The term "learning" creates a misleading impression when applied to large language models. Unlike human learning with understanding and reasoning, LLMs follow repetitive mathematical procedures billions of times, adjusting internal parameters to mimic text patterns. This distinction fundamentally changes how we should interpret their outputs.

At the foundation of LLM training lies the loss function - a scoring system that measures how wrong the model is. A good loss function must be specific, computable, and smooth. For LLMs, this means measuring next-word prediction accuracy using cross-entropy loss rather than simple accuracy counts. This mathematical choice explains why models can confidently reproduce false information from training data - they're rewarded for pattern matching, not truthfulness.

The training process relies on gradient descent, which adjusts billions of parameters by finding downhill directions in a high-dimensional landscape. Rather than evaluating all possible solutions (computationally impossible), the algorithm makes tiny, greedy adjustments based on local slopes. Modern LLMs use Stochastic Gradient Descent with random data batches, making training feasible with massive datasets. Each step is simple but billions are needed to reach optimal performance.