lucid.multiply¶

lucid.multiply(a: Tensor, b: Tensor, /) → Tensor¶

The multiply function performs element-wise multiplication between two Tensor objects. It returns a new Tensor representing the product, with gradient support for backpropagation.

Function Signature¶

def mul(a: Tensor, b: Tensor) -> Tensor

Parameters¶

a (Tensor): The first tensor in the multiplication operation.
b (Tensor): The second tensor in the multiplication operation.

Returns¶

Tensor:
A new Tensor representing the element-wise product of a and b. If either a or b requires gradients, the resulting tensor will also require gradients.

Forward Calculation¶

The forward calculation for the multiplication operation is:

\[\text{out} = a \cdot b\]

where \(a\) and \(b\) are the data contained in the tensors a and b, respectively.

Backward Gradient Calculation¶

For each tensor a and b involved in the multiplication, the gradient with respect to the output (out) is computed as follows:

\[\frac{\partial \text{out}}{\partial a} = b, \quad \frac{\partial \text{out}}{\partial b} = a\]

Examples¶

Using multiply to multiply two tensors:

>>> import lucid
>>> a = Tensor([1.0, 2.0, 3.0], requires_grad=True)
>>> b = Tensor([4.0, 5.0, 6.0], requires_grad=True)
>>> out = lucid.multiply(a, b)
>>> print(out)
Tensor([4.0, 10.0, 18.0], grad=None)

After calling backward() on out, gradients for a and b will be accumulated based on the backpropagation rules:

>>> out.backward()
>>> print(a.grad)
[4.0, 5.0, 6.0]
>>> print(b.grad)
[1.0, 2.0, 3.0]