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,
dilation = 1,
groups = 1,
bias = TRUE,
)

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

(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

(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

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.

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 $$k = \frac{groups}{C_{\mbox{in}} * \prod_{i=0}^{2}\mbox{kernel\_size}[i]}$$

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)
}