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Research · Teaching · Consulting

Cotonou, Benin

I develop mathematical methods for the shape and structure of data, and I work in three modes: research, teaching, and consulting. PhD in topology (UCT), MSc from AUST. My current work applies topological and geometric methods to machine learning, AI safety, and quantum-classical computation, on problems that show up in African contexts — epidemic surveillance, credit risk for unbanked populations, energy demand forecasting. As Head of R&D at AIRINA Labs, I lead a team of over 10 researchers across six African countries; sector coverage includes banking, energy, insurance, IT, and retail. I am also co-founder of AI-Technipreneurs, a Benin-based firm with offices in Togo, building custom software, data and analytics platforms, and digital-transformation training for African enterprises. The research and the consulting feed each other; neither is a side activity.

Researcher

My mathematical foundations are in asymmetric topology and fixed point theory in generalized metric spaces. The applied work below pushes those ideas into machine learning, AI safety, and quantum-classical computation.

Topological foundations of AI & RL

Convergence and stability proofs for learning algorithms in quasi-metric and generalized metric spaces. The aim: contraction-based guarantees that survive when the standard Banach setting breaks down — asymmetric distances, irreversible transitions, non-Euclidean structure.

Plain version: when does an RL algorithm provably converge, and what changes if the environment isn't reversible?

Quasi-Metrics Fixed Points AI Safety

TDA for robust machine learning

Persistent homology and sheaf-theoretic features for anomaly detection and interpretable ML. Two application areas I work on: cybersecurity (network intrusion as a topological signal) and clinical/biomedical pipelines where the geometric structure of the data carries diagnostic information that statistical baselines miss.

Plain version: when statistical methods can't see the pattern, the shape of the data sometimes can.

Persistent Homology Anomaly Detection Cybersecurity

Asymmetric topology & complexity

Ordered structures and quasi-metrics as models for computation where the cost of moving forward differs from the cost of moving back. The applications I find interesting: complexity arguments where symmetry-breaking buys efficiency, and cryptographic primitives where it buys post-quantum hardness.

Plain version: forward and backward aren't the same — that asymmetry is a resource for both algorithms and cryptography.

Ordered Spaces Quantum-Resistant Complexity

Quantum-topological AI for finance

Topological methods at the interface of quantum computation and quantitative finance: market simulation on hybrid classical-quantum hardware, derivative pricing with topology-aware ansätze, and post-quantum cryptography using topological primitives.

Plain version: applying the topology side of the lab's work to derivative pricing, market simulation, and post-quantum crypto.

Quantum AI Derivatives Crypto Schemes

Co-author of The Shape of Data (No Starch Press). Currently at AIRINA Labs and ACAS. Previously at Quantum Leap Africa, North-West University, and IMSP.

Publications Google Scholar ORCID arXiv Propose a collaboration

Educator

I teach graduate courses, short courses, and industry workshops at AIMS centres, IMSP, and partner institutions. The range goes from abstract topology to applied deep learning. The constant across all of it is trying to make the math do real work in students' own problems, not stay on the blackboard. - Pure Mathematics: Topology, Real Analysis, Abstract Algebra, Functional Analysis, Fixed Point Theory - Applied Mathematics: Probability, Stochastic Modeling, Quantitative Finance, Mathematical Programming, Simulation - Data Science & ML: TDA, Geometric Deep Learning, Deep RL, NLP, MLOps, Cloud Analytics (Azure) Organizer of the Workshop on Computational Topology & Quantum Computing (WoComToQC). Regular instructor for Data Science Africa and Data Science Makers. Most of my mentees are early-career African scientists; I treat that part of the job as load-bearing, not extracurricular.

Full course catalogue Lecture notes & materials (38 courses)

Consultant

I advise research teams and startups on applying topological and geometric methods to actual data problems, and I take on fractional R&D engagements where a team needs a math-heavy capability they don't have in-house. - AI strategy & architecture: roadmaps, ML pipelines, cloud deployment (Azure, AWS), reproducible model evaluation and monitoring - TDA-powered analytics: shape analysis, anomaly detection, persistent homology, data mining, segmentation - Advanced analytics & modeling: stochastic modeling, NLP, discrete event simulation, optimization, predictive analytics, recommendation systems, dashboards (Power BI, Tableau) - Deep reinforcement learning: resource allocation, optimization, decision systems - ML workshops & training: custom programmes for universities, research centres, and companies

Consulting services Data-science portfolio (13 projects) Discuss your project

Mentor

I supervise theses at IMSP and AIMS, mentor early-career African researchers through ACAS, and stay in touch with bootcamp alumni after their cohort ends. This is the slow, long-horizon part of the work; it's also the part I value most. - Thesis supervision: MSc and PhD candidates at IMSP and the AIMS centres — topology-and-data, fixed-point theory, geometric ML, applied AI on African problems - Early-career research mentoring: through ACAS, for African scholars at the postdoc and early-faculty stage working in AI, mathematics, and quantitative research - Bootcamp & alumni follow-up: Bootcamp participants retain a peer Slack channel and 1-on-1 instructor access for 3 months after their cohort

