Alexandru Crăciun

I am a PhD student at the Technical University of Munich, working in the Theoretical Foundations of Artificial Intelligence group under the supervision of Prof. Debarghya Ghoshdastidar.

My research sits at the intersection of geometry, topology, and optimization. I investigate how results in pure mathematics can be used to understand neural network training, bridging the gap between theoretical assumptions and practical deep learning architectures.

My current focus areas include:

• Optimization Dynamics: Analyzing how loss landscape geometry and algorithms introduce inductive biases.
• Theoretical Grounding: Validating structural assumptions of optimization theory (e.g., smoothness, non-singularity) in neural networks.
• Topological Data Analysis: Investigating how the topological properties of data manifolds impose fundamental limits on model performance in unsupervised learning.

Previously, I completed my MSc in Theoretical and Mathematical Physics at LMU Munich (supported by a DAAD Study Scholarship) and my BSc in Physics at the University of Bucharest.