| import torch.nn.functional as F | |
| from torch import Tensor | |
| from .module import Module | |
| __all__ = ["PairwiseDistance", "CosineSimilarity"] | |
| class PairwiseDistance(Module): | |
| r""" | |
| Computes the pairwise distance between input vectors, or between columns of input matrices. | |
| Distances are computed using ``p``-norm, with constant ``eps`` added to avoid division by zero | |
| if ``p`` is negative, i.e.: | |
| .. math :: | |
| \mathrm{dist}\left(x, y\right) = \left\Vert x-y + \epsilon e \right\Vert_p, | |
| where :math:`e` is the vector of ones and the ``p``-norm is given by. | |
| .. math :: | |
| \Vert x \Vert _p = \left( \sum_{i=1}^n \vert x_i \vert ^ p \right) ^ {1/p}. | |
| Args: | |
| p (real, optional): the norm degree. Can be negative. Default: 2 | |
| eps (float, optional): Small value to avoid division by zero. | |
| Default: 1e-6 | |
| keepdim (bool, optional): Determines whether or not to keep the vector dimension. | |
| Default: False | |
| Shape: | |
| - Input1: :math:`(N, D)` or :math:`(D)` where `N = batch dimension` and `D = vector dimension` | |
| - Input2: :math:`(N, D)` or :math:`(D)`, same shape as the Input1 | |
| - Output: :math:`(N)` or :math:`()` based on input dimension. | |
| If :attr:`keepdim` is ``True``, then :math:`(N, 1)` or :math:`(1)` based on input dimension. | |
| Examples:: | |
| >>> pdist = nn.PairwiseDistance(p=2) | |
| >>> input1 = torch.randn(100, 128) | |
| >>> input2 = torch.randn(100, 128) | |
| >>> output = pdist(input1, input2) | |
| """ | |
| __constants__ = ["norm", "eps", "keepdim"] | |
| norm: float | |
| eps: float | |
| keepdim: bool | |
| def __init__( | |
| self, p: float = 2.0, eps: float = 1e-6, keepdim: bool = False | |
| ) -> None: | |
| super().__init__() | |
| self.norm = p | |
| self.eps = eps | |
| self.keepdim = keepdim | |
| def forward(self, x1: Tensor, x2: Tensor) -> Tensor: | |
| return F.pairwise_distance(x1, x2, self.norm, self.eps, self.keepdim) | |
| class CosineSimilarity(Module): | |
| r"""Returns cosine similarity between :math:`x_1` and :math:`x_2`, computed along `dim`. | |
| .. math :: | |
| \text{similarity} = \dfrac{x_1 \cdot x_2}{\max(\Vert x_1 \Vert _2 \cdot \Vert x_2 \Vert _2, \epsilon)}. | |
| Args: | |
| dim (int, optional): Dimension where cosine similarity is computed. Default: 1 | |
| eps (float, optional): Small value to avoid division by zero. | |
| Default: 1e-8 | |
| Shape: | |
| - Input1: :math:`(\ast_1, D, \ast_2)` where D is at position `dim` | |
| - Input2: :math:`(\ast_1, D, \ast_2)`, same number of dimensions as x1, matching x1 size at dimension `dim`, | |
| and broadcastable with x1 at other dimensions. | |
| - Output: :math:`(\ast_1, \ast_2)` | |
| Examples:: | |
| >>> input1 = torch.randn(100, 128) | |
| >>> input2 = torch.randn(100, 128) | |
| >>> cos = nn.CosineSimilarity(dim=1, eps=1e-6) | |
| >>> output = cos(input1, input2) | |
| """ | |
| __constants__ = ["dim", "eps"] | |
| dim: int | |
| eps: float | |
| def __init__(self, dim: int = 1, eps: float = 1e-8) -> None: | |
| super().__init__() | |
| self.dim = dim | |
| self.eps = eps | |
| def forward(self, x1: Tensor, x2: Tensor) -> Tensor: | |
| return F.cosine_similarity(x1, x2, self.dim, self.eps) | |