EP09_03 — 🟡 Counting Trainable Parameters of a CNN

9.10.3.1 📋 Implementation Guidelines

1. Input: Read the integer \(L\) (number of layers in the architecture, in the order they are applied).

2. Layers: Read \(L\) lines, each describing a layer in one of three formats:

   • CONV kh kw cin cout bias — convolutional layer with kernel \(k_h \times k_w\), \(c_{in}\) input channels, \(c_{out}\) output channels, and bias (0 or 1), indicating whether there is a bias per filter;
   • POOL — pooling layer (max or average), which has no trainable parameters and preserves the number of channels;
   • FC in out bias — fully connected layer with in inputs, out outputs, and bias (0 or 1), indicating whether there is a bias per neuron.

3. Consistency between CONV layers: in a sequence of convolutional layers, the cin of a layer must correspond to the cout of the preceding convolutional layer. A POOL layer does not alter this number of channels.

   For example:

   CONV 3 3 1 8 1
   POOL
   CONV 3 3 8 16 1

   The first CONV produces 8 channels, which are received by the second CONV. Therefore, in the second layer, cin=8 and cout=16.

4. Parameters of a CONV layer:

   Each of the \(c_{out}\) filters has \(k_h \cdot k_w \cdot c_{in}\) weights. Therefore,

   \[ P_{\mathrm{CONV}} = k_h \cdot k_w \cdot c_{in} \cdot c_{out} + c_{out}\cdot\text{bias}. \]

5. Parameters of an FC layer:

   \[ P_{\mathrm{FC}} = \text{in}\cdot\text{out} + \text{out}\cdot\text{bias}. \]

6. Parameters of a POOL layer: always \(0\).

7. Network total: sum the trainable parameters of all layers.

8. Output: For each layer, in reading order, print Camada i: P, where \(i\) starts at \(1\) and \(P\) is the number of parameters for that layer. At the end, print Total: T.

9.10.3.2 📐 Example to understand cin and cout

Consider the sequence:

CONV 3 3 1 8 1
POOL
CONV 3 3 8 16 1

In the first layer:

• cin=1: one channel enters;
• cout=8: there are 8 filters and, therefore, 8 channels exit.

Each filter has

\[ 3\cdot3\cdot1=9 \]

weights. Since there are 8 filters:

\[ 9\cdot8=72 \]

weights. With one bias per filter:

\[ 72+8=80. \]

In the second layer:

• cin=8: the 8 channels produced by the first CONV enter;
• cout=16: there are 16 filters and, therefore, 16 channels exit.

Each filter has

\[ 3\cdot3\cdot8=72 \]

weights. Since there are 16 filters:

\[ 72\cdot16=1152 \]

weights. With 16 biases:

\[ 1152+16=1168. \]

Thus, the two layers have, respectively, 80 and 1168 trainable parameters.

Note that cout is not \(cin\) multiplied by the number of filters. The number of filters is exactly cout: each filter combines all input channels and produces a single output channel.

9.10.3.3 📌 Computational Constraints

• Independence from spatial dimension: the input does not provide \(H \times W\). The count for a CONV layer depends only on kh, kw, cin, and cout.
• Channel consistency: for two consecutive CONV layers, the cin of the second must equal the cout of the first. A POOL layer preserves the number of channels.
• bias always 0 or 1: multiply the bias term directly by this value.
• POOL layers with no additional arguments: the line contains only the word POOL.
• FC layers: the number of inputs in is provided explicitly. It is not necessary to compute the spatial dimensions produced by previous layers.
• All numerical input values are non-negative integers.

9.10.3.4 🧠 Theoretical Foundation

9.10.3.5 🧩 morph.py methods that may help

This exercise is purely arithmetic and does not directly use functions from morph.py. The count can, however, be checked in a real architecture implemented in PyTorch using:

sum(p.numel() for p in modelo.parameters())

This expression counts the model parameters, including weights and biases.

9.10.3.6 📦 Input and Output Specification (VPL)

Input:

• Line 1: Integer \(L\).
• Next \(L\) lines: description of each layer, in the format CONV kh kw cin cout bias, POOL, or FC in out bias.

Output:

• \(L\) lines in the format Camada i: P.
• Last line: Total: T.

9.10.3.7 📌 Examples

%%writefile EP09_03.py
# Python code

Overwriting EP09_03.py

TestSuite("EP09_03.py").run()

✔️ EP09_03.cases already exists in casos/
📋 3 case(s) loaded from casos/EP09_03.cases

🔍 Testing Python: EP09_03.py
⚠️ EP09_03.py: Empty file (fewer than 3 lines). Tests skipped.