How math powers AI: Inside large language models

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Large language models like GPT don’t just appear out of thin air. They’re built on solid mathematical foundations. Vectors, matrices, the transformer’s attention mechanism, there’s are fundamentals to each part of this, and you’ll need to link theory to code to work with them.

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What Math Do You Need to Know to Work with LLMs?

At the core of large language models lie several fundamental areas of mathematics that power their impressive language skills. If you want to work effectively with LLMs, grasping these key topics will help:

  • Linear Algebra: This is the backbone of neural networks. Concepts like vectors, matrices, and matrix multiplication underpin data representation and the calculations inside model layers. Embeddings, attention scores, and transformations all use linear algebra.

  • Probability and Statistics: Language models predict the next word based on probability distributions. Understanding concepts like conditional probability, likelihood, and distributions helps you interpret model behavior and loss functions.

  • Calculus: Specifically, multivariable calculus enables optimization. Gradients and derivatives tell the model how to adjust weights during training through backpropagation and gradient descent.

  • Optimization Theory: Knowing how optimization algorithms work helps you tune training to minimize errors efficiently.

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