Start from zero
Novice track
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.
Best if: New to the field, or returning after a long gap.
- 01
Start Here
How to use VibeFormer, how the three learning tracks differ, and the notation conventions used throughout.
5 of 5 lessons on this track
- 02
Linear Algebra
Vector spaces through SVD. The language every model in this curriculum is written in, built from first principles with worked numeric examples.
16 of 20 lessons on this track
- Vectors and Vector Spaces
- Subspaces, Span and Basis
- Linear Independence, Rank and Nullity
- Matrices and Their Operations
- Special Matrices
- Systems of Linear Equations
+10 more
- 03
Probability
Counting through Markov chains: the complete probability syllabus, with every distribution derived and applied to worked numeric problems.
19 of 28 lessons on this track
- Counting, Permutations and Combinationsready
- Inclusion–Exclusion and Pigeonholeready
- Sample Spaces and the Axioms of Probabilityready
- Events, Independence and Mutual Exclusivityready
- Joint, Marginal and Conditional Probabilityready
- The Law of Total Probabilityready
+13 more
- 04
Statistics and Inference
From descriptive summaries to hypothesis tests, estimation theory, experiment design and causal reasoning.
15 of 23 lessons on this track
- Descriptive Statistics
- Skewness and Kurtosis
- Populations, Samples and Sampling Methods
- Sampling Distributions and Standard Error
- Maximum Likelihood Estimation
- Confidence Intervals
+9 more
- 05
Programming, Data Structures and Algorithms
Python for data work, then the full DSA syllabus: complexity, linear structures, trees, hashing, sorting, searching and graph algorithms.
21 of 27 lessons on this track
+15 more
- 06
Data Visualisation and EDA
A principled approach to charts and exploratory analysis: what to plot, why it works perceptually, and how charts mislead.
9 of 9 lessons on this track
- The Grammar of Graphics
- Choosing the Right Chart
- Visualising Distributions
- Visualising Relationships
- Multivariate Visualisation
- Time Series and Geospatial Charts
+3 more
- 07
Machine Learning Foundations
The concepts every algorithm shares: risk minimisation, generalisation, the bias–variance trade-off, validation and metrics.
15 of 20 lessons on this track
- What Machine Learning Actually Isready
- Formulating a Learning Problemready
- Generalisation, Overfitting and Underfittingready
- The Bias–Variance Trade-offready
- Train, Validation and Test Splitsready
- Cross-Validationready
+9 more
- 08
Supervised Learning
Every supervised algorithm on the syllabus, each derived from its objective, traced on small numeric data, then coded from scratch.
18 of 25 lessons on this track
- Simple Linear Regression
- Multiple Linear Regression
- Regression Assumptions and Diagnostics
- Polynomial and Basis Expansion Regression
- Ridge Regression
- Logistic Regression
+12 more
- 09
Unsupervised Learning
Clustering, dimensionality reduction, association rules and anomaly detection, each traced numerically and derived where it matters.
13 of 26 lessons on this track
- The Unsupervised Landscape
- Distance and Similarity Measures
- k-Means Clustering
- Initialisation and Choosing k
- k-Medoids and PAM
- Agglomerative Hierarchical Clustering
+7 more
- 10
Neural Networks and Deep Learning
Backpropagation derived and computed by hand, then optimisers, CNNs, RNNs, autoencoders, VAEs, GANs and diffusion models.
28 of 38 lessons on this track
- From Perceptron to Deep Networks
- Forward Propagation
- Backpropagation
- Backpropagation: A Complete Numeric Example
- Activation Functions
- Loss Functions
+22 more
- 11
Natural Language Processing
Tokenisation and n-grams through embeddings, attention and the complete transformer, with shapes traced end to end.
25 of 32 lessons on this track
- The NLP Pipeline
- Text Normalisation
- Regular Expressions for Text
- Stemming and Lemmatisation
- n-Gram Language Models
- Perplexity
+19 more
- 12
Large Language Models
How modern LLMs are built, aligned, decoded, evaluated, served and turned into agents — with the mechanics, not the hype.
18 of 32 lessons on this track
- What an LLM Actually Is
- Decoder-Only Architecture in Detail
- Pretraining Objectives
- Scaling Laws
- Context Windows
- Decoding Strategies
+12 more