Modular Training Components

Welcome back to lesson 2 of "Building and Applying Your Neural Network Library"! You've made excellent progress in this course. In our previous lesson, we successfully transformed our neural network code into a well-structured C++ library by modularizing our core components — dense layers and activation functions. We created clean include paths and established the foundation for a professional-grade neural network library using proper header and source file organization.

Now we're ready to take the next crucial step: modularizing our training components. As you may recall from our previous courses, training a neural network involves two key components beyond the layers themselves: loss functions (which measure how well our network is performing) and optimizers (which update the network's weights based on the gradients we compute). Currently, these components are scattered throughout our training code, making them difficult to reuse and maintain.

In this lesson, we'll organize these training components into dedicated namespaces within our neuralnets library. We'll create a losses namespace to house our mean squared error (MSE) loss function and an optimizers namespace for our stochastic gradient descent (SGD) optimizer. By the end of this lesson, you'll have a complete, modular training pipeline that demonstrates the power of good software architecture in machine learning projects.

Before we dive into modularizing our training components, let's take a moment to understand the dataset we'll be using to test our library: the XOR (exclusive OR) problem. This is a classic toy problem in machine learning that serves as an excellent test case for neural networks because it's non-linearly separable — meaning a single linear classifier cannot solve it, but a simple multi-layer neural network can.

The XOR problem consists of four data points with two binary inputs and one binary output. The output is 1 when exactly one of the inputs is 1, and 0 otherwise. This creates the pattern: [0,0] → 0, [0,1] → 1, [1,0] → 1, [1,1] → 0. This is typically treated as a classification problem, but we can frame it as a regression task as well, which is what we'll do by using our mse loss. Despite its simplicity, if our network can learn XOR, then we know our forward pass, backward pass, loss calculation, and optimization code are all functioning properly.

// XOR dataset setup using Eigen matrices
Eigen::MatrixXd X_train(4, 2);
X_train << 0, 0,
           0, 1,
           1, 0,
           1, 1;

Eigen::MatrixXd y_train(4, 1);
y_train << 0,
           1,
           1,
           0;

While we're using XOR for rapid development and testing in this lesson, later in the course we'll apply our complete neural network library to a real-world dataset — the California housing dataset — where we'll predict house prices based on various features like location, population, and median income.

Let's start by organizing our loss functions into a dedicated namespace. We'll create a losses namespace within our neuralnets library, with the familiar MSE functions organized into clean, includable header and source files. The key insight here is separating the mathematical operations from the training logic, creating a clean interface that makes our code more testable and allows us to easily add other loss functions in the future.

include/neuralnets/losses/mse.hpp:

#ifndef NEURALNETS_LOSSES_MSE_HPP
#define NEURALNETS_LOSSES_MSE_HPP

#include <Eigen/Dense>

namespace neuralnets {
namespace losses {

/**
 * Calculate Mean Squared Error loss.
 * @param y_true True target values
 * @param y_pred Predicted values
 * @return MSE loss value
 */
double mse_loss(const Eigen::MatrixXd& y_true, const Eigen::MatrixXd& y_pred);

/**
 * Derivative of MSE loss w.r.t. y_pred.
 * @param y_true True target values
 * @param y_pred Predicted values
 * @return Gradient matrix
 */
Eigen::MatrixXd mse_loss_derivative(const Eigen::MatrixXd& y_true, const Eigen::MatrixXd& y_pred);

} // namespace losses
} // namespace neuralnets

#endif // NEURALNETS_LOSSES_MSE_HPP

src/losses/mse.cpp:

#include "neuralnets/losses/mse.hpp"

namespace neuralnets {
namespace losses {

double mse_loss(const Eigen::MatrixXd& y_true, const Eigen::MatrixXd& y_pred) {
    Eigen::MatrixXd diff = y_true - y_pred;
    return diff.array().square().mean();
}

Eigen::MatrixXd mse_loss_derivative(const Eigen::MatrixXd& y_true, const Eigen::MatrixXd& y_pred) {
    // Normalize by batch size (number of samples)
    return 2.0 * (y_pred - y_true) / y_true.rows();
}

} // namespace losses
} // namespace neuralnets

Similarly, let's organize our optimization algorithm into its own namespace. We'll implement our SGD optimizer as a class that encapsulates both the learning rate parameter and the update logic.

