深入浅出Pytorch函数——torch.nn.init.calculate_gain

分类目录：《深入浅出Pytorch函数》总目录
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torch.nn.init模块中的所有函数都用于初始化神经网络参数，因此它们都在torc.no_grad()模式下运行，autograd不会将其考虑在内。

该函数对于给定的非线性函数，返回推荐的增益值。这些值如下所示：

Nonlinearity	Gain
Linear / Identity	$1$
Conv1D / Conv2D / Conv3D	$1$
Sigmoid	$1$
Tanh	$\frac{5}{3}$
ReLU	$\sqrt{2}$
Leaky Relu	$\sqrt{\frac{2}{1+{\text{negative\_slope}}^2}}$
SELU	$\frac{4}{3}$

为了实现自归一化神经网络，应该使用nonlinearity='linear'而不是nonlinearity='selu'。这使得初始权重的方差为$\frac{1}{N}$，这对于在前向通道中引入稳定的固定点是必要的。相比之下，SELU的默认增益牺牲了矩形层中更稳定梯度流的归一化效应。

语法

torch.nn.init.calculate_gain(nonlinearity, param=None)

参数

• nonlinearity：[nn.functional] 非线性函数名称
• param：非线性函数的可选参数

实例

# leaky_relu with negative_slope=0.2
gain = nn.init.calculate_gain('leaky_relu', 0.2)  

函数实现

def calculate_gain(nonlinearity, param=None):
    r"""Return the recommended gain value for the given nonlinearity function.
    The values are as follows:

    ================= ====================================================
    nonlinearity      gain
    ================= ====================================================
    Linear / Identity :math:`1`
    Conv{1,2,3}D      :math:`1`
    Sigmoid           :math:`1`
    Tanh              :math:`\frac{5}{3}`
    ReLU              :math:`\sqrt{2}`
    Leaky Relu        :math:`\sqrt{\frac{2}{1 + \text{negative\_slope}^2}}`
    SELU              :math:`\frac{3}{4}`
    ================= ====================================================

    .. warning::
        In order to implement `Self-Normalizing Neural Networks`_ ,
        you should use ``nonlinearity='linear'`` instead of ``nonlinearity='selu'``.
        This gives the initial weights a variance of ``1 / N``,
        which is necessary to induce a stable fixed point in the forward pass.
        In contrast, the default gain for ``SELU`` sacrifices the normalisation
        effect for more stable gradient flow in rectangular layers.

    Args:
        nonlinearity: the non-linear function (`nn.functional` name)
        param: optional parameter for the non-linear function

    Examples:
        >>> gain = nn.init.calculate_gain('leaky_relu', 0.2)  # leaky_relu with negative_slope=0.2

    .. _Self-Normalizing Neural Networks: https://papers.nips.cc/paper/2017/hash/5d44ee6f2c3f71b73125876103c8f6c4-Abstract.html
    """
    linear_fns = ['linear', 'conv1d', 'conv2d', 'conv3d', 'conv_transpose1d', 'conv_transpose2d', 'conv_transpose3d']
    if nonlinearity in linear_fns or nonlinearity == 'sigmoid':
        return 1
    elif nonlinearity == 'tanh':
        return 5.0 / 3
    elif nonlinearity == 'relu':
        return math.sqrt(2.0)
    elif nonlinearity == 'leaky_relu':
        if param is None:
            negative_slope = 0.01
        elif not isinstance(param, bool) and isinstance(param, int) or isinstance(param, float):
            # True/False are instances of int, hence check above
            negative_slope = param
        else:
            raise ValueError("negative_slope {} not a valid number".format(param))
        return math.sqrt(2.0 / (1 + negative_slope ** 2))
    elif nonlinearity == 'selu':
        return 3.0 / 4  # Value found empirically (https://github.com/pytorch/pytorch/pull/50664)
    else:
        raise ValueError("Unsupported nonlinearity {}".format(nonlinearity))