Mathematics of LLMs Explained in Everyday Language, Understand How LLMs Think.
Course Description
Mathematics of Large Language Models (LLMs) Explained in Everyday Language
This course offers a guided journey through the mathematical foundations and transformative ideas behind large language models (LLMs), such as GPT-4—without requiring prior expertise in advanced mathematics or machine learning. Designed for intellectually curious learners, this series demystifies how machines “understand” and generate language, unpacking the key concepts behind today’s most powerful AI systems using everyday language and relatable analogies.
The first section of the course begins by tracing the conceptual evolution from early statistical models to modern deep learning architectures. We introduce foundational ideas like probability, tokenization, and embeddings, showing how language can be represented numerically and modeled computationally. Through vivid examples, we explore how early n-gram models evolved into systems that can grasp word meaning and context using high-dimensional vectors.
We then delve into the architecture that revolutionized the field: the transformer. You will learn how self-attention mechanisms allow models to understand relationships across entire sentences or documents, and how positional encoding helps them recognize word order. The lectures explain how these mechanisms work together mathematically to produce context-aware predictions that power everything from chatbots to search engines.
The course continues by examining how models learn through gradient descent, backpropagation, and advanced optimization techniques like Adam Optimizer. Concepts like entropy, temperature, and the balance between randomness and determinism are discussed to explain how LLMs make creative versus predictable choices.
The second major section explores the scaling of models—why size matters, and where it hits its limits. We investigate how techniques such as regularization, memory augmentation, and multimodality help models generalize and adapt. You’ll discover how LLMs are fine-tuned for specific tasks, how transfer learning and reinforcement learning from human feedback (RLHF) ensure alignment with human values, and how concepts like few-shot learning and meta-learning enable adaptability with minimal input.
Throughout the course, you will also engage with the deeper implications of this technology: from interpretability and ethical responsibility to the emerging role of LLMs in reshaping our relationship with intelligence and creativity.
By the end, you will not only understand how LLMs work, but also why they matter—and where they might take us next.
