reduce

→Tensor

reduce(tensor: Tensor, pattern: str, reduction: str, axes_lengths: int = {})

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Reduce tensor along axes implied by an einops pattern.

Generalises standard sum / mean / max / min / prod reductions to arbitrary axes selected by symbolic pattern. Any axis present on the left-hand side of -> but absent on the right-hand side is collapsed by the chosen reduction.

Parameters

tensorTensor

Input tensor to reduce.

patternstr

Einops pattern such as "b h w -> b w". A number on the left is an unnamed axis of that length, so "(h 2) (w 2) -> h w" pools 2x2 windows.

reductionstr

Reduction operation; one of "sum", "mean", "max", "min", "prod", "any", "all".

**axes_lengthsint= {}

Axis lengths, needed to split a dimension into a group and checked against the input wherever the input already fixes the axis.

Returns

Tensor

The reduced tensor.

Raises

lucid._C.engine.InvalidArgument

The pattern is malformed, the reduction is unknown, an axis appears only on the right, or a keyword names no axis.

lucid._C.engine.ShapeMismatch

The input's shape does not fit the pattern or the keyword lengths.

lucid._C.engine.NotImplementedError

reduction="mean" over a tensor that is not floating point.

Notes

Conceptually equivalent to a permutation followed by a reduction along contiguous trailing axes. For reduction="mean" the result is

y_{b w} = \frac{1}{H} \sum_{h=1}^{H} x_{b h w}.

Examples

>>> import lucid
>>> x = lucid.randn(2, 3, 4)
>>> lucid.einops.reduce(x, "b h w -> b w", "mean").shape
(2, 4)
>>> lucid.einops.reduce(lucid.randn(2, 4, 6), "b (h 2) (w 3) -> b h w", "max").shape
(2, 2, 2)

>>> import lucid >>> x = lucid.randn(2, 3, 4) >>> lucid.einops.reduce(x, "b h w -> b w", "mean").shape (2, 4) >>> lucid.einops.reduce(lucid.randn(2, 4, 6), "b (h 2) (w 3) -> b h w", "max").shape (2, 2, 2)