关于VGGNet论文中卷积层参数量计算公式的技术咨询

Hey there! Let's unpack this confusion step by step—this is a common point of mix-up when learning about convolutional neural networks, so you're not alone.

First: What are "Channels" here? #

In this context, channels refer to the depth dimension of a feature map:

• For the input to the first convolution layer, channels would be the depth of your input data (e.g., 3 channels for RGB images).
• For subsequent layers, the input channel count equals the output channel count of the previous layer (since each filter in the previous layer produces one output channel).

The article states the input and output of the 3-layer 3×3 convolution stack are both C channels—this means each layer in the stack takes a C-channel feature map as input and outputs another C-channel feature map (so every layer has exactly C filters, one per output channel).

Why does the formula look different from yours? #

First, let's clarify: your formula p = w*h*d*n + n includes bias terms (the +n part, one bias per output channel). The article's calculation is focused only on weight parameters (many academic papers omit biases when comparing parameter counts because they're a tiny fraction of the total, especially for larger layers).

Breaking down the 3-layer 3×3 convolution stack #

For a single 3×3 convolution layer with:

• Input channels: C
• Output channels: C (since the stack maintains C channels throughout)
• Filter size: 3×3

Each filter has 3*3*C weight parameters (3 width × 3 height × C input channels—each filter needs to connect to every channel in the input). Since we have C filters (one per output channel), the weight count for one layer is:
3*3*C*C = 9C²

Multiply this by 3 layers (the stack), and you get:
3*(9C²) = 27C²
Which matches the article's calculation.

Comparing to a single 7×7 convolution layer #

Using the same logic:

• Filter size:7×7
• Input channels: C, Output channels: C

The weight count is:
7*7*C*C =49C²
That's way more parameters than the 3-layer 3×3 stack, which is why VGGNet uses stacks of small filters—they achieve similar receptive fields with fewer parameters!

Connecting back to your formula #

If we included biases in the article's calculation:

• Each 3×3 layer would have 9C² + C parameters (weights + biases)
• The 3-layer stack would be 3*(9C² + C) =27C² +3C
  But since biases are negligible compared to weights in this context, the article opts to ignore them for simplicity.

内容的提问来源于stack exchange，提问作者ltcmdtuvok