fractional_max_pool2d

→Tensor or (Tensor, Tensor)

fractional_max_pool2d(x: Tensor, kernel_size: int | tuple[int, int], output_size: int | tuple[int, int] | None = None, output_ratio: float | tuple[float, float] | None = None, return_indices: bool = False, _random_samples: Tensor | None = None)

source

Fractional max-pooling over a 2-D input (Graham, 2014).

Performs max-pooling with a non-integer effective stride. Instead of a uniform window grid, random per-axis offsets pick "slightly irregular" window boundaries, yielding a smoother downsampling than the abrupt 2× reductions of standard max-pool. Acts as a structural regulariser for image classifiers.

Parameters

xTensor

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

kernel_sizeint or (int, int)

Size of the pooling window.

output_sizeint or (int, int)= None

Exact desired output spatial shape. Mutually exclusive with output_ratio.

output_ratiofloat or (float, float)= None

Multiplicative shrinkage factor per axis (e.g. 0.5 halves each dim). Mutually exclusive with output_size.

return_indicesbool= False

When True, also return per-output-cell argmax positions (flattened H × W index) as a second tensor.

_random_samplesTensor= None

Per-instance uniform samples of shape (N, C, 2) driving the window-boundary draws. Defaults to fresh lucid.rand.

Returns

Tensor or (Tensor, Tensor)

Output of shape (N, C, oH, oW); when return_indices, also the argmax indices of matching shape.

Notes

Window starts are drawn from Graham's formula (§3 of the paper)

\alpha = \frac{H - k}{H_{\text{out}} - 1},\quad \text{start}_i = \lfloor (i + u) \alpha \rfloor - \lfloor u \alpha \rfloor

where $u$ is a per-(sample, channel) uniform sample. The final start clamps to H - k so all windows lie inside the input. Implementation is a pure-Python composite — gradients flow through Tensor.max.

Examples

>>> import lucid
>>> from lucid.nn.functional import fractional_max_pool2d
>>> x = lucid.randn(1, 4, 14, 14)
>>> y = fractional_max_pool2d(x, kernel_size=2, output_ratio=0.5)
>>> y.shape
(1, 4, 7, 7)