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To calculate a PyTorch nn.Conv2d output shape, keep the batch and channel dimensions separate, then apply the documented formula to height and width. For each spatial axis, the result is the floor of the padded input size minus the dilated kernel extent, divided by stride, plus one. The output channel count is simply out_channels.
What nn.Conv2d expects and returns
PyTorch’s Conv2d applies a 2D convolution over an input with multiple planes. Its operation is implemented as cross-correlation, with a learned bias added for each output channel. The documented API is PyTorch nn.Conv2d.
A batched input has shape (N, C_in, H_in, W_in) and produces (N, C_out, H_out, W_out). An unbatched input may instead have shape (C_in, H_in, W_in), producing (C_out, H_out, W_out). Here, N is batch size, C_in must equal the layer’s in_channels, and C_out is the configured out_channels.
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For tuple-valued spatial parameters, where each pair is ordered as (height, width), calculate each axis independently:
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H_out = floor((H_in + 2*padding[0] - dilation[0]*(kernel_size[0] - 1) - 1) / stride[0] + 1)
W_out = floor((W_in + 2*padding[1] - dilation[1]*(kernel_size[1] - 1) - 1) / stride[1] + 1)For scalar values such as kernel_size=3, use the same value for both axes. The floor operation means a fractional result is rounded down; stride does not guarantee that the input dimensions will divide evenly into the output positions.
Worked example
Consider an input shaped (20, 16, 50, 100) and this documented configuration: nn.Conv2d(16, 33, (3, 5), stride=(2, 1), padding=(4, 2), dilation=(3, 1)).
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- Height:
floor((50 + 2*4 - 3*(3-1) - 1) / 2 + 1) = 27. - Width:
floor((100 + 2*2 - 1*(5-1) - 1) / 1 + 1) = 100.
The resulting shape is (20, 33, 27, 100). These dimensions follow from the documented formula and configuration.
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The module’s signature is:
nn.Conv2d(
in_channels,
out_channels,
kernel_size,
stride=1,
padding=0,
dilation=1,
groups=1,
bias=True,
padding_mode="zeros",
device=None,
dtype=None,
)| Parameter | What it controls | Effect to keep in mind |
|---|---|---|
in_channels |
Number of channels in the input. | Must match the input tensor’s channel dimension. |
out_channels |
Number of filters and output channels. | Sets the output channel dimension and affects weight and bias counts. |
kernel_size |
Height and width of the convolution window. | A pair permits non-square kernels; a larger effective kernel can reduce spatial output unless padding compensates. |
stride |
Distance the window moves between positions. | Values larger than one generally produce fewer positions; height and width can use different strides. |
padding |
Implicit padding on each side of each spatial axis. | Numeric pairs specify height then width; string options are 'valid' and 'same'. |
dilation |
Spacing between kernel points. | Raises the effective kernel extent without increasing the kernel’s stored weight dimensions. |
groups |
Partitions input and output channel connections. | Must divide both channel counts; larger grouping reduces connections and weight count. |
bias |
Whether to learn a bias for each output channel. | When false, there are no bias parameters. |
padding_mode |
How numeric padding is filled. | Documented modes are 'zeros', 'reflect', 'replicate', and 'circular'. |
device and dtype |
Optional device and data type for the layer’s parameters. | They do not alter the output-size formula. |
For kernel_size, stride, numeric padding, and dilation, an integer applies to both height and width. A two-value tuple gives separate values in height-then-width order.
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Padding choices
padding='valid'means no padding.padding='same'pads to preserve the input’s height and width, but only supports stride 1.- With numeric padding, each specified amount is applied on both sides of its axis. For example, height padding
4adds four positions at the top and four at the bottom for the shape calculation.
How many learnable parameters does Conv2d have?
The weight tensor has shape (out_channels, in_channels / groups, kernel_height, kernel_width). If bias is enabled, its shape is (out_channels,). Therefore:
parameters = out_channels * (in_channels / groups) * kernel_height * kernel_width
+ (out_channels if bias else 0)For Conv2d(16, 33, 3, stride=2), defaults include groups=1 and bias=True, so the count is 33 * 16 * 3 * 3 + 33 = 4,785. Stride changes the number of output positions, not the number of learned weights.
How groups change channel connectivity
Both in_channels and out_channels must be divisible by groups. With groups=1, each output channel can use every input channel. With groups=2, the input and output channels are divided into two channel groups, and connections stay within those groups.
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A depthwise convolution is the special case where groups == in_channels and out_channels == K * in_channels for a positive integer K. Each input channel is processed in its own group, with K output channels per input channel.
Complete shape example in Python
This snippet uses the same layer and input dimensions as the worked calculation:
import torch
from torch import nn
layer = nn.Conv2d(
in_channels=16,
out_channels=33,
kernel_size=(3, 5),
stride=(2, 1),
padding=(4, 2),
dilation=(3, 1),
)
x = torch.randn(20, 16, 50, 100)
y = layer(x)
print(y.shape) # (20, 33, 27, 100), from the documented shape formulaThe expected dimensions in the comment are calculated from the API formula.
Implementation details that can matter
The Conv2d reference documents support for TensorFloat32 and complex data types. It also notes that on certain ROCm devices, float16 inputs use different precision for backward computation. These are conditional backend details, not guarantees that apply identically to every device.
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The PyTorch functional conv2d reference notes that some CUDA/cuDNN circumstances may select a nondeterministic algorithm for performance. When determinism is preferred, it points to torch.backends.cudnn.deterministic = True; enabling it may reduce performance. This is an implementation option, not a claim that every convolution is nondeterministic.
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