pairwise_distance

→Tensor

pairwise_distance(x1: Tensor, x2: Tensor, p: float = 2.0, eps: float = 1e-06, keepdim: bool = False)

source

Element-wise $L_p$ distance between two equally-shaped tensors.

Computes the per-row $L_p$ norm of the difference — the standard metric in metric-learning triplet and contrastive losses.

Parameters

x1Tensor

Tensors of the same shape. Distance is reduced over the last dimension.

x2Tensor

Tensors of the same shape. Distance is reduced over the last dimension.

pfloat= 2.0

Order of the norm. 2 for Euclidean, 1 for Manhattan. Default 2.0.

epsfloat= 1e-06

Small constant added to |x1 - x2| before the power so the derivative is finite even at coincident points. Default 1e-6.

keepdimbool= False

If True, retain the reduced dimension with size 1. Default False.

Returns

Tensor

Distance tensor.

Notes

d_p(x_1, x_2) = \big\| |x_1 - x_2| + \epsilon \big\|_p = \Big(\sum_i (|x_{1,i} - x_{2,i}| + \epsilon)^p\Big)^{1/p}

The eps shift inside the norm matters for gradient stability — at $x_1 = x_2$ the bare $L_p$ distance is non-differentiable when $p < 2$ ; the offset converts the kink into a finite-slope smooth point.

Examples

>>> import lucid
>>> from lucid.nn.functional import pairwise_distance
>>> a = lucid.tensor([[1.0, 2.0]])
>>> b = lucid.tensor([[4.0, 6.0]])
>>> pairwise_distance(a, b, p=2.0)
Tensor([5.0000])