Concept simulators
Poke it. Break it. Understand it.
Ten interactive models of the ideas the Olympiad tests. Each takes a few minutes and works on your phone.
Linear regression & loss
Drag points and fit a line. Watch MSE and MAE react to every outlier.
Gradient descent
Roll downhill on a loss curve. Find the learning rate that converges — and the one that explodes.
Overfitting & model complexity
Raise the polynomial degree and see training error fall while test error climbs.
k-nearest neighbours
Tap anywhere to classify a point. Change k and watch the vote — and the borders — shift.
Decision tree splits
Pick a feature and a threshold. Minimise Gini impurity to find the best split.
k-means clustering
Step through assign-and-update until the centroids stop moving.
Thresholds, precision & ROC
Slide the decision threshold. Trade precision for recall and trace the ROC curve.
Bayes' theorem
See why a 99% accurate test can still be wrong most of the time.
PageRank
Iterate the random surfer on a tiny web. Add links and change damping.
Image convolution
Slide a 3×3 kernel over pixels: blur, sharpen and detect edges by hand.
Sorting & searching
Race bubble, insertion and merge sort, then binary search a sorted shelf. Count every comparison.
Shortest paths
Find the quickest route across a city map, step by step, the way maps apps do.
Pixels & colour
Zoom into an image until it becomes numbers. Mix RGB, brighten and threshold it.
Chance experiments
Toss coins and roll dice thousands of times. Watch frequencies settle on the true chance.
Logistic regression
Bend a line into a probability. Move the boundary and watch the log loss react.
A tiny neural network
Wire up neurons and train them. Discover why one neuron can never learn XOR.
Word embeddings
Explore a map of word meanings. Measure cosine similarity and try analogies.
Temperature & sampling
Turn the temperature dial on a language model. Watch top-k and top-p reshape its choices.
Matrix transformations
Drag a 2×2 matrix and watch the plane stretch, flip and rotate. Area = determinant.
Fairness & thresholds
Two groups, one model. Tune thresholds and see what equal opportunity costs.