Machine Learning and Data Science Seminar

Mr Oluwadamilola (Dami) Fasina will talk about; 'Learning with tensor paraproducts'

We discuss computational (Neural FIM) and analytical (tensor paraproducts) tools for learning structure of sets. In the first situation we focus on learning the metric amongst elements of a statistical manifold. To do so, we design a neural network which enables one to compute the Fisher information metric (FIM), so long the Jensen-Shannon divergences amongst probability distributions on the statistical manifold are preserved during training. In the second situation we focus on analyzing the structure of function compositions through separation of its low and high frequency components. This is accomplished by elaborating on J.M. Bony’s celebrated work on paraproducts by discretizing and allocating distinct scaling parameters along each dimension of the support of a function composition (with a prescribed regularity), permitting finer analytical control. A consequence of this extension is highlighted with a discussion of the regularity gains of kernels of integral operators. 

TBA 

Jian-Qing Zheng will talk about: 'Generative Models on the Space of Diffeomorphisms: A Deformation-Centric Framework for Multi-Organ Anatomy'

Generative models for images are typically formulated in pixel space, where the geometric structure of the underlying objects is not directly represented. For anatomical data, a more natural representation is provided by the deformation that maps one anatomical configuration to another, rather than by the intensities themselves. The set of such deformations forms a structured, non-Euclidean space, and working in this space changes how registration, generation, and representation learning can be approached. In this talk, a framework will be presented in which deformations, rather than images, are treated as the primary modeling object. Image registration is recast as the problem of recovering a deformation between two anatomies, and is extended to the multi-organ setting by modeling deformations of several organs jointly with their geometric couplings. A diffusion-based generative model is then introduced that operates directly on deformations, so that each generated sample is, by construction, an interpretable transformation of a real anatomy. The framework is extended into a foundation model trained across multiple modalities and anatomical regions, and is evaluated on medical imaging tasks including few-shot segmentation, registration, and phenotype-conditioned anatomical prediction.

Professor Pereyra will talk about; 'Physics-informed deep generative models: Applications to computational sensing'

This talk introduces a novel mathematical and computational framework for constructing high-dimensional Bayesian inversion methods that leverage state-of-the-art generative denoising diffusion models as highly informative priors. A central innovation is the construction of physics-informed generative models using Langevin diffusion processes and Markov chain Monte Carlo (MCMC) sampling techniques to develop stochastic neural network architectures capable of near-exact sampling. The obtained networks are modular and composed of interpretable layers that are directly related to statistical image priors and data likelihoods derived from forward observation models. The layers encoding the data likelihood function are designed for flexibility, enabling scene and instrument model parameters to be specified at inference time and seamlessly integrated with pre-trained foundational generative priors. To achieve high computational efficiency, we employ adversarial model distillation, which yields excellent sampling performance with as few as four Markov chain Monte Carlo steps, even in problems exceeding one million dimensions. Our approach is validated through non-asymptotic convergence analysis and extensive numerical experiments in computational image and video restoration. We conclude by discussing unsupervised training strategies that allow the models to be fine-tuned directly from measurement data, thereby bypassing the need for clean reference data.

The talk is based on recent work in physics-informed generative AI for Bayesian imaging: https://arxiv.org/abs/2503.12615 (ICCV 2025), which uses a distilled latent Stable Diffusion XL model trained on five billion clean images as a zero-shot prior, and  https://arxiv.org/pdf/2507.02686, which integrates pixel-based diffusion models with deep unfolding and diffusion distillation (TMLR 2025). The extension to video restoration is presented in https://arxiv.org/abs/2510.01339 (ICLR 2025). Our approach to unsupervised training of diffusion models is introduced in https://arxiv.org/abs/2510.11964.