max_pool2d

→Tensor

max_pool2d(x: Tensor, kernel_size: int | tuple[int, int], stride: int | tuple[int, int] | None = None, padding: int | tuple[int, int] = 0, dilation: int | tuple[int, int] = 1, return_indices: bool = False, ceil_mode: bool = False)

source

2-D max pooling over a sliding window.

Aggregates each spatial neighbourhood into its maximum value. The canonical downsampling primitive in classical image CNNs — provides invariance to small local shifts and reduces both spatial extent and compute for subsequent layers.

Parameters

xTensor

Input of shape (N, C, H, W).

kernel_sizeint or (int, int)

Size of the pooling window.

strideint or (int, int)= None

Window step. Defaults to kernel_size (non-overlapping).

paddingint or (int, int)= 0

Implicit zero-padding on each spatial side.

dilationint or (int, int)= 1

Spacing between window elements. Default 1.

return_indicesbool= False

Must currently be False — see max_pool1d.

ceil_modebool= False

Use ceil instead of floor in the output-size formula.

Returns

Tensor

Output of shape (N, C, H_out, W_out) where each dim obeys

H_{\text{out}} = \left\lfloor \frac{H + 2 p_H - d_H (k_H - 1) - 1}{s_H} + 1 \right\rfloor

Notes

Math:

y_{i,c,h,w} = \max_{m,n} x_{i,\,c,\,s_H h + m,\,s_W w + n}

Pure max is sub-differentiable; gradient routes to the per-window argmax position only. Empirically the strongest pooling operator for classification tasks (preserves high-magnitude features).

Examples

>>> import lucid
>>> from lucid.nn.functional import max_pool2d
>>> x = lucid.randn(1, 16, 32, 32)
>>> y = max_pool2d(x, kernel_size=2, stride=2)
>>> y.shape
(1, 16, 16, 16)