(shù),這里詳細(xì)講解一下torch卷積操作的初始化過(guò)程。
1. pytorch中的卷積運(yùn)算分類(lèi)
在pycharm的IDE中,按住ctrl+鼠標(biāo)點(diǎn)擊torch.nn.Conv2d可以進(jìn)入torch的內(nèi)部卷積運(yùn)算的源碼(conv.py)
搭建網(wǎng)絡(luò)經(jīng)常使用到的模塊
如下圖所示:
class _ConvNd(Module): class Conv1d(_ConvNd): class Conv2d(_ConvNd): class Conv3d(_ConvNd): class _ConvTransposeNd(_ConvNd): class ConvTranspose1d(_ConvTransposeNd): class ConvTranspose2d(_ConvTransposeNd): class ConvTranspose3d(_ConvTransposeNd):
可以看到:常用的卷積的父類(lèi)均是
class _ConvNd(Module):
并且點(diǎn)開(kāi) class Conv2d(_ConvNd): 并沒(méi)有發(fā)現(xiàn)參數(shù)初始化的具體方法,
如下圖所示
所以猜想卷積初始化參數(shù)的方法應(yīng)該在父類(lèi) _ConvNd(Module):
2. pytorch中的卷積操作的父類(lèi)
下面是父類(lèi) _ConvNd 的源碼,其中初始化參數(shù)的 方法是
def reset_parameters(self) -> None:
class _ConvNd(Module): __constants__ = ['stride', 'padding', 'dilation', 'groups', 'padding_mode', 'output_padding', 'in_channels', 'out_channels', 'kernel_size'] __annotations__ = {'bias': Optional[torch.Tensor]} def _conv_forward(self, input: Tensor, weight: Tensor, bias: Optional[Tensor]) -> Tensor: ... _in_channels: int out_channels: int kernel_size: Tuple[int, ...] stride: Tuple[int, ...] padding: Tuple[int, ...] dilation: Tuple[int, ...] transposed: bool output_padding: Tuple[int, ...] groups: int padding_mode: str weight: Tensor bias: Optional[Tensor] def __init__(self, in_channels: int, out_channels: int, kernel_size: Tuple[int, ...], stride: Tuple[int, ...], padding: Tuple[int, ...], dilation: Tuple[int, ...], transposed: bool, output_padding: Tuple[int, ...], groups: int, bias: bool, padding_mode: str) -> None: super(_ConvNd, self).__init__() if in_channels % groups != 0: raise ValueError('in_channels must be divisible by groups') if out_channels % groups != 0: raise ValueError('out_channels must be divisible by groups') valid_padding_modes = {'zeros', 'reflect', 'replicate', 'circular'} if padding_mode not in valid_padding_modes: raise ValueError("padding_mode must be one of {}, but got padding_mode='{}'".format( valid_padding_modes, padding_mode)) self.in_channels = in_channels self.out_channels = out_channels self.kernel_size = kernel_size self.stride = stride self.padding = padding self.dilation = dilation self.transposed = transposed self.output_padding = output_padding self.groups = groups self.padding_mode = padding_mode # `_reversed_padding_repeated_twice` is the padding to be passed to # `F.pad` if needed (e.g., for non-zero padding types that are # implemented as two ops: padding + conv). `F.pad` accepts paddings in # reverse order than the dimension. self._reversed_padding_repeated_twice = _reverse_repeat_tuple(self.padding, 2) if transposed: self.weight = Parameter(torch.Tensor( in_channels, out_channels // groups, *kernel_size)) else: self.weight = Parameter(torch.Tensor( out_channels, in_channels // groups, *kernel_size)) if bias: self.bias = Parameter(torch.Tensor(out_channels)) else: self.register_parameter('bias', None) self.reset_parameters() def reset_parameters(self) -> None: init.kaiming_uniform_(self.weight, a=math.sqrt(5)) if self.bias is not None: fan_in, _ = init._calculate_fan_in_and_fan_out(self.weight) bound = 1 / math.sqrt(fan_in) init.uniform_(self.bias, -bound, bound) def extra_repr(self): s = ('{in_channels}, {out_channels}, kernel_size={kernel_size}' ', stride={stride}') if self.padding != (0,) * len(self.padding): s += ', padding={padding}' if self.dilation != (1,) * len(self.dilation): s += ', dilation={dilation}' if self.output_padding != (0,) * len(self.output_padding): s += ', output_padding={output_padding}' if self.groups != 1: s += ', groups={groups}' if self.bias is None: s += ', bias=False' if self.padding_mode != 'zeros': s += ', padding_mode={padding_mode}' return s.format(**self.__dict__) def __setstate__(self, state): super(_ConvNd, self).__setstate__(state) if not hasattr(self, 'padding_mode'): self.padding_mode = 'zeros'
3. def reset_parameters(self) -> None
卷積操作的默認(rèn)的初始化方式:
def reset_parameters(self) -> None: init.kaiming_uniform_(self.weight, a=math.sqrt(5)) if self.bias is not None: fan_in, _ = init._calculate_fan_in_and_fan_out(self.weight) bound = 1 / math.sqrt(fan_in) init.uniform_(self.bias, -bound, bound)
該類(lèi)中的參數(shù)的初始化方式是: Kaiming
初始化
由我國(guó)計(jì)算機(jī)視覺(jué)領(lǐng)域?qū)<液蝿P明提出了針對(duì)于relu的初始化方法,pytorch默認(rèn)使用kaiming正態(tài)分布初始化卷積層參數(shù)。
Fills the input Tensor with values according to the method described in Delving deep into rectifiers: Surpassing human-level performance on ImageNet classification - He, K. et al. (2015),
using a uniform distribution.
