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Interactive AI tools & visualizers
Each tool turns one AI concept into something you can poke, drag, and actually understand — no math wall, no signup. They're the same demos woven through every Math to Machine lesson.
Foundations
Gradient descent, visualized
A free interactive gradient descent visualizer. Press Step and watch the algorithm roll downhill to the minimum — change the learning rate and see it overshoot or crawl.
Open the tool →The derivative, visualized
A free interactive derivative demo. Drag a point along a curve and shrink the gap to watch the secant line close in on the tangent — the limit that defines the derivative.
Open the tool →Eigenvalues & eigenvectors, visualized
A free interactive eigenvector visualizer. Drag a 2×2 matrix and watch which directions it only stretches (the eigenvectors) and by how much (the eigenvalues) — the maths behind PCA and more.
Open the tool →Singular Value Decomposition, visualized
A free interactive singular value decomposition (SVD) demo. Drag a 2×2 matrix and watch the unit circle become an ellipse whose semi-axes are the singular values — rotate, stretch, rotate.
Open the tool →The normal distribution, visualized
A free interactive normal distribution (bell curve) demo. Slide the mean and standard deviation and see the 68–95–99.7 rule light up — the distribution behind averages, noise, and normalization.
Open the tool →Bayes' theorem, visualized
A free interactive Bayes' theorem demo and calculator. Slide the prevalence, sensitivity, and false-positive rate and watch the posterior probability update — the base-rate fallacy made visible.
Open the tool →Classical ML
K-means clustering, visualized
A free interactive k-means demo. Step through assign and update and watch messy starting centroids snap to the real clusters — unsupervised learning made visual.
Open the tool →Linear regression, by hand
A free interactive linear regression demo. Drag the line to fit the points, watch the error shrink, then snap to the mathematically best fit — the first real ML model.
Open the tool →Principal Component Analysis, visualized
A free interactive Principal Component Analysis demo. Rotate an axis through a data cloud and watch the variance of the projections peak along the first principal component.
Open the tool →Deep Learning
Backpropagation, made visual
A free visual explainer for backpropagation: values flow forward through the network, gradients flow back through the chain rule. See the one idea that makes deep learning work.
Open the tool →The attention mechanism, visualized
A free interactive attention visualizer. Click a token and see how much it draws from every other token — the mechanism behind transformers, GPT, and every modern LLM.
Open the tool →A single neuron, made draggable
A free interactive demo of a single artificial neuron: inputs × weights + bias → activation. Drag the values and see the atom that every neural network is built from.
Open the tool →Convolution, visualized
A free interactive convolution demo. Slide a kernel across an image grid and watch the feature map light up — exactly how convolutional neural networks detect edges and shapes.
Open the tool →Generative AI
Word embeddings, visualized
A free interactive embeddings demo. Click a word and rank the rest by meaning — the semantic geometry behind search, recommendations, and every RAG system.
Open the tool →How an LLM predicts the next token
A free interactive demo of next-token prediction. See the probability bar chart over candidate words and slide the temperature from careful to wild — how ChatGPT actually generates text.
Open the tool →Tokenization, visualized
A free interactive tokenizer demo. Watch text split into the tokens a language model actually reads — and understand why models think, and bill, per token.
Open the tool →Diffusion models, visualized
A free interactive diffusion demo. Scrub an image into pure noise and back — the forward-and-reverse process behind Stable Diffusion, DALL·E, and Midjourney.
Open the tool →These are just the demos. The lessons wrap them in real teaching.
Every one of the 234 lessons builds a concept like these with predict-then-reveal teaching, worked examples, and a hands-on build. The first five are free.