lucid.concatenate

lucid.concatenate(arr: tuple[Tensor, ...], /, axis: int = 0) → Tensor

The concatenate function joins a sequence of tensors along an existing dimension. It concatenates the input tensors along the specified axis, combining them into a single tensor.

Function Signature

def concatenate(arr: tuple[Tensor, ...], axis: int = 0) -> Tensor

Parameters

  • arr (tuple[Tensor, …]):

    A sequence of tensors to concatenate. All tensors must have the same shape except in the dimension specified by axis.

  • axis (int, optional):

    The axis along which the tensors will be concatenated. Defaults to 0.

Returns

  • Tensor:

    A new tensor resulting from concatenating the input tensors along the specified axis. The resulting tensor has the same number of dimensions as the input tensors, with the size along the axis dimension being the sum of the sizes of the input tensors along that axis.

Forward Calculation

The concatenate operation joins the input tensors along the specified existing dimension axis.

\[\mathbf{out} = \text{concatenate}(\mathbf{a}_1, \mathbf{a}_2, \dots, \mathbf{a}_n; \text{axis} = k)\]

Where each (mathbf{a}_i) is a tensor and (k) is the axis along which concatenation occurs.

Backward Gradient Calculation

The gradient for the concatenate operation is split and passed to each of the input tensors along the concatenated axis.

\[\frac{\partial \mathbf{out}}{\partial \mathbf{a}_i} = \mathbf{I}_i\]

Example

>>> import lucid
>>> a = Tensor([[1.0, 2.0]], requires_grad=True)
>>> b = Tensor([[3.0, 4.0]], requires_grad=True)
>>> concatenated = lucid.concatenate((a, b), axis=0)
>>> print(concatenated)
Tensor([[1. 2.],
        [3. 4.]], grad=None)

>>> concatenated = lucid.concatenate((a, b), axis=1)
>>> print(concatenated)
Tensor([[1. 2. 3. 4.]], grad=None)

Note

  • All input tensors must have the same shape except in the dimension specified by axis.

  • The axis parameter specifies the dimension along which the tensors will be joined.

  • The resulting tensor will have the same number of dimensions as the input tensors.

  • If any of the input tensors require gradients, the resulting tensor will also require gradients.

  • Negative values for axis are supported and are interpreted as counting dimensions from the end (e.g., -1 refers to the last dimension).