The key benefit of this modular approach is that we encapsulate the optimization logic in a reusable class with a clean interface. The update method applies the SGD update rule to any layer that has trainable parameters, making our optimizer robust and flexible.

include/neuralnets/optimizers/sgd.hpp:

#ifndef NEURALNETS_OPTIMIZERS_SGD_HPP
#define NEURALNETS_OPTIMIZERS_SGD_HPP

#include "neuralnets/layers/dense.hpp"

namespace neuralnets {
namespace optimizers {

class SGD {
private:
    double learning_rate_;

public:
    /**
     * Constructor for SGD optimizer.
     * @param learning_rate Learning rate for weight updates
     */
    explicit SGD(double learning_rate = 0.01);

    /**
     * Update layer's weights and biases using stored gradients.
     * @param layer Reference to the layer to update
     */
    void update(layers::DenseLayer& layer);
};

} // namespace optimizers
} // namespace neuralnets

#endif // NEURALNETS_OPTIMIZERS_SGD_HPP

src/optimizers/sgd.cpp:

#include "neuralnets/optimizers/sgd.hpp"

namespace neuralnets {
namespace optimizers {

SGD::SGD(double learning_rate) : learning_rate_(learning_rate) {}

void SGD::update(layers::DenseLayer& layer) {
    // Update weights and biases using stored gradients
    if (layer.has_gradients()) {
        layer.weights_ -= learning_rate_ * layer.d_weights_;
        layer.biases_ -= learning_rate_ * layer.d_biases_;
    }
}

} // namespace optimizers
} // namespace neuralnets

Now comes the exciting part — putting all our modular components together into a complete training pipeline! This demonstrates the power of our modular design: clean includes, specific component usage, and a readable training setup that clearly separates concerns.

Our training pipeline combines the MLP class from our previous lesson with our newly modularized loss functions and optimizers. Notice how each component has a specific responsibility: the network handles forward and backward propagation, the loss namespace computes objectives and gradients, and the optimizer updates weights.

src/main.cpp:

#include <iostream>
#include <iomanip>
#include <Eigen/Dense>
#include "neuralnets/layers/dense.hpp"
#include "neuralnets/losses/mse.hpp"
#include "neuralnets/optimizers/sgd.hpp"

using namespace neuralnets;

int main() {
    // Sample data: XOR problem
    Eigen::MatrixXd X_train(4, 2);
    X_train << 0, 0,
               0, 1,
               1, 0,
               1, 1;

    Eigen::MatrixXd y_train(4, 1);
    y_train << 0,
               1,
               1,
               0;

    // Build MLP using modular components
    MLP mlp;
    mlp.add_layer(std::make_unique<layers::DenseLayer>(2, 4, "relu"));
    mlp.add_layer(std::make_unique<layers::DenseLayer>(4, 1, "sigmoid"));

    // Use modular optimizer
    optimizers::SGD optimizer(0.5);

    // Training loop
    int epochs = 1000;
    std::cout << "Training MLP for XOR problem for " << epochs 
              << " epochs with LR=0.5" << std::endl;

    for (int epoch = 0; epoch < epochs; ++epoch) {
        // 1. Forward pass
        Eigen::MatrixXd y_pred = mlp.forward(X_train);
        
        // 2. Calculate loss using modular loss function
        double loss = losses::mse_loss(y_train, y_pred);
        
        // 3. Calculate gradient using modular derivative
        Eigen::MatrixXd d_loss_wrt_pred = losses::mse_loss_derivative(y_train, y_pred);
        
        // 4. Backward pass through network
        mlp.backward(d_loss_wrt_pred);
        
        // 5. Update weights using modular optimizer
        for (auto& layer : mlp.get_layers()) {
            optimizer.update(*layer);
        }
        
        if ((epoch + 1) % 200 == 0 || epoch == 0) {
            std::cout << "Epoch " << std::setw(4) << (epoch + 1) << "/" << epochs 
                      << ", Loss: " << std::fixed << std::setprecision(6) << loss << std::endl;
        }
    }

    // Test final performance
    std::cout << "\n--- After Training ---" << std::endl;
    Eigen::MatrixXd final_preds = mlp.forward(X_train);
    std::cout << "Input | True Output | Predicted Output | Rounded Prediction" << std::endl;
    
    for (int i = 0; i < X_train.rows(); ++i) {
        double pred_val = final_preds(i, 0);
        int rounded_pred = static_cast<int>(std::round(pred_val));
        
        std::cout << "[" << X_train(i, 0) << " " << X_train(i, 1) << "] | " 
                  << std::setw(11) << static_cast<int>(y_train(i, 0)) << " | " 
                  << std::setw(16) << std::fixed << std::setprecision(4) << pred_val << " | " 
                  << std::setw(18) << rounded_pred << std::endl;
    }

    return 0;
}

To compile our modular training pipeline, we need to update our build system to include the new source files. Here's the updated CMakeLists.txt:

CMakeLists.txt:

cmake_minimum_required(VERSION 3.10)
project(NeuralNets)

set(CMAKE_CXX_STANDARD 17)

# Find Eigen3
find_package(Eigen3 REQUIRED)

# Include directories
include_directories(include)

# Source files
set(SOURCES
    src/layers/dense.cpp
    src/losses/mse.cpp
    src/optimizers/sgd.cpp
    src/main.cpp
)

# Create executable
add_executable(neuralnets ${SOURCES})

# Link Eigen3
target_link_libraries(neuralnets Eigen3::Eigen)

To build and run:

mkdir build && cd build
cmake ..
make
./neuralnets

When we run our complete training pipeline, we can observe how our modular neural network library learns to solve the XOR problem. The training output demonstrates both the learning process and the final performance of our network:

Training MLP for XOR problem for 1000 epochs with LR=0.5
Epoch    1/1000, Loss: 0.250048
Epoch  200/1000, Loss: 0.036447
Epoch  400/1000, Loss: 0.006105
Epoch  600/1000, Loss: 0.002965
Epoch  800/1000, Loss: 0.001892
Epoch 1000/1000, Loss: 0.001377

--- After Training ---
Input | True Output | Predicted Output | Rounded Prediction
[0 0] |           0 |           0.0580 |                  0
[0 1] |           1 |           0.9745 |                  1
[1 0] |           1 |           0.9748 |                  1
[1 1] |           0 |           0.0291 |                  0

The output shows excellent convergence — our loss decreases steadily from 0.25 to just 0.0014 over 1000 epochs. More importantly, the final predictions demonstrate that our network has successfully learned the XOR logic: it outputs values close to 0 for inputs [0,0] and [1,1], and values close to 1 for inputs [0,1] and [1,0]. When rounded, these predictions perfectly match the expected XOR outputs, confirming that our modular library components work together seamlessly.

Excellent work! We've successfully completed the next major step in building our neural network library by modularizing our training components. We've organized our loss functions and optimizers into dedicated namespaces with proper header and source file separation, creating a clean separation of concerns that makes our code more maintainable, testable, and extensible. The successful training on the XOR problem validates that our modular components work together seamlessly, setting us up perfectly for the next phase of development.

Looking ahead, we have two exciting milestones remaining in our library-building journey. In our next lesson, we'll create a high-level Model orchestrator class that will provide an even cleaner interface for defining, training, and evaluating neural networks. After that, we'll put our completed library to the test on the California housing dataset, demonstrating its capabilities on real-world regression problems. But first, it's time to get hands-on! The upcoming practice section will give you the opportunity to extend and experiment with the modular components we've built, reinforcing your understanding through practical application.