Ten weeks of manifold geometry are now archived—next we turn toward singular learning theory and its machine learning implications.
Phase 1 consolidated manifold learning foundations; Phase 2 brings singular learning theory and new ML experiments.
We navigated geometry, Laplace–Beltrami analysis, neighbourhood selection, and intrinsic dimension estimation with weekly notes and mind maps.
We are aligning algebraic geometry perspectives with singular learning theory to understand model complexity and real-world ML behaviour.
BatON is a research-driven study group committed to understanding manifold learning together.
The BatON Research Group unites three mathematician candidates and a mathematician at different stages of their journeys. We study advanced topics side by side, exchange insights, and support one another as we grow into mathematicians.
Three close friends met as undergraduates at Galatasaray University in Istanbul. Today they reunite to explore manifold learning together.
We design each week around collaboration, clarity, and mutual support.
Each week one member charts a specific topic, prepares resources, and presents it to the group.
We break manifold learning into manageable themes—geometry, algorithms, and applications—to build shared intuition.
Discussion, open questions, and collective notes help us turn individual study into collective understanding.
Phase 2 links algebraic geometry, singular learning theory, and manifold techniques to probe modern ML models.
Our study group now extends manifold learning intuition to the singular learning landscape: we cross-reference algebraic invariants, manifold-based diagnostics, and ML experiments to uncover structure inside "black box" models.
We keep the same collaborative spirit—divide topics, teach one another, and synthesise notes—but the emphasis is on how manifold ideas interact with singularities, algebraic geometry, and explainability.
Differential geometry, algebraic geometry, and singular learning theory provide the shared language for our investigations.
We explore PCA, Isomap, LLE, t-SNE, UMAP, polynomial networks, and resultant-based tools to see how geometry informs data analysis.
Rotating presenters curate references, prepare slides, and guide the group through the week's material.
Lecture notes, slides, and documents are working materials drawn from the literature—they support study rather than present original research.
Academic integrity anchors our work. If you notice a missing citation or something we should clarify, please reach out and we will update our materials promptly.
Share a correction →Three graduate students and a mathematician, learning together from Istanbul to Marseille, Luxembourg, and Barcelona.
Coordinator & Lead
After completing his mathematics degree at Galatasaray University, Oğuzhan continues his graduate studies at Aix-Marseille University. He orchestrates meetings and study plans for the group.
[email protected]Research Member
Naki graduated from Galatasaray University and now pursues his master's degree at the University of Luxembourg, bringing a measure-theoretic perspective to our discussions.
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A Galatasaray University alumnus pursuing the Masters in Advanced Mathematics and Mathematical Engineering at Universitat Politècnica de Catalunya, Alptuğ bridges theory with applications.
[email protected]Everything shared on this website is part of an ongoing learning process. If you discover inaccuracies or missing citations, we warmly invite you to tell us so we can correct them quickly.
Phase 2 focuses on singular learning theory while Phase 1 mind maps remain available for reference.
Phase 2 mind map captures singular learning theory themes, algebraic geometry links, and machine learning experiments.
Explore the cumulative manifold learning map from Weeks 1–10.