Don’t just vibe code. Form the vibe.
Master AI and machine learning from scratch so you can dictate the code — not just copy-paste it. Every result derived in full, then worked through with numbers small enough to check with a pen.
One continuous path from probability and linear algebra to transformers, fine-tuning and retrieval. Each of the 574 lessons names what it assumes, so you can always trace back to the piece you are missing.
No credit card. No sign-up. All 25 modules and 574 lessons are free — permanently.
A screening test catches 99% of true cases and is 95% specific. The disease affects 1 in 200 people. Your result is positive. What is the chance you are ill?
Translate the words into probabilities
prevalence P(D) = 1/200 = 0.005 sensitivity P(+|D) = 0.99 specificity P(−|¬D) = 0.95
Derive the two values not given directly
P(¬D) = 1 − P(D) = 1 − 0.005 = 0.995 P(+|¬D) = 1 − P(−|¬D) = 1 − 0.95 = 0.05
Total probability of a positive test
P(+) = P(+|D)P(D) + P(+|¬D)P(¬D)
= 0.99(0.005) + 0.05(0.995)
= 0.00495 + 0.04975 = 0.0547Apply Bayes' theorem
P(D|+) = P(+|D)P(D) / P(+)
= 0.00495 / 0.0547 = 0.09059.0%. Almost everyone guesses 95% or higher. The answer is dominated by the 0.995 of healthy people, because 5% of a large group outnumbers 99% of a tiny one — the same arithmetic that wrecks fraud and anomaly detection on imbalanced data.
an actual excerpt — every lesson ends like this
The topic list is not a matter of taste. It is cross-checked against university data-science curricula and graduate entrance syllabi, which is why the routinely skipped material — relational algebra, KKT conditions, the EM derivation, d-separation, second-order logic, Kalman filters — sits here alongside transformers and RAG.
See full coverageThree ways through
A beginner and a researcher need different routes through the same 522 lessons. Pick a track and the site sequences the modules for you — you can switch or ignore it entirely at any point.
Start from zero
Concept first, notation second. Every lesson opens with an intuition section and a diagram before any symbol appears, and the heavier derivations are collapsed out of your way.
For: New to the field, or returning after a long gap.
Ship working systems
Weighted towards code, metrics, failure modes and deployment. You get the maths you need to debug a model, plus the engineering the textbooks leave out.
For: Building models or LLM applications in industry.
Derive it yourself
Full derivations, proofs, theoretical framing and the papers behind each idea. Assumes you want the ELBO derived rather than quoted.
For: Preparing for GATE DA, postgraduate study or research work.
The curriculum
Ordered so every lesson only assumes what came before it. Search by topic — probability, SVM, LoRA, HNSW, Kalman — or filter by stage.
25 modules · 574 lessons
MODULE 00
How to use VibeFormer, how the three learning tracks differ, and the notation conventions used throughout.
5 lessons
MODULE 01
Vector spaces through SVD. The language every model in this curriculum is written in, built from first principles with worked numeric examples.
20 lessons
MODULE 02
Single- and multi-variable calculus, convexity, Lagrange multipliers and KKT — the machinery behind every training loop.
17 lessons
MODULE 03
Counting through Markov chains: the complete probability syllabus, with every distribution derived and applied to worked numeric problems.
28 lessons
MODULE 04
From descriptive summaries to hypothesis tests, estimation theory, experiment design and causal reasoning.
23 lessons
Python for data work, then the full DSA syllabus: complexity, linear structures, trees, hashing, sorting, searching and graph algorithms.
27 lessons
MODULE 06
Relational modelling, algebra, SQL, normalisation and indexing, then OLAP, dimensional schemas and the preprocessing pipeline.
23 lessons
MODULE 07
A principled approach to charts and exploratory analysis: what to plot, why it works perceptually, and how charts mislead.
9 lessons
MODULE 08
Linear and integer programming, duality, first-order and interior-point methods, metaheuristics and Bayesian optimisation.
27 lessons
MODULE 09
Strategic interaction from Nash equilibrium to mechanism design, Shapley values and the games hidden inside GANs and multi-agent systems.
25 lessons
MODULE 10
Propositional through higher-order logic, proof systems, decidability, and the modal, temporal, description and non-classical families.
30 lessons
MODULE 11
Search, adversarial games, planning, knowledge representation, and exact and approximate inference in Bayesian networks.
19 lessons
MODULE 12
The concepts every algorithm shares: risk minimisation, generalisation, the bias–variance trade-off, validation and metrics.
20 lessons
MODULE 13
Every supervised algorithm on the syllabus, each derived from its objective, traced on small numeric data, then coded from scratch.
25 lessons
MODULE 14
Clustering, dimensionality reduction, association rules and anomaly detection, each traced numerically and derived where it matters.
26 lessons
MODULE 15
Backpropagation derived and computed by hand, then optimisers, CNNs, RNNs, autoencoders, VAEs, GANs and diffusion models.
38 lessons
MODULE 16
Bandits and MDPs through to PPO: the full progression from tabular dynamic programming to deep policy-gradient methods.
26 lessons
MODULE 17
Tokenisation and n-grams through embeddings, attention and the complete transformer, with shapes traced end to end.
32 lessons
MODULE 18
How modern LLMs are built, aligned, decoded, evaluated, served and turned into agents — with the mechanics, not the hype.
32 lessons
MODULE 19
Spectral graph theory, PageRank and node embeddings through to GCN, GraphSAGE, GAT and graph transformers.
26 lessons
MODULE 20
Full fine-tuning, LoRA and QLoRA, quantisation, distributed training and data curation — with the maths behind each.
26 lessons
MODULE 21
Chunking, embeddings, vector indexes, hybrid retrieval, reranking and evaluation, through to agentic and graph RAG.
28 lessons
MODULE 22
Stationarity, ACF/PACF, the ARIMA family, exponential smoothing, state-space models and deep forecasting.
15 lessons
MODULE 23
Getting models into production and keeping them honest: versioning, monitoring, drift, fairness, privacy and governance.
16 lessons
MODULE 24
Formula sheets, banks of fully solved problems, GATE-DA style question sets and interview preparation.
11 lessons
What you get
Most tutorial sites give you a definition, one toy example and a code snippet. That is enough to recognise a term and not enough to use it, debug it, or answer a question about it under pressure.
Real typeset notation, not ASCII approximations. Every symbol is defined in a notation table before it is used.
Numbers small enough to verify with a pen. No step skipped, no 'it can be shown that'.
Decision boundaries, gradient descent paths, attention matrices, dendrograms and pipelines — drawn where the explanation needs them.
NumPy implementations first so the mechanism is visible, then scikit-learn, PyTorch and TensorFlow equivalents.
The mistakes that actually cost people: leakage, misread p-values, wrong metric under imbalance, template mismatch.
Practice at the end of every lesson, plus exam-style sets and a vault of fully worked problems.
Or jump anywhere — every lesson lists its prerequisites, so you can always trace back to the piece you are missing.