Recent years have witnessed a surge of interest in deep learning methods to tackle inverse problems arising in various domains such as medical imaging, remote sensing, and the arts and humanities. This talk offers an overview of recent advances in the foundations and applications of deep learning for inverse problems, with a focus on model-based deep learning methods. Concretely, this talk will overview our work relating to theoretical advances in the area of mode-based learning, including learning guarantees; algorithmic advances in model-based learning; and, finally it will showcase a portfolio of emerging signal & image processing challenges that benefit from model based learning, including image separation / deconvolution challenges arising in the arts and humanities.

Bio:

Miguel Rodrigues is a Professor of Information Theory and Processing at University College London; he leads the Information, Inference and Machine Learning Lab at UCL, and he has also been the founder and director of the master programme in Integrated Machine Learning Systems at UCL. He has also been the UCL Turing University Lead and a Turing Fellow with the Alan Turing Institute — the UK National Institute of Data Science and Artificial Intelligence.

He held various appointments with various institutions worldwide including Cambridge University, Princeton University, Duke University, and the University of Porto, Portugal. He obtained the undergraduate degree in Electrical and Computer Engineering from the Faculty of Engineering of the University of Porto, Portugal and the PhD degree in Electronic and Electrical Engineering from University College London.

Dr. Rodrigues's research lies in the general areas of information theory, information processing, and machine learning. His most relevant contributions have ranged from the information-theoretic analysis and design of communications systems, information-theoretic security, information-theoretic analysis and design of sensing systems, and the information-theoretic foundations of machine learning.

He serves or has served as Editor of IEEE BITS, Editor of the IEEE Transactions on Information Theory, and Lead Guest Editor of various Special Issues of the IEEE Journal on Selected Topics in Signal Processing, Information and Inference, and Foundations and Trends in Signal Processing.

Dr. Rodrigues has been the recipient of various prizes and awards including the Prize for Merit from the University of Porto, the Prize Engenheiro Cristian Spratley, the Prize Engenheiro Antonio de Almeida, fellowships from the Portuguese Foundation for Science and Technology, and fellowships from the Foundation Calouste Gulbenkian. Dr. Rodrigues research on information-theoretic security has also attracted the IEEE Communications and Information Theory Societies Joint Paper Award 2011.  

He has also been elevated to Fellow of the Institute of Electronics and Electrical Engineers (IEEE) for his contributions to the ‘multi-modal data processing and reliable and secure communications.’

Attention-based models, such as Transformer, excel across various tasks but lack a comprehensive theoretical understanding, especially regarding token-wise sparsity and internal linear representations. To address this gap, we introduce the single-location regression task, where only one token in a sequence determines the output, and its position is a latent random variable, retrievable via a linear projection of the input. To solve this task, we propose a dedicated predictor, which turns out to be a simplified version of a non-linear self-attention layer. We study its theoretical properties, by showing its asymptotic Bayes optimality and analyzing its training dynamics. In particular, despite the non-convex nature of the problem, the predictor effectively learns the underlying structure. This work highlights the capacity of attention mechanisms to handle sparse token information and internal linear structures.

This is a joint work with Pierre Marion, Gérard Biau and Raphaël Berthier

Cost-sensitive loss functions are crucial in many real-world prediction problems, where different types of errors are penalized differently; for example, in medical diagnosis, a false negative prediction can lead to worse consequences than a false positive prediction. However, traditional learning theory has mostly focused on the symmetric zero-one loss, letting cost-sensitive losses largely unaddressed. In this work, we extend the celebrated theory of boosting to incorporate both cost-sensitive and multi-objective losses. Cost-sensitive losses assign costs to the entries of a confusion matrix, and are used to control the sum of prediction errors accounting for the cost of each error type. Multi-objective losses, on the other hand, simultaneously track multiple cost-sensitive losses, and are useful when the goal is to satisfy several criteria at once (e.g., minimizing false positives while keeping false negatives below a critical threshold). We develop a comprehensive theory of cost-sensitive and multi-objective boosting, providing a taxonomy of weak learning guarantees that distinguishes which guarantees are trivial (i.e., can always be achieved), which ones are boostable (i.e., imply strong learning), and which ones are intermediate, implying non-trivial yet not arbitrarily accurate learning. For binary classification, we establish a dichotomy: a weak learning guarantee is either trivial or boostable. In the multiclass setting, we describe a more intricate landscape of intermediate weak learning guarantees. Our characterization relies on a geometric interpretation of boosting, revealing a surprising equivalence between cost-sensitive and multi-objective losses.

Inverse problems involve reconstructing unknown physical quantities from indirect measurements. They appear in various fields, including medical imaging (e.g., MRI, Ultrasound, CT), material sciences and molecular biology (e.g., electron microscopy), as well as remote sensing just to name a few examples. While deep neural networks are currently able to achieve state-of-the-art performance in many imaging tasks, in this talk we argue that  many inverse imaging problems cannot be solved convincingly using a black-box solution. Instead, they require a well-crafted combination of computational tools taking the underlying signal, the physical constraints and acquisition characteristics into account.

In the first part of the talk, we introduce INDigo+, a novel INN-guided probabilistic diffusion algorithm for arbitrary image restoration tasks. INDigo+ combines the perfect reconstruction property of invertible neural networks (INNs) with the strong generative capabilities of pre-trained diffusion models. Specifically, we leverage the invertibility of the network to condition the diffusion process and in this way we generate high quality restored images consistent with the measurements.

In the second part of the talk, we discuss the unfolding techniques which is an approach that allows embedding priors and models in the neural network architecture. In this context we discuss the problem of monitoring the dynamics of large populations of neurons over a large area of the brain. Light-field microscopy (LFM), a type of scanless microscopy, is a particularly attractive candidate for high-speed three-dimensional (3D) imaging which is needed for monitoring neural activity. We review fundamental aspects of LFM and then present computational methods based on deep learning for neuron localization and activity estimation from light-field data.
Finally, we look at the multi-modal case and present an application in art investigation. Often X-ray images of Old Master paintings contain information of the visible painting and of concealed sub-surface design, we therefore introduce a model-based neural network capable of separating from the “mixed X-ray”  the X-ray image of the visible painting and the X-ray of the concealed design.

This is joint work with  A. Foust, P. Song, C. Howe, H. Verinaz, J. Huang, Di You and Y. Su from Imperial College London, M. Rodrigues and W. Pu from University College London, I. Daubechies from Duke University, Barak Sober from the Hebrew University of Jerusalem and C. Higgitt and N. Daly from The National Gallery in London.

We investigate a stochastic differential game in which a major player has a private information (the knowledge of a random variable), which she discloses through her control to a population of small players playing in a Nash Mean Field Game equilibrium. The major player’s cost depends on the distribution of the population, while the cost of the population depends on the random variable known by the major player. We show that the game has a relaxed solution and that the optimal control of the major player is approximatively optimal in games with a large but finite number of small players. Joint work with Pierre Cardaliaguet and Catherine Rainer.

This talk is rescheduled and will take place on 21 January 2025

According to a conjecture by Landau-Pekar (1948) and by Spohn (1986), the effective mass of the Fröhlich Polaron should diverge in the strong coupling limit like a quartic power of the coupling constant. In a recent joint with R. Bazaes, M. Sellke and S.R.S. Varadhan, we prove this conjecture.