Build a Mini LLM from Scratch in NumPy: RoPE, GQA, SwiGLU Visual Guide
How to build a mini LLM from scratch in NumPy — RoPE, GQA, QK-Norm, SwiGLU, tied embeddings, and a 3.87M chat companion with full architecture visuals.
Cross-Entropy Loss Explained: From Logits to Language Model Training
What is cross-entropy loss? Derive softmax + negative log-likelihood step by step, work a 3-class numeric example, see why MSE fails for classification, and build the loss GPT training actually uses.
Adam and AdamW Explained: How Modern LLMs Actually Update Their Weights
How does the Adam optimizer work? Derive momentum, RMSprop, and bias correction, see why AdamW decouples weight decay, and walk a one-parameter numeric update step by step.
Token Embeddings Explained: How LLMs Turn Token IDs Into Meaning Vectors
What is a token embedding? How LLMs map token IDs to learned vectors — the embedding matrix, gather lookup vs one-hot matmul, parameter counts, and a from-scratch NumPy implementation.
Positional Encoding Explained: How Transformers Learn Word Order
What is positional encoding in transformers? Why attention is order-blind, learned vs sinusoidal position embeddings, why we add instead of concatenate, and a from-scratch NumPy implementation.
Byte Pair Encoding (BPE) Explained: How GPT Tokenizers Turn Text Into Numbers
What is byte pair encoding (BPE)? Learn how GPT tokenizers split text into IDs — pretokenization, merge rules, byte-level vocab, and a from-scratch implementation you can actually debug.
Numerical Gradient Checking: How to Debug Your Autograd Engine Before Training GPT
What is numerical gradient checking? Learn the central difference formula, why you never train with finite differences, and how to build a grad checker that catches bugs in your autograd before LayerNorm or attention.
Transformer from Scratch: The Full Forward Pass, Backprop, and Weight Update Math
One full transformer training step worked by hand — embeddings, positional encoding, attention, layer norm, the encoder-decoder, cross-entropy loss, backprop, and Adam.
Build GPT-2 from Scratch in PyTorch: A Full Walkthrough
How to build GPT-2 from scratch in PyTorch — tokenization, causal self-attention, transformer blocks, weight tying, and a working training loop — implemented step by step and trained locally (124M parameters).
Backpropagation from Scratch: Build an Autograd Engine in Python
How does backpropagation work? Build a working autograd engine from scratch in ~80 lines of Python — computation graphs, the chain rule, and reverse-mode autodiff — the same core idea behind PyTorch's .backward().