👉 At its core, an internal math model, like those used in large language models (LLMs), leverages a combination of linear algebra, calculus, and probability theory to process and generate text. Linear algebra is fundamental for representing words and sentences as high-dimensional vectors in a space called an embedding layer, where each dimension captures some aspect of meaning or context. Calculus, particularly gradient descent, is used during training to optimize these vectors by minimizing a loss function that measures the difference between predicted and actual outputs, effectively adjusting the model's parameters to better predict human language. Probability theory underpins the generation process, where models learn the statistical distribution of words and phrases from vast amounts of text data, allowing them to predict the next word in a sequence based on the preceding words. This interplay of mathematical concepts enables the model to understand, generate, and even reason about language in a way that mimics human cognitive processes.
