# nn_conv2d: Conv2D module In torch: Tensors and Neural Networks with 'GPU' Acceleration

 nn_conv2d R Documentation

## Conv2D module

### Description

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

### Usage

nn_conv2d(
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 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}) + ∑_{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: ≤ft\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

### 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} = ≤ft\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} = ≤ft\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}(-√{k}, √{k}) where k = \frac{groups}{C_{\mbox{in}} * ∏_{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}(-√{k}, √{k}) where k = \frac{groups}{C_{\mbox{in}} * ∏_{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)
}


torch documentation built on Oct. 24, 2022, 5:08 p.m.