Most working ML practitioners — including talented self-taught engineers — skipped the math foundations, or carry only a shallow grasp of them. The cost shows up later: papers that can't be read past the abstract, models that fail in ways nobody can diagnose, design choices made by analogy rather than by reasoning.
AIRINA's research signature is mathematical depth. This 5-day intensive gives ML practitioners and engineers the working math they need to read modern papers, debug deep models, and reason about why models fail. Derivations on the board, working code in the notebook, and the same problem attacked from both sides — in equal measure.
Program Overview
Five days, full-day sessions, taught in Cotonou or live online — bilingual, cohort-paced. Mornings on the board: definitions, theorems, derivations. Afternoons in the notebook: implementing what was derived, breaking it on purpose, understanding why the math constrains what the code can do. The final day is a synthesis project: read a modern ML paper, derive its math, implement the core algorithm, defend it.
Program structure
- Day 1. Linear algebra for deep learning — vector spaces, eigendecompositions, SVD, matrix calculus, the math of gradient backpropagation.
- Day 2. Optimization — gradient descent and its variants (SGD, Adam, momentum), convexity, second-order methods, the loss landscape of neural networks.
- Day 3. Probability and information theory for ML — random variables, KL divergence, entropy, mutual information, variational methods.
- Day 4. Geometry of representations — the manifold hypothesis, low-dimensional embeddings, an introduction to geometric and topological methods. A bridge into AIRINA's TDA program.
- Day 5. Synthesis and project — read a modern ML paper, derive its math, implement the core algorithm. Final defense in front of AIRINA faculty.
Certificate
Successful completion — attendance plus the final defended project — earns an AIRINA Mathematical Foundations for Modern AI certificate, graded, with reviewer comments on the final defense. No defense, no certificate.
Learning Outcomes
By the end of the program, participants will be able to:
- Read the linear-algebra and matrix-calculus content of a modern ML paper without skipping equations — following derivations, recognizing standard tricks, spotting errors.
- Derive the backpropagation update for a custom architecture from first principles, and implement it from scratch in NumPy.
- Reason about the loss landscape of a neural network — convex vs non-convex regimes, saddle points, conditioning — and choose an optimizer accordingly with justification.
- Use probabilistic and information-theoretic vocabulary fluently — KL divergence, entropy, mutual information, ELBO — in the contexts where they appear in modern ML.
- Recognize when a problem has manifold structure, and apply geometric or topological methods (or know when not to).
- Take an unfamiliar ML paper, decompose its mathematical content into derivations and assumptions, and implement its core algorithm.
- Defend an implementation choice with reasoning rooted in the math, not in analogy to other papers.
Program curriculum (5 days)
- Vector spaces, bases, change of basis — revisited with neural-network eyes
- Eigendecompositions and the spectral theorem
- SVD — geometry, low-rank approximation, PCA as SVD
- Matrix calculus — Jacobians, gradients, the chain rule on matrices
- The math of backpropagation, derived from scratch
- Gradient descent — convergence under convexity, behavior off-convex
- SGD, momentum, Adam — what each one actually does to the iterates
- Second-order methods — Newton, quasi-Newton, why they're rare in deep learning
- The loss landscape of neural networks — saddle points, flat minima, the lottery-ticket picture
- Random variables, joint and conditional distributions, expectation in practice
- Entropy, cross-entropy, KL divergence — and what they actually measure
- Mutual information — the InfoNCE picture of contrastive learning
- Variational methods — the ELBO, reparameterization, the VAE derivation
- The manifold hypothesis — what it claims, what evidence supports it, what's overstated
- Low-dimensional embeddings — t-SNE, UMAP, isomap, and how they break
- Curvature, distance distortion, intrinsic dimension
- An introduction to geometric and topological methods — a bridge to AIRINA's TDA program
Each participant picks (or is assigned) a modern ML paper. The task: derive its math from scratch, implement the core algorithm in PyTorch or JAX, and present both the derivation and a working notebook to AIRINA faculty. Defense before the cohort. Written critique returned within a week.
Who Should Attend
This program is for ML practitioners and engineers who want the math foundations they skipped — not as decoration, but as a working tool.
- ML engineers and applied data scientists who built their working capability without formal math training, and feel the ceiling.
- Graduate students transitioning from computer science to machine learning — especially those moving toward research.
- Quantitative analysts (banking, insurance, trading) moving into AI roles, who need to bring modern ML into a discipline that already takes math seriously.
- Researchers at banks and microfinance institutions working on ML pipelines who want to deepen their understanding of what the pipelines actually do.
Prerequisites
- Mathematics. Undergraduate linear algebra and calculus — matrix multiplication, eigenvalues, partial derivatives, the chain rule. Basic probability — random variables, expectation, variance.
- Programming. Comfortable reading Python ML code — NumPy at the level of small matrix manipulations, PyTorch or TensorFlow at the level of training a simple model.
- Time commitment. Full days, 5 consecutive days. Pre-reading sent two weeks before the cohort starts.
Selection
For oversubscribed cohorts, applicants complete a one-question selection prompt drawn from their stated background — typically a short derivation, with the candidate's reasoning shown. Selection priority is given to applicants from the BCEAO zone and to underrepresented groups in technical fields.
Brochure
The detailed program brochure (PDF, EN/FR) is sent on request — including day-by-day curriculum, pre-reading list, paper-list for the Day 5 project, and the cohort calendar.
To receive the current brochure, write to contact@airina.africa with "Math & Modeling for Modern AI — brochure request" in the subject. The brochure is updated each cohort; we send the version current at the time of your request.