Program

Abstract: 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.

Abstract: Abstract: This paper addresses the approximation of real and complex Grassmannian frames, namely sets of unit-norm vectors with minimum mutual coherence. We recast this problem as a collection of feasibility problems aiming to design frames with given target coherence, that evolves during the execution of the algorithm. The feasibility problems are solved by an accelerated alternating projection algorithm, leveraging a Gram matrix representation of the frames. Numerical experiments indicate that our proposed Targeted coherence with Accelerated Alternating Projection (TAAP) algorithm outperforms state-of-the-art methods regarding the mutual coherence vs computational cost criterion, exhibiting the largest performance gap with existing methods when the frame dimension is comparable to the dimension of the ambient space. 

Abstract: 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.

Abstract: 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)

Abstract: Before any processing, radar signals need to be digitized using Analog-to-Digital Converters (ADCs).
Recently, the Unlimited Sensing Framework (USF), where modulo-ADCs replace classic ADCs, has been studied in radar systems to alleviate the stringent requirements on the acquisition chain when encountering high dynamic range (HDR) scenes.
In USF, the recovery of a signal from its modulo measurements relies on the embedded redundant information.
This redundancy often appears through oversampling or the collections of modulo measurements of the same signal using different modulo thresholds.
In this work, we leverage, using the Hilbert Transform, the structure between channels of radars equipped with quadrature or IQ coherent demodulation to design a computational system that does not require oversampling nor the multiple acquisition of the same signal.
We introduce a new algorithm, namely Hilbert-Pencil of Function (Hilbert-PoF), and we show theoretically and through simulations that it achieves perfect reconstructions in this challenging setting.

Abstract: 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.

Abstract: Computer-generated holography is a practical technique based on coherent light sources and interferometry for 3D imaging using high-definition digital spatial light modulators. Estimating and transferring the phase information is a challenging problem that depends on the pixel-pitch, the bit depth and the illumination wavelength that are device-dependent parameters. When the visual content is of low complexity, such as depth-resolved natural images, the phase retrieval problem is ill-posed and over-parameterized because the phase contains only a marginal amount of information for allowing a continuous eye refocusing.

This work introduces a practical Nesterov-accelerated optimization method for estimating progressively a compatible phase from a sparse focal stack of low-resolution compressed amplitude images instead of storing and transferring a pre-generated complex amplitude and phase pattern. The rationale is trading data transmission of the phase information with online device-driven computation. We implement band limitation and Fourier-domain interpolation in the forward model such that a high-quality super-resolution digital hologram may be estimated in real-time from the consensus of a short focal stack made of lossy-compressed low-resolution amplitude images.