Low-Rank Learning & Optimization
Matrix factorization, implicit regularization, and efficient optimization with guarantees.
Low-rank structure represents high-dimensional data and parameters using compact factors. I develop optimization methods that exploit this structure, identify model complexity, and remain reliable under corrupted measurements.
Robust recovery with unknown rank
Our ICML 2025 work analyzes an overparameterized, preconditioned subgradient algorithm for recovering asymmetric low-rank matrices from corrupted measurements. The analysis establishes linear convergence rates independent of the true rank under the stated assumptions, addressing recovery when the rank is unknown.
Nonconvex low-rank regularization
Our NeurIPS 2020 work develops a variational representation of the Schatten-$p$ quasi-norm for $p \in (0,1]$. Expressing the regularizer through matrix factors connects rank selection to group sparsity and enables algorithms that avoid repeated singular value decompositions.
Parameter-efficient adaptation
A current research direction is to use low-rank structure for parameter-efficient fine-tuning of foundation models, including language, diffusion, and flow-based models. This connects my work on structured optimization with efficient model adaptation.
Selected publications
- Paris Giampouras, Hanqin Cai, and René Vidal. Guarantees of a Preconditioned Subgradient Algorithm for Overparameterized Asymmetric Low-rank Matrix Recovery. ICML 2025.
- Paris Giampouras, René Vidal, Athanasios Rontogiannis, and Benjamin Haeffele. A Novel Variational Form of the Schatten-p Quasi-Norm. NeurIPS 2020.
- Paris Giampouras, Athanasios Rontogiannis, and Konstantinos Koutroumbas. Alternating Iteratively Reweighted Least Squares Minimization for Low-Rank Matrix Factorization. IEEE Transactions on Signal Processing, 2019.