Abstract: In this talk, I will first focus on the problem of robust low-rank matrix estimation from corrupted measurements. Building on a matrix factorization (MF) approach, I will present a novel optimization algorithm that employs preconditioned-type updates for the matrix factors. This algorithm provably addresses two longstanding challenges in MF-based methods: (a) reliance on awareness of the rank of the target matrix in advance, and (b) slow convergence when the underlying matrix is ill-conditioned. Next, I will introduce an inverse algorithm for deep generative models. I will discuss new theoretical guarantees that relax the commonly used assumption of randomized model weights, demonstrating that a gradient-descent-based approach globally converges for a broad class of inverse problems. Finally, I will present a unifying theoretical framework that provides new insights into state-of-the-art strategies for continual learning i.e., training neural networks on a series of tasks while mitigating catastrophic forgetting. This framework not only sheds light on the strengths and weaknesses of existing methods but also paves the way for the development of more efficient continual learning techniques.

 

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