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Applies a 2D convolution over an input signal composed of several input planes.


  stride = 1,
  padding = 0,
  dilation = 1,
  groups = 1,
  bias = TRUE,
  padding_mode = "zeros"



(int): Number of channels in the input image


(int): Number of channels produced by the convolution


(int or tuple): Size of the convolving kernel


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


(int or tuple or string, optional): Zero-padding added to both sides of the input. controls the amount of padding applied to the input. It can be either a string 'valid', 'same' or a tuple of ints giving the amount of implicit padding applied on both sides. Default: 0


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


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


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


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


In the simplest case, the output value of the layer with input size \((N, C_{\mbox{in}}, H, W)\) and output \((N, C_{\mbox{out}}, H_{\mbox{out}}, W_{\mbox{out}})\) can be precisely described as:

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

where \(\star\) is the valid 2D cross-correlation operator, \(N\) is a batch size, \(C\) denotes a number of channels, \(H\) is a height of input planes in pixels, and \(W\) is width in pixels.

  • stride controls the stride for the cross-correlation, a single number or a tuple.

  • 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 height and width dimension

  • a tuple of two ints -- in which case, the first int is used for the height dimension, and the second int for the width dimension


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 :math:(N, C_{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 backends_cudnn_deterministic = TRUE.


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

  • Output: \((N, C_{out}, H_{out}, W_{out})\) where $$ H_{out} = \left\lfloor\frac{H_{in} + 2 \times \mbox{padding}[0] - \mbox{dilation}[0] \times (\mbox{kernel\_size}[0] - 1) - 1}{\mbox{stride}[0]} + 1\right\rfloor $$ $$ W_{out} = \left\lfloor\frac{W_{in} + 2 \times \mbox{padding}[1] - \mbox{dilation}[1] \times (\mbox{kernel\_size}[1] - 1) - 1}{\mbox{stride}[1]} + 1\right\rfloor $$


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

  • 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 \(k = \frac{groups}{C_{\mbox{in}} * \prod_{i=0}^{1}\mbox{kernel\_size}[i]}\)


if (torch_is_installed()) {

# With square kernels and equal stride
m <- nn_conv2d(16, 33, 3, stride = 2)
# non-square kernels and unequal stride and with padding
m <- nn_conv2d(16, 33, c(3, 5), stride = c(2, 1), padding = c(4, 2))
# non-square kernels and unequal stride and with padding and dilation
m <- nn_conv2d(16, 33, c(3, 5), stride = c(2, 1), padding = c(4, 2), dilation = c(3, 1))
input <- torch_randn(20, 16, 50, 100)
output <- m(input)