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

## Usage

```
nn_conv2d(
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 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- 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

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 dimensiona

`tuple`

of two ints -- in which case, the first`int`

is used for the height dimension, and the second`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 :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`

.

## Shape

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

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

## Attributes

weight (Tensor): the learnable weights of the module of shape \((\mbox{out\_channels}, \frac{\mbox{in\_channels}}{\mbox{groups}}\), \(\mbox{kernel\_size[0]}, \mbox{kernel\_size[1]})\). 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 \(k = \frac{groups}{C_{\mbox{in}} * \prod_{i=0}^{1}\mbox{kernel\_size}[i]}\)

## Examples

```
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)
}
```