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Rafael Molina

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Machine Learning cond-mat.mes-hall Applications eess.IV math.OC physics.optics Systems and Control

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preprint2026arXiv

Conditional Diffusion Sampling

Sampling from unnormalized multimodal distributions with limited density evaluations remains a fundamental challenge in machine learning and natural sciences. Successful approaches construct a bridge between a tractable reference and the target distribution. Parallel Tempering (PT) serves as the gold standard, while recent diffusion-based approaches offer a continuous alternative at the cost of neural training. In this work, we introduce Conditional Diffusion Sampling (CDS), a framework that combines these two paradigms. To this end, we derive Conditional Interpolants, a class of stochastic processes whose transport dynamics are governed by an exact, closed-form stochastic differential equation (SDE), requiring no neural approximation. Although these dynamics require sampling from a non-trivial initialization distribution, we show both theoretically and empirically that the cost of this initialization diminishes for sufficiently short diffusion times. CDS leverages this by a two-stage procedure: (1) PT is used to efficiently sample the initial distribution, and then (2) samples are transported via the transport SDE. This combination couples the robust global exploration of PT with efficient local transport. Experiments suggest that CDS has the potential to achieve a superior trade-off between sample quality and density evaluation cost compared to state-of-the-art samplers.

preprint2025arXiv

Tunable plasmon modes and topological transitions in single- and bilayer semi-Dirac materials

We investigate the plasmonic response of single- and bilayer semi-Dirac materials under the influence of a tunable parameter $δ$ that governs topological transitions via Dirac cone generation/merging and incorporating band inversion terms. For single-layer systems, we demonstrate that the emergence of Dirac cones leads to an enhanced plasmon frequency range and that the plasmonic spectrum exhibits strong anisotropy, especially for finite $δ$ and vanishing inversion terms. In the bilayer configurations, we uncover a second plasmon mode whose relative phase, with respect to the first mode, can be actively controlled by rotating the upper layer which impacts the symmetry of the charge oscillations across the layers. This tunability enables switching between in- and out-of-phase plasmonic modes, offering a route toward phase-controlled collective excitations. Our results highlight the potential of semi-Dirac systems for topological plasmonics and interferometric applications in next-generation optoelectronic devices.

preprint2020arXiv

Photoprotected spin Hall effect on graphene with substrate induced Rashba spin-orbit coupling

We propose an experimental realization of the Spin Hall effect in graphene by illuminating a graphene sheet on top of a substrate with circularly polarized monochromatic light. The substrate induces a controllable Rashba type spin-orbit coupling which breaks the spin-degeneracy of the Dirac cones but it is gapless. The circularly polarized light induces a gap in the spectrum and turns graphene into a Floquet topological insulator with spin dependent edge states. By analyzing the high and intermediate frequency regimes, we find that in both parameter limits, the spin-Chern number can be tuned by the effective coupling strength of the charge particles to the radiation field and determine the condition for the photoinduced topological phase transition.

preprint2020arXiv

Self-supervised Fine-tuning for Correcting Super-Resolution Convolutional Neural Networks

While Convolutional Neural Networks (CNNs) trained for image and video super-resolution (SR) regularly achieve new state-of-the-art performance, they also suffer from significant drawbacks. One of their limitations is their lack of robustness to unseen image formation models during training. Other limitations include the generation of artifacts and hallucinated content when training Generative Adversarial Networks (GANs) for SR. While the Deep Learning literature focuses on presenting new training schemes and settings to resolve these various issues, we show that one can avoid training and correct for SR results with a fully self-supervised fine-tuning approach. More specifically, at test time, given an image and its known image formation model, we fine-tune the parameters of the trained network and iteratively update them using a data fidelity loss. We apply our fine-tuning algorithm on multiple image and video SR CNNs and show that it can successfully correct for a sub-optimal SR solution by entirely relying on internal learning at test time. We apply our method on the problem of fine-tuning for unseen image formation models and on removal of artifacts introduced by GANs.

preprint2011arXiv

Sparse Bayesian Methods for Low-Rank Matrix Estimation

Recovery of low-rank matrices has recently seen significant activity in many areas of science and engineering, motivated by recent theoretical results for exact reconstruction guarantees and interesting practical applications. A number of methods have been developed for this recovery problem. However, a principled method for choosing the unknown target rank is generally not provided. In this paper, we present novel recovery algorithms for estimating low-rank matrices in matrix completion and robust principal component analysis based on sparse Bayesian learning (SBL) principles. Starting from a matrix factorization formulation and enforcing the low-rank constraint in the estimates as a sparsity constraint, we develop an approach that is very effective in determining the correct rank while providing high recovery performance. We provide connections with existing methods in other similar problems and empirical results and comparisons with current state-of-the-art methods that illustrate the effectiveness of this approach.