Pillar /01 · Research

Research at AIRINA.

We work where applied AI is mathematical. The unit's current research sits at the intersection of topology, learning theory, and the problems African financial systems put on the table.

Output Papers, code, open benchmarks Collaborators AIMS · ACAS · university partners Funding model Grants + industry-paid engagements

Fundamental sciences

Underneath every technology, mathematics.

Quantum technologies, cybersecurity, artificial intelligence — mathematics remains the foundation of technological sovereignty and the marker of scientific excellence in francophone Africa. AIRINA also runs the ambitious "Mathematical Residency" program, which will invite and bring together leading researchers in the fundamental sciences.

Active research themes

Six lines, one direction.

/01

Topological Data Analysis

TDA studies the shape of data: which clusters connect, which loops persist, which voids resist filling as a scale parameter slides. The unit publishes on persistent homology, stability of persistence diagrams, multi-parameter persistence, and vectorization for downstream ML. Current work focuses on persistence-based features for financial time series and for graphs built from mobile-money transaction logs.

Code: GUDHI · Ripser · giotto-tda · cripser · Output: arXiv preprints, peer-reviewed papers, open Jupyter notebooks

/02

Symbolic and Interpretable AI

Production ML in regulated industries cannot answer the question regulators actually ask: why this decision, for this person. The unit works on interpretable-by-design models, decision-rule extraction, and neuro-symbolic methods that keep the inductive power of deep learning while exposing what was learned. We test against the realities of African credit data: sparse labels, semi-formal income, intermittent observations, and the regulatory constraints that make some standard tricks unusable.

Applied to: credit scoring, fraud detection, model risk management for BCEAO-supervised institutions

/03

Topological foundations of AI and Reinforcement Learning

Deep networks learn representations that live on manifolds. We are interested in what topological structure those representations have, when topology predicts generalization, and whether topological invariants can stabilize policy optimization in RL settings where the reward landscape is irregular. This line connects to the unit's mathematical-foundations work and informs the 2-week summer school on topological foundations of deep learning.

Related: manifold hypothesis · topological signatures of generalization · differentiable persistence

/04

TDA for robust machine learning

Adversarial robustness and out-of-distribution detection both have a topological flavor: small perturbations move points off the data manifold. We ask whether persistent homology gives signals that pure-norm-based methods miss, and whether topological regularizers reduce sensitivity to distribution shift without paying the usual robustness tax in accuracy. Work in progress; the corresponding training program comes online once the publications are in.

/05

Asymmetric topology and complexity

The director's pure-mathematics specialty: quasi-metric and bipolar metric spaces, fixed-point theory in asymmetric settings, and complexity-theoretic applications. This is the unit's deepest mathematical line. It connects to denotational semantics in theoretical computer science and to similarity learning in ML, where dissimilarity is naturally asymmetric (a customer is more like a salaried worker than the reverse, for credit-risk purposes).

Output: peer-reviewed math papers (Springer book series, journals in topology and analysis)

/06

Quantum-topological AI for finance

Quantum machine learning has been overhyped and under-delivered in roughly equal measure. We are studying where topological features and quantum-kernel methods together give measurable lift on financial problems where classical baselines plateau: regime detection in non-stationary series, volatility-surface modeling under heavy-tailed assumptions, and portfolio construction when correlations break down. The honest answer to "does it help?" is: sometimes, on specific problems, and we are working out which.

Stack: Qiskit · PennyLane · classical TDA pipeline · paired against strong classical baselines

How the unit works

What we promise, and what we do not.

Publish before claim

The unit's standard for "what we do" is what is on arXiv, in a peer-reviewed venue, or in a public repository. Not what is on a website. If a research thread has no public output yet, we say so.

Open the code

Methods, code, and evaluation benchmarks live in the AIRINA-Labs GitHub organization. We open the data when we can share it, and document what we cannot share and why.

Co-author

The unit has standing collaborations with AIMS Senegal, AIMS South Africa, AIMS Rwanda, and ACAS. We co-supervise master's and PhD students at partner universities, and write papers with them as authors, not contributors-in-the-acknowledgments.

Decline what we cannot teach

If a topic does not have a working practitioner in the unit, we either co-host with someone who does, or we do not run it. The catalog gets longer slowly, on purpose.

Collaborate with us

Three paths in.

Joint research

Write to contact@airina.africa with a one-page sketch of the question and the data you can share.

Graduate supervision

For master's or PhD work involving AIRINA, write through the director's academic page at gabayae.github.io.

Open source

Read or contribute at github.com/AIRINA-Labs.