Erfan Mirzaei
Stanserhorn, Switzerland.
I am an ELLIS Ph.D. student in Applied Mathematics and Machine Learning at the Istituto Italiano di Tecnologia, École Polytechnique, and the Università di Genova. I am fortunate to be advised by Massimiliano Pontil, Karim Lounici, and Andreas Maurer.
My research interests broadly lie in (machine/deep) learning theory, using tools from high-dimensional probability, information theory, stochastic optimization, and statistical physics. I aim to develop mathematical explanations and understanding for empirical phenomena arising in modern machine learning, including generalization in overparameterized models and how stochasticity and optimization dynamics shape the solutions they learn.
My PhD asks how to predict test performance when overparameterized models fit their training data so well that training error alone is uninformative. For Gibbs posteriors, I show that PAC-Bayesian complexity can be expressed as an integral of mean training loss along a temperature path, connecting higher-noise (“hot”) models to the generalization of lower-noise (“cold”) ones. I extend this connection to Langevin and stochastic gradient-based algorithms, where training dynamics at higher noise can provide practical signals of lower-noise test performance.
If you are interested in discussing machine learning theory, deep learning theory, or potential collaborations, feel free to reach out via email!
I co-organize the Learning Theory Circle, an online community for discussing learning theory and related topics in Persian. If you are interested, please visit the website and join us.
