This article explains how PyTorch uses Stochastic Gradient Descent (SGD) to train machine learning models by minimizing prediction error.The author introduces a simple linear regression model defined by the equation y = wx + b and demonstrates how the model learns the optimal weight and bias values through iterative updates.The discussion begins with the Mean Squared Error (MSE) loss function, which measures the difference between predicted and actual outputs.During training, the model calculates gradients of the loss with respect to the parameters and updates them using a learning rate.

The article provides a detailed explanation of forward propagation, where predictions and loss values are computed, and backward propagation, where gradients are calculated using the chain rule.

To illustrate the process, the author breaks down the computational graph used by PyTorch's automatic differentiation system and derives the mathematical formulas for the gradients of both the weight and bias parameters.A numerical example is then presented using a reference equation y = 2x + 10.A small dataset is divided into mini-batches, and SGD updates are manually calculated for each batch.The resulting gradients, losses, and parameter updates demonstrate how the model gradually adjusts its values toward the target relationship.Finally, the article verifies the manual calculations with a PyTorch implementation using the SGD optimizer and MSE loss function.

The Python code reproduces the same results, confirming the correctness of the mathematical derivations and illustrating how PyTorch automates gradient computation and parameter optimization during training.