Machine learning, as applied in IX — Mission

Conceptual art, not a diagram: an original underground city of precision machines, inspired by the machine planet Ix in Frank Herbert’s Dune. It shows nothing about the IX crates or their code. Generated on the author’s machine with ComfyUI 0.36.0 and Z-Image-Turbo (Apache 2.0 licence), seed 20260927; one 36 × 20 pixel indicator panel was blurred to remove glyph-like marks. Prompt, workflow and timings.

How this course is tested

Every result in this course is printed by a program in code/machine-learning-ix: a Cargo project that depends on the IX crates at commit 490c395. .github/workflows/ml-ix-examples.yml runs cargo fmt, clippy, the unit tests and every example on Linux, Windows and macOS, and compares each output with the file in expected/. On Linux only, the same workflow recomputes the results that don’t depend on IX with numpy 2.4.2 and scikit-learn 1.8.0, and compares them too. The outputs in the lessons were captured with Rust 1.94 on Windows in September 2026, and are the same on the three systems.

Why I’m learning this

IX is a Rust workspace of machine learning and math algorithms that Claude Code can call as tools: k-means, decision trees, gradient descent, and about eighty crates more. When a tool answers “3 clusters, silhouette 0.50”, I want to know what was computed, whether it’s right, and what a better answer would look like.

The way I learn an algorithm is to write it. Each lesson writes an algorithm in a few dozen lines, runs it and IX’s version on the same data, and compares the two to the last printed digit. When they differ, one of the two is wrong, and finding out which is where I learn the most: this is what the journal records, lesson by lesson.

Who this course is for

You write C# or Java. You’re comfortable with high-school algebra: a straight line y = w·x + b, a sum Σ, a square root, a derivative. You don’t need to know any machine learning. You don’t need to know Rust well either: the code uses loops, closures and the matrices of ndarray, and the Rust course covers the rest.

If you’ve used ML.NET, Tribuo or Deeplearning4j, each lesson maps what you know to what IX does.

IX, ML.NET and Tribuo in one table

	ML.NET	Tribuo	IX
Language	C#, F#	Java	Rust
A data set	IDataView, typed columns	Dataset<T> of Example<T>	two ndarray matrices: Array2<f64> features, Array1 labels
A model	IEstimator.Fit returns an ITransformer	Trainer.train returns a Model	a struct with fit and predict (traits Regressor, Classifier, Clusterer)
Preprocessing	NormalizeMeanVariance, fitted like a model	TransformationMap	StandardScaler::fit, then transform
From an AI assistant	—	—	MCP tools such as ix_kmeans and ix_ml_pipeline

Sources: ML.NET tasks and trainers, Tribuo clustering, IX README.

The data

No downloaded data set: both files come from this repository, and data/extract.py rebuilds them from the CI history the DuckDB course exported on 2026-09-14 (runs.json and jobs.json) and from Git:

• builds.csv, for regression: the 65 successful builds of this site, in commit order, with the number of Markdown pages at that commit (18 to 289) and the seconds of the step that builds them (10 to 48). Does the build time grow with the number of pages?
• jobs.csv, for classification, clustering and everything after: 186 CI jobs, each with five timings in whole seconds (waiting in the queue, setting up the job, checking out the repository, cleaning up the checkout, completing the job) and the OS of the runner: 121 Ubuntu, 34 Windows, 31 macOS. Can the timings tell which OS ran a job?

IX, pinned

The course uses seven IX crates so far: ix-math (statistics, scaling, splitting, calculus), ix-supervised (regression, classification, metrics, cross-validation), ix-optimize (gradient descent, annealing, particle swarm), ix-unsupervised (k-means, DBSCAN, Gaussian mixtures, PCA), ix-ensemble (random forests, gradient boosting), ix-nn (layers, losses, attention) and ix-voicings (the silhouette score and the clustering of guitar voicings). Cargo.toml takes them from Git, pinned to one commit, as the Cargo reference describes:

ix-supervised = { git = "https://github.com/GuitarAlchemist/ix", rev = "490c39533627d296bf9f8f050e6fafc14d7a20c2" }

Every link to IX code in the lessons points to that commit, so the line numbers stay right when IX changes.

By the end of this course, I will be able to

• split data for training and testing, pick a baseline, and score a model with the metric that fits the question;
• fit a straight line two ways, by the closed form and by gradient descent, and say why descent diverges;
• train and compare logistic regression, k nearest neighbours and a decision tree, with cross-validation;
• group data without labels with k-means, DBSCAN and a Gaussian mixture, and judge the groups;
• reduce five dimensions to two, and say exactly what the reduction cost;
• combine weak models by bagging and by boosting, and know which of the two forgives a bad setting;
• differentiate a network by hand and check the answer against finite differences;
• choose an update rule, and recognize a run that diverged from one that converged;
• read an algorithm in IX, check it against a hand-written version and scikit-learn, and describe a difference precisely.

Outline

Lessons 1 to 9 are written. The rest is the plan, one lesson per family of algorithms IX implements, and each will be published with its code and its cross-check like the others.

#	Lesson	IX crates	If you know ML.NET
1	Data, features and evaluation	ix-math	IDataView, TrainTestSplit, RegressionMetrics
2	Linear regression and gradient descent	ix-supervised, ix-optimize	Ols, OnlineGradientDescent
3	Classification: logistic regression, k nearest neighbours, decision trees	ix-supervised	LbfgsLogisticRegression, FastTree, CrossValidate
4	Clustering: k-means, DBSCAN, Gaussian mixtures	ix-unsupervised, ix-voicings	KMeansTrainer
5	Principal components, and what a variance ratio means	ix-unsupervised	ProjectToPrincipalComponents
6	Ensembles: bagging, random forests and gradient boosting	ix-ensemble	FastForest, LightGbm
7	Neural networks, and finite differences as the judge	ix-nn	—
8	Optimization: descent, momentum, Adam, and searches without a gradient	ix-optimize, ix-math	—
9	The other reducers: MDS, kernel PCA, NMF, LDA, t-SNE	ix-unsupervised	—
10	Sequences: Markov chains, hidden Markov models and Viterbi	ix-graph	—
11	Counting without counting: Bloom filters, HyperLogLog, count-min, cuckoo	ix-probabilistic	—
12	Automatic differentiation: the Wengert tape	ix-autograd	—
13	Attention, layer normalization and a transformer block	ix-nn	—
14	Reinforcement learning: bandits and Q-learning	ix-rl	—
15	Signals: the Fourier transform, wavelets, filters and Kalman	ix-signal	—
16	Search: A*, Monte-Carlo tree search, local search	ix-search, ix-graph	—
17	Evolution: genetic algorithms, differential evolution, Pareto fronts	ix-evolution	—
18	Adversarial examples, poisoning and the defences	ix-adversarial	—
19	The shape of data: persistent homology	ix-topo, ix-manifold	—
20	On the GPU: matrix products, distances and k nearest neighbours in WGSL	ix-gpu	—
21	Pipelines end to end, and the MCP tools an assistant calls	ix-pipeline, ix-agent	MLContext
—	Every crate and every public function	the 80 with a public surface	—
—	Journal

Resources

• IX at commit 490c395, and its docs/ folder of tutorials
• scikit-learn user guide, the reference the cross-check uses, and its page on common pitfalls
• ML.NET documentation and Tribuo documentation
• An Introduction to Statistical Learning, by James, Witten, Hastie, Tibshirani and Taylor: free online, the book behind most of the formulas here
• Deep Learning, by Goodfellow, Bengio and Courville, for lessons 7, 8 and 12 to 14
• ndarray, the matrix crate IX and this course share