Derived, not described
Probability, statistics, machine learning, deep learning, generative AI and game theory, derived rather than described. Every worked example is checkable by hand, and every claim is traced to the book it came from. This site is also where Kudos-1 is being built: a reasoning model trained to show its work.
Training
Structured, gamified tracks. Reach 90% mastery to unlock the next stage.
Reason about uncertainty precisely, then meet the central problem of learning from data: separating the error you can remove from the error you cannot.
5 modules · 540 XP
IntermediateDerive the workhorse supervised methods rather than merely calling them: least squares, logistic regression, shrinkage penalties, and tree ensembles.
4 modules · 500 XP
IntermediateDeciding what to do when another agent is deciding too: optimal play against an adversary, pruning the search, and equilibrium when interests only partly conflict.
2 modules · 260 XP
Blog
Deep, technically rigorous writing across 25+ knowledge domains.
Start here
New to the mathematics behind machine learning? Follow the guided path from first principles.
Probability Foundations · Probability from Zero: The Language of Uncertainty
One bimodal target, one Gaussian, and two directions of the same divergence. Minimising KL(P||Q) puts the Gaussian across both modes with almost no mass where the target actually lives; minimising KL(Q||P) puts it on one mode at a value of 0.6931 nats, which is ln 2 to four decimals and not a coincidence. Each fit is judged catastrophic by the other objective, 2.0976 against 15.2799.
Take the most likely state on each day and write them down in order, and you have a report the model assigns probability exactly zero: on a four-day machine-monitoring example the day-by-day answer is healthy, healthy, failed, failed, and healthy to failed is a transition that cannot occur. What the two questions actually are, why smoothing and Viterbi answer different ones, and what the 0.411 posterior on the best path means for anyone who has to act on it.
A variable that determines another with a correlation of exactly 0.0000000000, and a pair of features whose every pairwise mutual information with the target is exactly zero while the two together determine it completely. Univariate screening discards both, and the second case is the one that matters: the features it removes are removed because they matter.
Projects
Every project links to articles and learning tracks so you can build, read, and learn in one loop.
A decoder-only transformer built up one component at a time - tokenizer, embeddings, attention, blocks, pretraining loop - with no modelling code imported from a library.
A feed-forward network in NumPy with hand-derived backpropagation, validated against numerical gradients so the calculus is proven rather than trusted.
Least squares, logistic regression, ridge and lasso, and k-fold cross-validation implemented from their estimating equations and checked against scikit-learn.
Tools
Browser tools and packages you can use today, and the modular Kudos AI platform in active development.
Enter a prevalence, a sensitivity, and a false-positive rate to see what a positive test result is actually worth - as a probability and as whole people out of ten thousand.
Edit two distributions side by side and read off entropy, cross entropy, and KL divergence in bits, with the identity H(p, q) = H(p) + KL(p ‖ q) held on screen.
Move a decision threshold across an imbalanced population and watch precision, recall, F1, and the ROC point move with it - including the regime where accuracy looks excellent and the model is useless.
Freelance marketplace
Machine learning and data science freelancing, connected to the learning that gets you there. Clients post needs, professionals list profiles, and both sides reach out directly.
Roadmap
Built for longevity, not shortcuts. Here is what is shipping, building, and planned.
Articles, encyclopedia entries, papers and pioneers across mathematics, statistics, machine learning and AI, each grounded in the reference library.
Ordered lessons with XP, quizzes and a 90% pass threshold, from the probability foundations up to reinforcement learning and logic.
Client-side figures and calculators - entropy, base rates, classifier metrics, attention weights - each a live version of something an article derives.
Python cells that execute in the browser over numpy and scipy, so a derivation can be checked rather than believed.
A reasoning model for mathematics and machine learning that shows its work, cites what it invokes, and declines what it cannot justify.
Narrated Manim scenes for the results that are hard to see in prose. The scenes are rendered; publishing them is the remaining step.
Forum, member directory, freelancer profiles and a jobs board, so the site is a place to work with people rather than only to read.
More paths and lessons - optimisation, computer vision, and the classical-AI material the library can genuinely support.
Newsletter
New articles, tools, and learning paths, sent when there is something worth your time.
“The rare resource that respects both the mathematics and the practitioner. This is how technical education should feel.”
Start a learning path, explore the tools, or read a landmark-paper review.