ACAS — research mentoring ML & AI Bootcamp syllabus Thesis supervision inquiry

news

Jun 15, 2025	New blog post: LLMs Meet Topology — exploring how topological data analysis can improve large language model interpretability. Read it here.

latest posts

Aug 01, 2025	Persistence landscapes as ML features: a complete pipeline
Jul 01, 2025	Building AI research labs in Africa: lessons from AIRINA Labs
Jun 15, 2025	LLMs meet topology: can TDA improve language model interpretability?

selected publications

Book
The Shape of Data: Geometry-Based Machine Learning and Data Analysis in R

Colleen M. Farrelly and Yaé Ulrich Gaba

2024

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A comprehensive guide to geometry-based machine learning and data analysis, covering topological data analysis, persistent homology, and geometric methods with practical implementations in R.
@book{farrelly2024shape, title = {The Shape of Data: Geometry-Based Machine Learning and Data Analysis in {R}}, author = {Farrelly, Colleen M. and Gaba, Ya{\'e} Ulrich}, year = {2024}, publisher = {No Starch Press}, isbn = {9781718503083}, }
arXiv
Bellman Operator Convergence Enhancements in Reinforcement Learning Algorithms

David Krame Kadurha, Domini Jocema Leko Moutouo, and Yaé Ulrich Gaba

2025

Abs arXiv Bib

This paper reviews the topological groundwork for the study of reinforcement learning by focusing on the structure of state, action, and policy spaces, and illustrates how the Banach fixed-point theorem explains the convergence of RL algorithms. Alternative Bellman operator formulations are explored and tested on standard environments including MountainCar, CartPole, and Acrobot.
@article{kadurha2025bellman, title = {Bellman Operator Convergence Enhancements in Reinforcement Learning Algorithms}, author = {Kadurha, David Krame and Moutouo, Domini Jocema Leko and Gaba, Ya{\'e} Ulrich}, year = {2025}, archiveprefix = {arXiv}, primaryclass = {cs.LG}, }
arXiv
Topological Foundations of Reinforcement Learning

David Krame Kadurha and Yaé Ulrich Gaba

2024

Abs arXiv Bib

This work serves as a foundation for deep studies of the topology of state, action, and policy spaces in reinforcement learning. It connects the Banach fixed point theorem to RL algorithm convergence and demonstrates how mathematical insights from topology can inform more efficient RL algorithm design.
@article{kadurha2024topological, title = {Topological Foundations of Reinforcement Learning}, author = {Kadurha, David Krame and Gaba, Ya{\'e} Ulrich}, year = {2024}, archiveprefix = {arXiv}, primaryclass = {cs.LG}, }
TopAppl
Splitting metrics by T_0-quasi-metrics

Yaé Ulrich Gaba and Hans-Peter A. Künzi

Topology and its Applications, 2015

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We investigate under which conditions a metric can be produced by a T0-quasi-metric. We introduce the notion of a splitting quasi-metric and study its properties in detail, establishing connections between the theory of quasi-metric spaces and classical metric space theory.
@article{gaba2015splitting, title = {Splitting metrics by {$T_0$}-quasi-metrics}, author = {Gaba, Ya{\'e} Ulrich and K{\"u}nzi, Hans-Peter A.}, journal = {Topology and its Applications}, volume = {193}, pages = {84--96}, year = {2015}, doi = {10.1016/j.topol.2015.06.003}, }
TopAppl
Partially ordered metric spaces produced by T_0-quasi-metrics

Yaé Ulrich Gaba and Hans-Peter A. Künzi

Topology and its Applications, 2016

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We study partially ordered metric spaces that are produced by T0-quasi-metrics. We establish conditions under which a partial order on a metric space can be induced by a T0-quasi-metric compatible with the metric, and investigate the topological properties of such structures.
@article{gaba2016partially, title = {Partially ordered metric spaces produced by {$T_0$}-quasi-metrics}, author = {Gaba, Ya{\'e} Ulrich and K{\"u}nzi, Hans-Peter A.}, journal = {Topology and its Applications}, volume = {202}, pages = {366--383}, year = {2016}, doi = {10.1016/j.topol.2016.01.028}, }
JMath
Startpoints and (α, γ)-Contractions in Quasi-Pseudometric Spaces

Yaé Ulrich Gaba

Journal of Mathematics, 2014

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Introduces the concept of startpoint and endpoint for multivalued maps defined on a quasi-pseudometric space and investigates the relation between these new concepts and the existence of fixed points.
@article{gaba2014startpoints, title = {Startpoints and ($\alpha$, $\gamma$)-Contractions in Quasi-Pseudometric Spaces}, author = {Gaba, Ya{\'e} Ulrich}, journal = {Journal of Mathematics}, year = {2014}, publisher = {Wiley/Hindawi}, doi = {10.1155/2014/709253}, }