Convolutional Neural Networks: CNN Math Explained
How do convolutional neural networks work? CNN math explained with kernels, padding, stride, pooling, receptive fields, and a full backpropagation example.
AI and Machine Learning Blog
Deep-dives into transformers, LLMs, and the math that runs underneath them — every post with full derivations and code you can run.
DeepSeek V4 Inside: One Token Through Every Block
How does DeepSeek V4 process one token? I follow the byte p in deepseek through CSA, HCA, mHC, MoE, and MTP on a toy width, with Flash-0731 sizes.
Looped Transformers Explained: Recurrent Depth and Astra
What is a looped transformer? How recurrent depth reuses layers, why Nanbeige 4.2 runs a 22-layer stack twice, and why that does not hide chain of thought.
Natural Language Inference Explained: Entailment in NLP
What is natural language inference (NLI)? How models label a premise and hypothesis as entailment, contradiction, or neutral on SNLI, MNLI, and BERT.
Build a Mini LLM from Scratch in NumPy: RoPE, GQA, SwiGLU
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.
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.
Numerical Gradient Checking: Debug Your Autograd Engine
What is numerical gradient checking? The central difference formula, why you never train with finite differences, and a grad checker that catches real bugs.
Transformer from Scratch: Forward Pass and Backprop by Hand
One full transformer training step worked by hand: embeddings, positional encoding, attention, layer norm, cross-entropy loss, backprop, and Adam.
DeepSeek V4 Explained: Long-Context Engineering and Math
A verification-first look at DeepSeek V4 claims, plus the real math behind sparse attention, KV-cache scaling, and long-context training stability.
How Attention Works in Transformers: Queries, Keys, Values
How does attention work in transformers? Queries, keys, values, the attention pattern, masking, and multi-head attention, with real GPT-3 parameter counts.
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.
Linear Algebra for Machine Learning: The Visual Intuition
Linear algebra for machine learning explained visually: vectors, matrices, dot products, determinants, eigenvectors, and the basis changes that make it click.
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 124M training loop that runs.
Backpropagation from Scratch: Build an Autograd Engine
How does backpropagation work? Build a working autograd engine from scratch in ~80 lines of Python: computation graphs, chain rule, reverse-mode autodiff.
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