What Does Conv2d Output with 14×14 Input, Kernel 3, Stride 2?

Formula Breakdown

The Conv2d output size formula is:

output_size = floor((input_size - kernel_size + 2 * padding) / stride) + 1

Plugging in the values for 14×14 input:

output = floor((14 - 3 + 2*1) / 2) + 1
output = floor((14 - 3 + 2) / 2) + 1
output = floor(13 / 2) + 1
output = floor(6.5) + 1
output = 7

So the spatial dimensions go from 14×14 to 7×7.

PyTorch Code Example

import torch
import torch.nn as nn

# Define the Conv2d layer
conv = nn.Conv2d(in_channels=64, out_channels=128, kernel_size=3, stride=2, padding=1)

# Create input tensor: (batch, channels, height, width)
x = torch.randn(1, 64, 14, 14)
output = conv(x)
print(output.shape) # torch.Size([1, 128, 7, 7])

# Verify with formula
expected = (14 + 2 * 1 - 3) // 2 + 1
print(f"Expected output size: {expected}x{expected}") # 7x7

Architecture Context

This is a strided convolution that halves spatial dimensions. Modern architectures like ResNet and ConvNeXt use this instead of max-pooling for downsampling.

Parameter Count

A Conv2d(64, 128, 3) layer has:

parameters = in_channels * out_channels * kernel_size^2 + out_channels (bias)
parameters = 64 * 128 * 3 * 3 + 128
parameters = 73,856

This layer has 73,856 trainable parameters (73728 weights + 128 bias terms).

Practical Tips

• Memory usage. The output feature map for a single image is 128 × 7 × 7 = 6,272 float values (0.02 MB in float32).
• Batch dimension. Multiply memory by batch size. A batch of 32 uses 0.8 MB for this layer's output alone.
• Same padding rule. For any kernel, setting padding = (kernel_size - 1) / 2 with stride=1 preserves spatial dimensions.