trunc_normal_函数的含义和作用。

Posted 2022-05-28 AI浩

trunc_normal_函数：截断正太分布。
截断正态分布是截断分布(Truncated Distribution)的一种，那么截断分布是什么？截断分布是指，限制变量xx 取值范围(scope)的一种分布。如下图：

将正态分布的变量范围限制在【$u-3\delta ,u+3\delta$】内，那么我们就说我们截断了正态分布。
pytorch代码：

def _no_grad_trunc_normal_(tensor, mean, std, a, b):
    # Method based on https://people.sc.fsu.edu/~jburkardt/presentations/truncated_normal.pdf
    def norm_cdf(x):
        # Computes standard normal cumulative distribution function
        return (1. + math.erf(x / math.sqrt(2.))) / 2.

    if (mean < a - 2 * std) or (mean > b + 2 * std):
        warnings.warn("mean is more than 2 std from [a, b] in nn.init.trunc_normal_. "
                      "The distribution of values may be incorrect.",
                      stacklevel=2)

    with torch.no_grad():
        # Values are generated by using a truncated uniform distribution and
        # then using the inverse CDF for the normal distribution.
        # Get upper and lower cdf values
        l = norm_cdf((a - mean) / std)
        u = norm_cdf((b - mean) / std)

        # Uniformly fill tensor with values from [l, u], then translate to
        # [2l-1, 2u-1].
        tensor.uniform_(2 * l - 1, 2 * u - 1)

        # Use inverse cdf transform for normal distribution to get truncated
        # standard normal
        tensor.erfinv_()

        # Transform to proper mean, std
        tensor.mul_(std * math.sqrt(2.))
        tensor.add_(mean)

        # Clamp to ensure it's in the proper range
        tensor.clamp_(min=a, max=b)
        return tensor

def trunc_normal_(tensor: Tensor, mean: float = 0., std: float = 1., a: float = -2., b: float = 2.) -> Tensor:
    r"""Fills the input Tensor with values drawn from a truncated
    normal distribution. The values are effectively drawn from the
    normal distribution :math:`\\mathcalN(\\textmean, \\textstd^2)`
    with values outside :math:`[a, b]` redrawn until they are within
    the bounds. The method used for generating the random values works
    best when :math:`a \\leq \\textmean \\leq b`.

    Args:
        tensor: an n-dimensional `torch.Tensor`
        mean: the mean of the normal distribution
        std: the standard deviation of the normal distribution
        a: the minimum cutoff value
        b: the maximum cutoff value

    Examples:
        >>> w = torch.empty(3, 5)
        >>> nn.init.trunc_normal_(w)
    """
    return _no_grad_trunc_normal_(tensor, mean, std, a, b)

何时使用，比如我们使用ImageNet的预训练权重，修改了类别，这时候就要对其参数做初始化，调用方法：

 model_ft = convvit_base_patch16()
 model_ft.load_state_dict(torch.load('checkpoint.pth'),strict=False)
 numftr=model_ft.head.in_features
 model_ft.head=torch.nn.Linear(numftr,classes)
 nn.init.trunc_normal_(model_ft.head.weight, std=2e-5)# 将参数初始化为整态分布

timm也提供了trunc_normal_，导入方法：

from timm.models.layers import trunc_normal_

调用方法同上。

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