A note on the mathematics of LLMs

Getting into the mathematical center of LLMs can be a bit of work, but understanding their core principles reveals a lot about how the most powerful and widely used AIs today function. So, if you want to make these AI models and research them, the mathematics is very interesting:

• Foundations in linear algebra: The bedrock of LLMs lies in linear algebra, where matrices and vectors rule. Words are mapped to high-dimensional vectors, capturing their meanings and relationships within a vast semantic space. Each word is a point in a multi-dimensional space, with related words clustering closer together.
• Backpropagation and optimization: Training LLMs requires massive datasets and sophisticated optimization algorithms. One powerful tool is backpropagation, a mathematical technique that calculates the error gradient – how much each parameter in the model contributes to the overall deviation from the desired output. By iteratively adjusting...