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Research · Teaching · Consulting

Cotonou, Benin

I develop mathematical methods for understanding the shape and structure of data, and I make them available as research, teaching, and consulting. With a PhD in Topology from UCT and an MSc from AUST, my work sits at the frontier where topology, geometry, and machine learning meet. My mission: bringing world-class mathematical AI to Africa’s hardest problems, from epidemic surveillance to credit scoring for the unbanked. As Head of R&D at a technology startup, I lead a team of 5 researchers bridging methodological innovation and operational deployment across 6 African countries, with cross-industry experience in banking, energy, insurance, IT, and retail. I’m a researcher whose knowledge takes three forms, not a consultant who happens to publish.

Researcher

I develop and publish mathematical methods for understanding the shape and structure of data. My foundations are in asymmetric topology and fixed point theory in generalized metric spaces; my current work applies these ideas to machine learning, AI safety, and quantum-classical computation.

Topological foundations of AI & RL

Rigorous convergence, stability, and safety proofs for learning algorithms via quasi-metric and generalized metric spaces, building predictable, resilient autonomous agents with verifiable guarantees.

In plain terms: we prove mathematically that AI algorithms converge reliably and remain stable — so autonomous systems behave as intended.

Quasi-Metrics Fixed Points AI Safety

TDA for robust machine learning

Persistent homology and sheaf theory for feature extraction and anomaly detection, with applications in cybersecurity, network intrusion detection, and interpretable, privacy-preserving AI.

In plain terms: we use the "shape" of data to detect anomalies, intrusions, and hidden patterns that traditional statistics miss.

Persistent Homology Anomaly Detection Cybersecurity

Asymmetric topology & complexity

Ordered structures and quasi-metrics to model non-commutative, time-irreversible computation, addressing algorithmic efficiency, quantum-resistant security, and quantum-inspired algorithms.

In plain terms: we model irreversible processes to strengthen algorithmic security and build faster, quantum-resistant systems.

Ordered Spaces Quantum-Resistant Complexity

Quantum-topological AI for finance

Topological principles for quantum computational AI in finance: quantum-topological neural networks for market simulation, derivative pricing on hybrid hardware, and topology-based cryptographic schemes.

In plain terms: we combine topology and quantum computing to build next-generation financial models and cryptographic tools.

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 workshops that make rigorous mathematical ideas accessible to scientists, engineers, and ML practitioners, from abstract topology to hands-on deep learning. - 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. Committed to mentoring the next generation of African scientists.

Full course catalogue Lecture notes & materials (38 courses)

Consultant

I advise research teams, startups, and organizations on how to apply topological and geometric methods to real problems, and serve as a fractional R&D partner for teams building at the frontier. - 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

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}, }