lucid.abs¶
The abs function computes the element-wise absolute value of each element in the input tensor.
Function Signature¶
def abs(a: Tensor) -> Tensor
Parameters¶
a (Tensor): The input tensor whose absolute values are computed.
Returns¶
- Tensor:
A new tensor containing the absolute values of the elements in the input tensor. If a requires gradients, the resulting tensor will also require gradients.
Forward Calculation¶
\[\mathbf{out}_i = |\mathbf{a}_i|\]
Backward Gradient Calculation¶
\[\begin{split}\frac{\partial \mathbf{out}_i}{\partial \mathbf{a}_i} =
\begin{cases}
1 & \text{if } \mathbf{a}_i > 0 \\
-1 & \text{if } \mathbf{a}_i < 0 \\
0 & \text{if } \mathbf{a}_i = 0
\end{cases}\end{split}\]
Example¶
>>> import lucid
>>> a = Tensor([-1, -0.5, 0, 0.5, 1], requires_grad=True)
>>> out = lucid.abs(a)
>>> print(out)
Tensor([1. 0.5 0. 0.5 1.], grad=None)