Articles

Interactive lessons with live demos that run in the page.

14 lessons · every demo runs locally

Why Softmax Needs Temperature

A network's raw scores are not probabilities. Temperature is the dial that decides how much the differences between them matter.

1 interactive demo

Linear Algebra8 min

Eigenvectors You Can See

Most arrows change direction when a matrix acts on them. A few stay on their own line — and those are the ones worth finding.

1 interactive demo

Optimization9 min

Gradient Descent from MSE to Logistic

One update rule, two losses. Watch the same recipe fit a line by squared error and by cross-entropy.

1 interactive demo

ML Fundamentals7 min

K-Means: Assignment to Convergence

Two alternating steps, one stubborn goal. Step through the loop and watch the total spread only ever fall.

1 interactive demo

Deep Learning8 min

Attention Is a Heatmap

Strip away the code and attention is a table of dot products, a softmax on every row, and a weighted average of values.

1 interactive demo

NLP7 min

Tokenization: Byte-Pair Encoding

Before a model reads a word, it reads a merge list. BPE decides how text becomes tokens — and tokens decide cost, context, and where a model fails.

1 interactive demo

NLP8 min

Embeddings & Cosine Similarity

A good embedding puts dog near puppy and far from semiconductor. Cosine similarity is how that claim gets measured.

1 interactive demo

Deep Learning9 min

Quantization: INT8 to FP8

Fewer bits per weight means less memory and faster decoding. The price is a rounding error you can steer.

1 interactive demo

Deep Learning11 min

KV Cache & FlashAttention

Attention costs time that grows with the square of the sequence and memory that never shrinks. The KV cache is why long context costs what it costs — and FlashAttention is why it fits.

1 interactive demo

NLP10 min

RAG: From Chunks to Citations

Retrieval-augmented generation is a pipeline, not a prompt. Most failures happen before the model reads a single token.

1 interactive demo

Reinforcement Learning11 min

Post-Training: RLHF → DPO → GRPO

Pretraining teaches the model language. Post-training teaches it behavior — and by 2026 the human preference label gave way to the reward a program can check.

1 interactive demo

Linear Algebra8 min

PCA & SVD in Practice

The eigenvector article ends at Av = λv. This one starts there: project the cloud, keep the top axes, rebuild — and account for every bit of what you threw away.

1 interactive demo

ML Fundamentals7 min

Calibration & Uncertainty

A model that says 90% should be right 90% of the time. Modern networks are not — and one number fitted on held-out data fixes most of the gap.

1 interactive demo

Deep Learning9 min

LoRA / PEFT: Low-Rank Fine-Tuning

Freeze the model, train a small rank-16 shadow. In 2026 that shadow is most fine-tuning — and at serving time it disappears into the weights.

1 interactive demo