Mathematical foundations
How Machines Learn
Follow one mistake through vectors, loss, gradients, backpropagation, depth, vision, and generalization.
- Perceptron
- Gradient descent
- Backpropagation
- Convolution
AI Learning Lab
See what the model is doing.
Work through 26 interactive lessons on machine learning, language models, and AI agents. Each lesson pairs a focused explanation with a small experiment you can run in the browser.
- Paths
- 3 connected courses
- Lessons
- 26 interactive lessons
- Default runtime
- Runs in your browser
The learning loop
Make a prediction, then test it.
Each lesson focuses on one mechanism. You predict the result, run the example, and explain what the evidence shows.
- 01
Predict
Choose what you think will happen before you run the example.
- 02
Inspect
Change one variable and watch how the mechanism responds.
- 03
Explain
Compare the hand calculation with the trace shown by the lesson.
- 04
Verify
Answer a checkpoint and identify the evidence behind your answer.
The curriculum
Learn the parts, then connect them.
The three courses build on one another, with the explanation next to the experiment that demonstrates it.
Inside the transformer
How LLMs Work
Follow one sentence from text and tokens to contextual states, attention, and the next-token distribution.
- Tokenization
- Embeddings
- Attention
- Residual stream
Controlled execution
How AI Agents Work
Follow one bounded research goal through context, proposals, tools, policy, evidence, and evaluation.
- Context
- Tools
- Guardrails
- Evaluation
What the examples show
Every result says where it came from.
The core lessons use deterministic browser examples, so you can repeat each calculation. A pinned GPT-2 snapshot adds a real, downloadable model trace; every lesson still labels teaching data and live systems separately.
01
Exact hand calculation
Included02
Versioned model trace
Included03
Local AI comparison
Local edition onlyFree public beta
Try the Lab and tell me where it falls short.
The full 26-lesson curriculum is open while I test the explanations, experiments, and course flow with learners. You do not need an account to start.