LLM
Published on: September 10, 2025
Tags: #llm #ai #mathematics
The Core Process: How an LLM Generates Text
graph TD subgraph "User Input" A[Raw Text: The cat sat on the...] end subgraph "LLM Core Processing" B(Tokenization) --> C(Embeddings); subgraph "Inside the Transformer Block" direction TB D["Input Embeddings
+
Positional Encoding
(to understand word order)"]; E["Self-Attention Mechanism
(weighs word importance & context)"]; F["Neural Network Layers
(for deep processing)"]; D --> E --> F; end C --> D; F --> G(Probability Calculation); end subgraph "Model Output" G --> H[Output Token: mat]; end A --> B; style A fill:#f9f,stroke:#333,stroke-width:2px style H fill:#ccf,stroke:#333,stroke-width:2px
The Learning Cycle: How an LLM Improves
graph TD A(Start With a Base Model) --> B["Make a Prediction"]; B --> C["Calculate Error
(Cost Function)"]; C --> D["Adjust Model Parameters
(Gradient Descent &
Backpropagation)"]; D --> B; subgraph "Guiding the Learning Process" E(Regularization Techniques
e.g., Dropout) -- Prevents Overfitting --> D; F(Optimizers
e.g., Adam) -- Improves Efficiency --> D; end style A fill:#f9f,stroke:#333,stroke-width:2px
From General Knowledge to Aligned Specialist
graph TD subgraph "Phase 1: Foundation Building" A["Pretraining
Model learns general
language patterns,
grammar, and facts from a
massive, diverse dataset
(the entire internet, books,
etc.)."]; end subgraph "Phase 2: Specialization" B["Fine-Tuning/Transfer Learning
The foundational model is
adapted for a specific task
(e.g., medical analysis,
legal summaries) using a
smaller, domain-specific
dataset."]; end subgraph "Phase 3: Alignment" C["Reinforcement Learning
from Human Feedback
(RLHF)
Humans rank model outputs
for helpfulness and safety.
This feedback trains the
model to align its behavior
with human values and
expectations."]; end subgraph "Result" D["A Specialized,
Helpful, and Aligned LLM
(e.g., ChatGPT, Gemini)"]; end A --> B --> C --> D;
Timeline of Key Breakthroughs
timeline 1940s-1960s : Early Foundations : Claude Shannon's Information Theory (Language as probability) : ELIZA Chatbot (Pattern matching) 1980s : Statistical Approaches : N-gram Models (Predicting words based on the last few words) 2013 : The Meaning Revolution : Word2Vec (Representing word meaning as vectors/embeddings) 2017 : The Architecture Breakthrough : "Attention Is All You Need" paper introduces the Transformer Architecture 2020s-Present : The Age of Scale & Multimodality : Massive models (GPT series, Gemini) with trillions of parameters : Integration of text, images, and audio (Multimodality)