taha [at] mis [dot] mpg [dot] de)This is the first iteration of the “Mathematics and Machine Learning Praktikum,” organized between the Max Planck Institute for Mathematics in the Sciences (MPI MIS), the Center for Scalable Data Analytics and Artificial Intelligence (ScaDS.AI), and Leipzig University. The internship involves designing, analysing, and implementing algorithms and models at the intersection of mathematics and machine learning. Several projects will be offered, which are worked on in small groups of 1–5 participants.
The deliverables include:
For more details, refer to the module description.
This list may be updated with more projects before the organizational meeting. Participants who want to propose projects that fit the scope of the internship can contact the organizer no later than the first organizational meeting.
Mentor: Diaaeldin Taha
Members: TBA
Description: Mathematics, as a fundamentally creative human endeavor, involves formulating conjectures, testing them experimentally through computation, and gaining insights into patterns, potential proofs, or counterexamples. Inspired by recent advancements in AI-assisted mathematical discovery, this project investigates how artificial intelligence techniques, such as reinforcement learning, generative models, and symbolic computation, can systematically support mathematicians in identifying new conjectures, verifying mathematical patterns, or finding explicit counterexamples. Participants will learn how to translate mathematical problems into computational tasks, implement suitable AI methods, interpret results, and potentially contribute original results to open mathematical questions.
Prerequisites:
References:
Mentor: Diaaeldin Taha
Members: TBA
Description: Whereas correlation is concerned with patterns between variables in data, causation is concerned with how changes in one variable influence another. While correlations can be learned directly from data, uncovering causal structure often requires subtle assumptions and careful reasoning. Causal deep learning aims to offer tools to navigate these challenges by combining data-driven deep models with causal discovery and effect estimation. In this project, participants will get familiar with the basics of causal deep learning, implement selected methods from recent literature, and gain hands-on experience reasoning about cause and effect in data.
Prerequisites:
References:
Mentor: Diaaeldin Taha
Members: TBA
Description: Modern machine learning models are trained by optimizing highly non-convex loss functions, yet in practice, simple gradient-based methods often work remarkably well. This project investigates the geometry of these optimization landscapes: how structure, symmetry, and overparameterization shape the behavior of gradient descent. Participants will explore recent theoretical and empirical work connecting optimization dynamics to generalization and model performance. The goal is to implement simple model families, visualize their loss surfaces, and analyze how different training regimes (e.g. width, initialization, learning rate) interact with the landscape geometry.
Prerequisites:
References:
Mentor: Diaaeldin Taha
Members: TBA
Description: In many real-world applications, data lie on non-Euclidean spaces, such as spheres, tori, or hyperbolic surfaces, rather than in flat, high-dimensional vector spaces. This project explores how to model data that lives on non-Euclidean space. Participants will learn how to implement models that respect or exploit the underlying structure (e.g., Riemannian gradient descent, manifold-aware neural networks, or geodesic convolution). Depending on interest, the project can lean toward visualization or other machine learning problems.
Prerequisites:
References: