In this project, I developed a Feed Forward Neural Network from scratch using only fundamental mathematical principles, without relying on high-level machine learning libraries. By implementing the mathematical foundations of neural networks directly, I gained a deep understanding of how these models work at their core. The network was built to classify images from the MNIST dataset with impressive accuracy.
Instead of using abstracted APIs provided by libraries like TensorFlow or PyTorch, I implemented each component of the neural network myself: forward propagation, backpropagation, gradient descent, activation functions, and weight initialization. This approach required a thorough understanding of linear algebra, calculus, and optimization techniques.
The project also included the implementation of regularization techniques such as early stopping to prevent overfitting and ensure the model generalizes well to unseen data. By focusing on the fundamental mathematics, I was able to create a transparent neural network where every operation was explicitly defined and understandable.
Below is an interactive visualization of a simple feed-forward neural network with one hidden layer. You can start the training simulation to see how data flows through the network and how weights are updated during the learning process.
This project demonstrated that understanding the mathematical foundations of neural networks is crucial for effective implementation and optimization. By building a neural network from scratch, I gained deep insights into how these models learn and make predictions. The performance achieved on the MNIST dataset validates that even without using high-level libraries, a well-implemented neural network based on sound mathematical principles can achieve excellent results.
The knowledge gained from this project has been invaluable for my work with more complex models and has given me the ability to debug and optimize neural networks at a fundamental level. It also provides a strong foundation for understanding more advanced deep learning concepts and architectures.