lucid.log2¶

lucid.log2(a: Tensor, /) → Tensor¶

The log2 function computes the base-2 logarithm of each element in the input tensor.

Function Signature¶

def log2(a: Tensor) -> Tensor

Parameters¶

a (Tensor): The input tensor for which the base-2 logarithm is computed.

Returns¶

Tensor: A new tensor containing the element-wise base-2 logarithm of the input tensor. If a requires gradients, the resulting tensor will also require gradients.

Forward Calculation¶

The forward calculation for log2 is:

\[\mathbf{out}_i = \log_2(\mathbf{a}_i)\]

where \(\mathbf{a}_i\) is the element of the input tensor a, and \(\mathbf{out}_i\) is the corresponding element of the output tensor.

Backward Gradient Calculation¶

For a tensor a involved in the log2 operation, the gradient with respect to the output (out) is computed as:

\[\frac{\partial \mathbf{out}_i}{\partial \mathbf{a}_i} = \frac{1}{\mathbf{a}_i \log(2)}\]

This means that for each element in the input tensor, the gradient is the reciprocal of the corresponding value multiplied by \(\log(2)\).

Example¶

>>> import lucid
>>> a = Tensor([1, 2, 3], requires_grad=True)
>>> out = lucid.log2(a)
>>> print(out)
Tensor([0.         1.         1.5849625], grad=None)

The log2 function supports tensors of arbitrary shape:

>>> import lucid
>>> a = Tensor([[1, 2], [3, 4]], requires_grad=True)
>>> out = lucid.log2(a)
>>> print(out)
Tensor([[0.        1.       ]
        [1.5849625 2.       ]], grad=None)