Applies a 2D convolution over an input signal composed of several input planes.
nn_conv2d(
in_channels,
out_channels,
kernel_size,
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'
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
\(k = \frac{groups}{C_{\mbox{in}} * \prod_{i=0}^{1}\mbox{kernel\_size}[i]}\)
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
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)
}
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