👨‍🏫 Tutorial The Math of Large Language Models Transformer Architectures

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The Math of Large Language Models Transformer Architectures
Published 6/2026
Created by Bhushan S
MP4 | Video: h264, 1920x1080 | Audio: AAC, 44.1 KHz, 2 Ch
Level: Intermediate | Genre: eLearning | Language: English | Duration: 48 Lectures ( 3h 23m ) | Size: 2.6 GB
A deep mathematical dive into how Transformers route tokens, compute attention matrices, and optimize memory dur...

What you'll learn
Master the core principles of Self-Attention Mechanics.
Deconstruct the architecture and tradeoffs of Multi-Query Attention (MQA).
Analyze the design patterns governing KV Caching.
Build a deep mental model of Positional Encodings (RoPE) at scale.
Requirements
No coding experience is required. We focus entirely on system design and core theoretical concepts.
A basic interest in technology systems, algorithms, or computer science architecture.
No special software or local development environment setup is needed.
Description
"This course contains the use of artificial intelligence."
Build a Deep Mathematical Understanding of Modern LLMs - Without Writing a Single Line of Code
Large Language Models are transforming the future of AI, but understandingwhy they work is far more valuable than simply learning how to use them. This course is designed to help you master the mathematical foundations and architectural principles behind Transformer-based models without requiring any programming experience.
Rather than focusing on coding frameworks or implementation details, you'll develop the conceptual thinking needed to understand how modern language models process information, scale efficiently, and make intelligent predictions.
Whether you're an AI professional, researcher, student, or technology leader, this course provides the theoretical foundation required to confidently understand and discuss modern LLM architectures.
What you'll learn
Build a strong mathematical foundation in linear algebra, vectors, matrices, probability, optimization, and neural network fundamentals.
Understand how Transformer architectures revolutionized Natural Language Processing.
Master the mathematics behind Self-Attention and why it enables context-aware language understanding.
Learn how Multi-Query Attention (MQA) improves inference efficiency while reducing computational costs.
Explore KV Caching and understand how modern LLMs generate text efficiently.
Discover Rotary Positional Embeddings (RoPE) and other positional encoding techniques.
Analyze computational complexity, memory Requirements, and scalability trade-offs in Transformer architectures.
Understand embedding spaces, token representations, and semantic relationships.
Explore gradient propagation, optimization strategies, and training dynamics.
Study reinforcement learning concepts that contribute to modern language model alignment.
Learn Explainable AI principles, model auditing, and responsible AI governance.
Identify common architectural anti-patterns and understand best practices for designing scalable AI systems.
Course Curriculum
Module 1: Mathematical Foundations
Linear Algebra for Deep Learning
Matrix Operations and Vector Spaces
Probability and Statistics
Calculus for Optimization
Gradient Descent Fundamentals
Module 2: Neural Networks
Artificial Neural Networks
Forward and Backward Propagation
Activation Functions
Loss Functions
Optimization Algorithms
Module 3: Transformer Architecture
Evolution from RNNs to Transformers
Encoder-Decoder Architecture
Tokenization Concepts
Embedding Representations
Transformer Pipeline
Module 4: Self-Attention Mathematics
Query, Key, and Value Vectors
Scaled Dot-Product Attention
Attention Weight Calculations
Multi-Head Attention
Mathematical Intuition Behind Attention
Module 5: Multi-Query Attention (MQA)
Motivation Behind MQA
Computational Advantages
Memory Optimization
Performance Trade-offs
Practical Design Considerations
Module 6: KV Caching
Key-Value Memory Mechanism
Autoregressive Inference
Cache Management
Latency Optimization
Real-World LLM Inference
Module 7: Positional Encoding
Why Position Information Matters
Sinusoidal Positional Encoding
Rotary Positional Embeddings (RoPE)
Relative Position Encoding
Long-Context Modeling
Module 8: Architecture Trade-offs
Compute vs Memory
Latency vs Accuracy
Model Scaling Laws
Context Window Considerations
Efficient Transformer Design
Module 9: NLP and Embedding Geometry
Word Embeddings
Semantic Vector Spaces
Similarity Metrics
Contextual Representations
Language Understanding
Module 10: Advanced AI Concepts
Reinforcement Learning Fundamentals
Explainable AI
Model Auditing
Ethical AI Principles
Future Directions of Large Language Models
Why Take This Course?
No programming required
Strong emphasis on mathematical intuition
Clear visual and conceptual explanations
Covers the core building blocks of modern LLMs
Ideal preparation for advanced AI and Machine Learning studies
Designed for long-term conceptual understanding rather than memorizing implementation details
Who this course is for
AI Engineers, Software Architects, Research Students
Homepage

https://www.udemy.com/course/the-math-of-large-language-models-transformer-architectures

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