nn.MaxPool3d

class lucid.nn.MaxPool3d(kernel_size: int | tuple[int, ...] = 1, stride: int | tuple[int, ...] = 1, padding: int | tuple[int, ...] = 0)

The MaxPool3d module applies a three-dimensional maximum pooling operation over an input signal composed of several input channels. This layer is commonly used in convolutional neural networks for tasks such as video processing and volumetric data analysis. The maximum pooling operation reduces the spatial and temporal dimensions of the input by selecting the maximum value within sliding windows, thereby highlighting prominent features and reducing computational complexity.

Class Signature

class lucid.nn.MaxPool3d(
    kernel_size: int | tuple[int, ...] = 1,
    stride: int | tuple[int, ...] = 1,
    padding: int | tuple[int, ...] = 0
)

Parameters

  • kernel_size (int or tuple[int, …], optional):

    Size of the window to take a maximum over. Can be a single integer or a tuple specifying the size in each spatial dimension. Default is 1.

  • stride (int or tuple[int, …], optional):

    Stride of the window. Can be a single integer or a tuple specifying the stride in each spatial dimension. If not provided, it defaults to the same value as kernel_size. Default is 1.

  • padding (int or tuple[int, …], optional):

    Zero-padding added to all sides of the input. Can be a single integer or a tuple specifying the padding in each spatial dimension. Default is 0.

Attributes

  • None

Forward Calculation

The MaxPool3d module performs the following operation:

\[\mathbf{y}_{d,h,w} = \max \left( \mathbf{x}_{d \times s_d + m - p_d,\ h \times s_h + n - p_h,\ w \times s_w + o - p_w} \right) \quad \text{for} \quad m = 0, \dots, k_d-1; \ n = 0, \dots, k_h-1; \ o = 0, \dots, k_w-1\]

Where:

  • \(\mathbf{x}\) is the input tensor of shape \((N, C, D_{in}, H_{in}, W_{in})\).

  • \(\mathbf{y}\) is the output tensor of shape \((N, C, D_{out}, H_{out}, W_{out})\).

  • \(k_d\), \(k_h\), \(k_w\) are the kernel sizes for depth, height, and width.

  • \(s_d\), \(s_h\), \(s_w\) are the strides for depth, height, and width.

  • \(p_d\), \(p_h\), \(p_w\) are the padding for depth, height, and width.

  • \(N\) is the batch size.

  • \(C\) is the number of channels.

  • \(D_{in}\), \(H_{in}\), \(W_{in}\) are the depth, height, and width of the input.

  • \(D_{out}\), \(H_{out}\), \(W_{out}\) are the depth, height, and width of the output, determined by the pooling parameters.

Backward Gradient Calculation

During backpropagation, the gradient with respect to the input is routed to the position of the maximum value in each pooling window, and zero elsewhere.

\[\begin{split}\frac{\partial \mathbf{y}_{d,h,w}}{\partial \mathbf{x}_{m,n,o}} = \begin{cases} 1 & \text{if } \mathbf{x}_{m,n,o} \text{ is the max in its pooling window} \\ 0 & \text{otherwise} \end{cases}\end{split}\]

This ensures that only the input element contributing to the maximum value receives the gradient.

Examples

Using `MaxPool3d` with a simple input tensor:

>>> import lucid.nn as nn
>>> input_tensor = Tensor([[
...     [[1.0, 3.0],
...      [2.0, 4.0]],
...     [[5.0, 6.0],
...      [7.0, 8.0]]
... ]], requires_grad=True)  # Shape: (1, 2, 2, 2, 2)
>>> max_pool = nn.MaxPool3d(kernel_size=2, stride=2, padding=0)
>>> output = max_pool(input_tensor)  # Shape: (1, 2, 1, 1, 1)
>>> print(output)
Tensor([[
    [[[4.0]]],
    [[[8.0]]]
]], grad=None)

# Backpropagation
>>> output.backward(Tensor([[
...     [[[1.0]]],
...     [[[1.0]]]
... ]]))
>>> print(input_tensor.grad)
Tensor([[
    [[[0.0, 0.0],
      [0.0, 1.0]],
    [[[0.0, 0.0],
      [0.0, 1.0]]]
]])  # Gradients with respect to input_tensor

Integrating `MaxPool3d` into a Neural Network Model:

>>> import lucid.nn as nn
>>> class MaxPool3dModel(nn.Module):
...     def __init__(self):
...         super(MaxPool3dModel, self).__init__()
...         self.conv1 = nn.Conv3D(in_channels=2, out_channels=4, kernel_size=3, stride=1, padding=1)
...         self.max_pool = nn.MaxPool3d(kernel_size=2, stride=2, padding=0)
...         self.fc = nn.Linear(in_features=4 * 1 * 1 * 1, out_features=1)
...
...     def forward(self, x):
...         x = self.conv1(x)
...         x = self.max_pool(x)
...         x = x.view(x.size(0), -1)
...         x = self.fc(x)
...         return x
...
>>> model = MaxPool3dModel()
>>> input_data = Tensor([[
...     [[[1.0, 2.0],
...       [3.0, 4.0]],
...      [[5.0, 6.0],
...       [7.0, 8.0]]]
... ]], requires_grad=True)  # Shape: (1, 2, 2, 2, 2)
>>> output = model(input_data)
>>> print(output)
Tensor([[[...]]], grad=None)  # Output tensor after passing through the model

# Backpropagation
>>> output.backward(Tensor([[[1.0]]]))
>>> print(input_data.grad)
Tensor([[
    [[[0.0, 0.0],
      [0.0, 1.0]],
    [[[0.0, 0.0],
      [0.0, 1.0]]]
]])  # Gradients with respect to input_data