Neural Networks & Backpropagation from Scratch

Neural Networks & Backpropagation from Scratch

What it is

A neural network is a mathematical system of interconnected layers that transforms input data into a prediction. At its core, it is a series of matrix multiplications followed by non-linear functions. Training this network involves "backpropagation," a process that calculates how much each individual weight in the network contributed to the total error of a prediction.

Why it matters

Modern AI frameworks like PyTorch and TensorFlow automate the complex calculus required to update model weights. However, relying solely on these abstractions hides the mechanics of gradient flow. Understanding the manual process allows engineers to debug vanishing or exploding gradients, optimize memory usage, and design custom architectures that are mathematically sound rather than based on trial and error.

Core concepts to master

• The Forward Pass: The process of moving input data through the network layers to produce an output.
• The Loss Function: A mathematical measure of the distance between the network's prediction and the actual target value.
• The Chain Rule: The fundamental calculus principle used to calculate the derivative of a complex function by multiplying the derivatives of its nested components.
• Gradient Descent: The optimization process of adjusting weights in the opposite direction of the gradient to minimize the loss.
• Autograd: The logic of tracking operations in a computational graph to automate the derivative calculations during the backward pass.

Common mistakes

• Incorrect Shape Alignment: Attempting matrix multiplication on tensors with incompatible dimensions.
• Forgetting the Non-linearity: Failing to apply an activation function (like ReLU or Sigmoid), which effectively collapses the network into a single linear regression regardless of depth.
• Gradient Mismanagement: Updating weights before the full backward pass is complete or failing to reset gradients between iterations.

Connection to the track

This concept serves as the foundation for the Applied ML & Model Engineering track. Once the manual mechanics of backpropagation are mastered, the learner can transition to high-level frameworks with a clear understanding of what the software is doing under the hood. This knowledge is prerequisite for studying advanced architectures like Transformers and Diffusion models, where gradient stability is critical.