Plenary Speakers

Beyond traditional PnP: equivariance and restoration priors.

Plug-and-Play (PnP) algorithms have emerged as a flexible and powerful framework for solving inverse problems in imaging, relying on pre-trained denoisers to implicitly define image priors. Their modularity enables the reuse of learned priors across tasks, eliminating the need to train task-specific models. In this presentation, we revisit the foundations of PnP and pose two central questions: (1) Can the instabilities often observed in PnP algorithms be mitigated at test time alone? (2) While denoisers are widely used as implicit priors, can we generalize PnP to incorporate other types of restoration networks?

We answer both affirmatively. For (1), we demonstrate that enforcing equivariance of the denoiser with respect to common transformation groups—such as rotations, reflections, and translations—significantly improves both the stability and the reconstruction quality of PnP algorithms. For (2), we show that with minimal modifications to the algorithm, any restoration network (e.g., for inpainting or super-resolution) can serve as a valid prior, greatly expanding the applicability and flexibility of the PnP framework.

This presentation will be based on:

• Equivariant PnP image reconstruction, CVPR 2024 (pdf)

• FiRe: Fixed-points of Restoration Priors for Solving Inverse Problems, CVPR 2025 (arXiv)

Training Deep Learning Models with Norm-Constrained LMOs

In this talk, I discuss optimization methods that leverage the linear minimization oracle (LMO) over a norm-ball and their application to training huge neural networks. We propose a new stochastic family of algorithms that uses the LMO to adapt to the geometry of the problem and, perhaps surprisingly, show that they can be applied to unconstrained problems. The resulting update rule unifies several existing optimization methods under a single framework. Furthermore, we propose an explicit choice of norm for deep architectures, which, as a side benefit, leads to the transferability of hyperparameters across model sizes. Experimentally, we demonstrate significant speedups on nanoGPT training without any reliance on Adam. The proposed method is memory-efficient, requiring only one set of model weights and one set of gradients, which can be stored in half-precision.

Hidden convexity in factorization problems

Several nonconvex formulations of factorization problems have been shown to lack spurious local minima. This includes the Burer-Monteiro formulation of semidefinite programs and the training problem for linear neural networks. In this talk, we discuss a convex programming approach that can be used to generate proofs of benign nonconvexity in a semi-automated way. We illustrate this approach on various factorization problems and explore promising new nonconvex landscapes that could be addressed using this technique.

A Langevin sampler for quantum tomography

We propose a Langevin sampler for quantum tomography, that relies on a new formulation of Bayesian quantum tomography exploiting the Burer-Monteiro factorization of Hermitian positive-semidefinite matrices. If the rank of the target density matrix is known, this formulation allows us to define a posterior distribution that is only supported on matrices whose rank is upper-bounded by the rank of the target density matrix. Conversely, if the target rank is unknown, any upper bound on the rank can be used by our algorithm, and the rank of the resulting posterior mean estimator is further reduced by the use of a low-rank promoting prior density.