import math import warnings import torch from torch.nn.init import _calculate_fan_in_and_fan_out def _no_grad_trunc_normal_(tensor, mean, std, a, b): # Cut & paste from PyTorch official master until it's in a few official releases - RW # Method based on https://people.sc.fsu.edu/~jburkardt/presentations/truncated_normal.pdf def norm_cdf(x): # Computes standard normal cumulative distribution function return (1.0 + math.erf(x / math.sqrt(2.0))) / 2.0 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(2.0)) tensor.add_(mean) # Clamp to ensure it's in the proper range tensor.clamp_(min=a, max=b) return tensor def trunc_normal_( tensor: torch.Tensor, mean=0.0, std=1.0, a=-2.0, b=2.0 ) -> torch.Tensor: r"""Fills the input Tensor with values drawn from a truncated normal distribution. The values are effectively drawn from the normal distribution :math:`\mathcal{N}(\text{mean}, \text{std}^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 \text{mean} \leq b`. NOTE: this impl is similar to the PyTorch trunc_normal_, the bounds [a, b] are applied while sampling the normal with mean/std applied, therefore a, b args should be adjusted to match the range of mean, std args. 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) def trunc_normal_tf_( tensor: torch.Tensor, mean=0.0, std=1.0, a=-2.0, b=2.0 ) -> torch.Tensor: r"""Fills the input Tensor with values drawn from a truncated normal distribution. The values are effectively drawn from the normal distribution :math:`\mathcal{N}(\text{mean}, \text{std}^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 \text{mean} \leq b`. NOTE: this 'tf' variant behaves closer to Tensorflow / JAX impl where the bounds [a, b] are applied when sampling the normal distribution with mean=0, std=1.0 and the result is subsquently scaled and shifted by the mean and std args. 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) """ _no_grad_trunc_normal_(tensor, 0, 1.0, a, b) with torch.no_grad(): tensor.mul_(std).add_(mean) return tensor def variance_scaling_(tensor, scale=1.0, mode="fan_in", distribution="normal"): fan_in, fan_out = _calculate_fan_in_and_fan_out(tensor) if mode == "fan_in": denom = fan_in elif mode == "fan_out": denom = fan_out elif mode == "fan_avg": denom = (fan_in + fan_out) / 2 variance = scale / denom # type: ignore if distribution == "truncated_normal": # constant is stddev of standard normal truncated to (-2, 2) trunc_normal_tf_(tensor, std=math.sqrt(variance) / 0.87962566103423978) elif distribution == "normal": tensor.normal_(std=math.sqrt(variance)) elif distribution == "uniform": bound = math.sqrt(3 * variance) # pylint: disable=invalid-unary-operand-type tensor.uniform_(-bound, bound) else: raise ValueError(f"invalid distribution {distribution}") def lecun_normal_(tensor): variance_scaling_(tensor, mode="fan_in", distribution="truncated_normal")