The resulting tensor will have values sampled from U(?−?bound,?bound) where bound?=?gain?×?√((3)/(?fan_mode))Also known as He initialization.
3.1 卷積核部分的參數(shù)初始化:
init.kaiming_uniform_(self.weight, a=math.sqrt(5))
關(guān)于init.kaiming_uniform_這個(gè)函數(shù),源碼如下:
def kaiming_uniform_(tensor, a=0, mode='fan_in', nonlinearity='leaky_relu'): r"""Fills the input `Tensor` with values according to the method described in `Delving deep into rectifiers: Surpassing human-level performance on ImageNet classification` - He, K. et al. (2015), using a uniform distribution. The resulting tensor will have values sampled from :math:`\mathcal{U}(-\text{bound}, \text{bound})` where .. math:: \text{bound} = \text{gain} \times \sqrt{\frac{3}{\text{fan\_mode}}} Also known as He initialization. Args: tensor: an n-dimensional `torch.Tensor` a: the negative slope of the rectifier used after this layer (only used with ``'leaky_relu'``) mode: either ``'fan_in'`` (default) or ``'fan_out'``. Choosing ``'fan_in'`` preserves the magnitude of the variance of the weights in the forward pass. Choosing ``'fan_out'`` preserves the magnitudes in the backwards pass. nonlinearity: the non-linear function (`nn.functional` name), recommended to use only with ``'relu'`` or ``'leaky_relu'`` (default). Examples: >>> w = torch.empty(3, 5) >>> nn.init.kaiming_uniform_(w, mode='fan_in', nonlinearity='relu') """ fan = _calculate_correct_fan(tensor, mode) gain = calculate_gain(nonlinearity, a) std = gain / math.sqrt(fan) bound = math.sqrt(3.0) * std # Calculate uniform bounds from standard deviation with torch.no_grad(): return tensor.uniform_(-bound, bound)
torch中卷積核默認(rèn)的初始化的詳細(xì)參數(shù)為:
?init.kaiming_uniform_(self.weight, a=math.sqrt(5),mode='fan_in', nonlinearity='leaky_relu'))
關(guān)于 init.kaiming_uniform_中所使用的其他函數(shù) ,如下不做進(jìn)一步的分析,不過(guò)還是簡(jiǎn)單介紹一下。
_calculate_correct_fan(tensor, mode) # 用于計(jì)算計(jì)算當(dāng)前網(wǎng)絡(luò)層的fan_in(輸入神經(jīng)元個(gè)數(shù))或 fan_out(輸出神經(jīng)元個(gè)數(shù)的),取決于 mode 的值 'fan_in' 'fan_out' calculate_gain:# 對(duì)于給定的非線性函數(shù),返回推薦的增益值,其實(shí)就是一個(gè)數(shù),從下面圖中的列表中選出對(duì)應(yīng)的值
- _calculate_correct_fan:在這里 model = fan_in, 計(jì)算 的是 當(dāng)前網(wǎng)絡(luò)層的fan_in(輸入神經(jīng)元個(gè)數(shù))
- calculate_gain: 在這里 nonlinearity='leaky_relu',param = a = math.sqrt(5) 得到的值就是:(negative_slope = param = math.sqrt(5))
gan = math.sqrt(2.0 / (1 + negative_slope ** 2))
前文講到,
The resulting tensor will have values sampled from U(?−?bound,?bound) where bound?=?gain?×?√((3)/(?fan_mode))
所以上面的一通計(jì)算得到了bound
下面的 uniform_(from=0, to=1) → Tensor, 將tensor用從均勻分布中抽樣得到的值填充。
3.2 bias部分的初始化
這里不做詳細(xì)介紹了,相信認(rèn)真看了 weights部分的初始化過(guò)程,這部分自然會(huì)明白。
if self.bias is not None: fan_in, _ = init._calculate_fan_in_and_fan_out(self.weight) bound = 1 / math.sqrt(fan_in) init.uniform_(self.bias, -bound, bound)
附加的:
init._calculate_fan_in_and_fan_out(self.weight)?
函數(shù)來(lái)計(jì)算當(dāng)前網(wǎng)絡(luò)層的fan_in(輸入神經(jīng)元個(gè)數(shù))和fan_out(輸出神經(jīng)元個(gè)數(shù)的)
總結(jié)
以上為個(gè)人經(jīng)驗(yàn),希望能給大家一個(gè)參考,也希望大家多多支持腳本之家。
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