nn_conv3d {torch}

Conv3D module

Description

Applies a 3D convolution over an input signal composed of several input planes. In the simplest case, the output value of the layer with input size (N, C_{in}, D, H, W) and output (N, C_{out}, D_{out}, H_{out}, W_{out}) can be precisely described as:

Usage

nn_conv3d(
  in_channels,
  out_channels,
  kernel_size,
  stride = 1,
  padding = 0,
  dilation = 1,
  groups = 1,
  bias = TRUE,
  padding_mode = "zeros"
)

Arguments

in_channels

(int): Number of channels in the input image

out_channels

(int): Number of channels produced by the convolution

kernel_size

(int or tuple): Size of the convolving kernel

stride

(int or tuple, optional): Stride of the convolution. Default: 1

padding

(int, tuple or str, optional): padding added to all six sides of the input. Default: 0

dilation

(int or tuple, optional): Spacing between kernel elements. Default: 1

groups

(int, optional): Number of blocked connections from input channels to output channels. Default: 1

bias

(bool, optional): If TRUE, adds a learnable bias to the output. Default: TRUE

padding_mode

(string, optional): 'zeros', 'reflect', 'replicate' or 'circular'. Default: 'zeros'

Details

out(N_i, C_{out_j}) = bias(C_{out_j}) + \sum_{k = 0}^{C_{in} - 1} weight(C_{out_j}, k) \star input(N_i, k)

where \star is the valid 3D cross-correlation operator

• stride controls the stride for the cross-correlation.

• padding controls the amount of implicit zero-paddings on both sides for padding number of points for each dimension.

• dilation controls the spacing between the kernel points; also known as the à trous algorithm. It is harder to describe, but this link_ has a nice visualization of what dilation does.

• groups controls the connections between inputs and outputs. in_channels and out_channels must both be divisible by groups. For example,

• At groups=1, all inputs are convolved to all outputs.

• At groups=2, the operation becomes equivalent to having two conv layers side by side, each seeing half the input channels, and producing half the output channels, and both subsequently concatenated.

• At groups= in_channels, each input channel is convolved with its own set of filters, of size \left\lfloor\frac{out\_channels}{in\_channels}\right\rfloor.

The parameters kernel_size, stride, padding, dilation can either be:

• a single int – in which case the same value is used for the depth, height and width dimension

• a tuple of three ints – in which case, the first int is used for the depth dimension, the second int for the height dimension and the third int for the width dimension

Shape

• Input: (N, C_{in}, D_{in}, H_{in}, W_{in})

• Output: (N, C_{out}, D_{out}, H_{out}, W_{out}) where

  D_{out} = \left\lfloor\frac{D_{in} + 2 \times \mbox{padding}[0] - \mbox{dilation}[0] \times (\mbox{kernel\_size}[0] - 1) - 1}{\mbox{stride}[0]} + 1\right\rfloor

  H_{out} = \left\lfloor\frac{H_{in} + 2 \times \mbox{padding}[1] - \mbox{dilation}[1] \times (\mbox{kernel\_size}[1] - 1) - 1}{\mbox{stride}[1]} + 1\right\rfloor

  W_{out} = \left\lfloor\frac{W_{in} + 2 \times \mbox{padding}[2] - \mbox{dilation}[2] \times (\mbox{kernel\_size}[2] - 1) - 1}{\mbox{stride}[2]} + 1\right\rfloor

Attributes

• weight (Tensor): the learnable weights of the module of shape (\mbox{out\_channels}, \frac{\mbox{in\_channels}}{\mbox{groups}}, \mbox{kernel\_size[0]}, \mbox{kernel\_size[1]}, \mbox{kernel\_size[2]}). The values of these weights are sampled from \mathcal{U}(-\sqrt{k}, \sqrt{k}) where k = \frac{groups}{C_{\mbox{in}} * \prod_{i=0}^{2}\mbox{kernel\_size}[i]}

• bias (Tensor): the learnable bias of the module of shape (out_channels). If bias is True, then the values of these weights are sampled from \mathcal{U}(-\sqrt{k}, \sqrt{k}) where k = \frac{groups}{C_{\mbox{in}} * \prod_{i=0}^{2}\mbox{kernel\_size}[i]}

Note

Depending of the size of your kernel, several (of the last) columns of the input might be lost, because it is a valid cross-correlation, and not a full cross-correlation. It is up to the user to add proper padding.

When groups == in_channels and out_channels == K * in_channels, where K is a positive integer, this operation is also termed in literature as depthwise convolution. In other words, for an input of size (N, C_{in}, D_{in}, H_{in}, W_{in}), a depthwise convolution with a depthwise multiplier K, can be constructed by arguments (in\_channels=C_{in}, out\_channels=C_{in} \times K, ..., groups=C_{in}).

In some circumstances when using the CUDA backend with CuDNN, this operator may select a nondeterministic algorithm to increase performance. If this is undesirable, you can try to make the operation deterministic (potentially at a performance cost) by setting torch.backends.cudnn.deterministic = TRUE. Please see the notes on :doc:⁠/notes/randomness⁠ for background.

Examples

if (torch_is_installed()) {
# With square kernels and equal stride
m <- nn_conv3d(16, 33, 3, stride = 2)
# non-square kernels and unequal stride and with padding
m <- nn_conv3d(16, 33, c(3, 5, 2), stride = c(2, 1, 1), padding = c(4, 2, 0))
input <- torch_randn(20, 16, 10, 50, 100)
output <- m(input)
}