One neuron
Follow two ticket features through weights, a score, and a probability. See why changing a routing threshold does not change the model.
Open lesson →Fundamentals of Machine Learning · All lessons
From a prediction to a better model
Learn how a small model calculates a prediction, measures error, and updates its weights. See how the same learning process applies to different prediction tasks. Each lesson includes a worked example, browser controls, and AI feedback on your explanation.
Loss functions
Measure how much probability reaches the right answer, then apply the same calculation to demonstrated response tokens in SFT.
Open lesson →Gradients and backpropagation
Find which direction a weight should move, and check the derivative by making a small change yourself.
Open lesson →Optimizers and training loops
Compare learning rates, repeat parameter updates, and find out why a training checkpoint needs more than weights.
Open lesson →Batches and shapes
Work out how one set of weights processes many requests, what shape comes out, and why batching can improve throughput.
Open lesson →Softmax and class probabilities
Convert competing class scores into probabilities without numerical overflow. Understand why the correct class is a training target, not a random draw.
Open lesson →Ready to apply this to language?
N-grams, embeddings, and transformers are now in Building Language Models from Scratch. This ML track ends with softmax; the language-model track is an optional next step.
Want to work through the code?
The shared NumPy examples run locally and show the calculations without a training framework. The slides and PowerPoint are optional references.