GPT Math Explained: The Full Forward Pass Beyond Attention
How does GPT math work end to end? One training step from token IDs through Q/K/V, attention, MLP, logits, cross-entropy loss, backprop, and AdamW.
Cross-Entropy Loss Explained: From Logits to LLM Training
What is cross-entropy loss? Derive softmax and negative log-likelihood, work a 3-class example, and see why MSE fails for language model classification.
Adam and AdamW Explained: How LLMs Update Their Weights
How does the Adam optimizer work? Derive momentum, RMSprop and bias correction, see why AdamW decouples weight decay, and walk a numeric update by hand.
Token Embeddings Explained: How LLMs Turn IDs Into Vectors
What is a token embedding? How LLMs map token IDs to learned vectors: the embedding matrix, gather vs one-hot matmul, and a from-scratch NumPy build.
Positional Encoding Explained: How Transformers Learn Order
What is positional encoding in transformers? Why attention is order-blind, learned vs sinusoidal embeddings, and a from-scratch NumPy implementation.
Byte Pair Encoding (BPE) Explained: How GPT Tokenizers Work
What is byte pair encoding (BPE)? How GPT tokenizers turn text into IDs: pretokenization, merge rules, byte-level vocab, and a from-scratch build.
How GPT Actually Works: A Visual Guide to Transformers
How does a GPT actually work? A visual walkthrough of transformers: tokens, word embeddings, dot products, softmax and temperature, with real GPT-3 numbers.