BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Joan Bruna (NYU Courant) DTSTART:20210420T121500Z DTEND:20210420T134500Z DTSTAMP:20260422T212528Z UID:MathDeep/1 DESCRIPTION:Title: Mathematical aspects of neural network approximation and learning\nby Joan Bruna (NYU Courant) as part of Mathematics of Deep Learning\n\n\nAbs tract\nHigh-dimensional learning remains an outstanding phenomena where ex perimental evidence outpaces our current mathematical understanding. Neura l Networks provide a rich yet intricate class of functions with statistica l abilities to break the curse of dimensionality\, and where physical prio rs can be tightly integrated into the architecture to improve sample effic iency. Despite these advantages\, an outstanding theoretical challenge in these models is computational\, by providing an analysis that explains suc cessful optimization and generalization in the face of existing worst-case computational hardness results.\n\nIn this talk\, we will describe snippe ts of such challenge\, covering respectively optimization and approximatio n. First\, we will focus on the framework that lifts parameter optimizatio n to an appropriate measure space. We will overview existing results that guarantee global convergence of the resulting Wasserstein gradient flows\, and present our recent results that study typical fluctuations of the dyn amics around their mean field evolution\, as well as extensions of this fr amework beyond vanilla supervised learning to account for symmetries in th e function. Next\, we will discuss the role of depth in terms of approxima tion\, and present novel results establishing so-called ‘depth separatio n’ for a broad class of functions. We will conclude by discussing conseq uences in terms of optimization\, highlighting current and future mathemat ical challenges.\n\nJoint work with: Zhengdao Chen\, Grant Rotskoff\, Eric Vanden-Eijnden\, Luca Venturi\, Samy Jelassi and Aaron Zweig.\n LOCATION:https://researchseminars.org/talk/MathDeep/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Gitta Kutyniok (LMU Munich) DTSTART:20210427T101500Z DTEND:20210427T114500Z DTSTAMP:20260422T212528Z UID:MathDeep/2 DESCRIPTION:Title: Deep Learning meets Shearlets: On the Path Towards Interpretable Imaging< /a>\nby Gitta Kutyniok (LMU Munich) as part of Mathematics of Deep Learnin g\n\n\nAbstract\nPure model-based approaches are today often insufficient for solving complex inverse problems in medical imaging. At the same time\ , methods based on artificial intelligence\, in particular\, deep neural n etworks\, are extremely successful\, often quickly leading to state-of-the -art algorithms. However\, pure deep learning approaches often neglect kno wn and valuable information from the modeling world and suffer from a lack of interpretability.\n\nIn this talk\, we will develop a conceptual appro ach by combining the model-based method of sparse regularization by shearl ets with the data-driven method of deep learning. Our solvers pay particul ar attention to the singularity structures of the data. Focussing then on the inverse problem of (limited-angle) computed tomography\, we will show that our algorithms significantly outperform previous methodologies\, incl uding methods entirely based on deep learning. Finally\, we will also touc h upon the issue of how to interpret such algorithms\, and present a novel \, state-of-the-art explainability method based on information theory.\n LOCATION:https://researchseminars.org/talk/MathDeep/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Möller (University of Siegen) DTSTART:20210504T101500Z DTEND:20210504T114500Z DTSTAMP:20260422T212528Z UID:MathDeep/3 DESCRIPTION:Title: On the Confluence of Deep Learning and Energy Minimization Methods for In verse Problems\nby Michael Möller (University of Siegen) as part of M athematics of Deep Learning\n\n\nAbstract\nMany practical applications req uire to infer a desired quantity from measurements that contain implicit i nformation about them\, commonly resulting in ill-posed inverse reconstruc tion problems. While classical approaches formulate their solution as the argument that minimizes a suitable cost function\, recent works dominate i mage reconstruction benchmarks using deep learning. This talk discusses po ssible ways of combining ideas from energy minimization and deep learning\ , including algorithmic schemes that introduce learned regularity\, networ ks that iteratively minimize a model based cost function\, and techniques that aim at learning suitable regularizers. For the latter\, I will highli ght recent advances and future challenges in the design of such parameteri zed regularizers as well as the solution of the bi-level optimization prob lems resulting from their training.\n LOCATION:https://researchseminars.org/talk/MathDeep/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Enrique Zuazua (FAU Erlangen-Nürnberg) DTSTART:20210511T101500Z DTEND:20210511T114500Z DTSTAMP:20260422T212528Z UID:MathDeep/4 DESCRIPTION:Title: Neural Differential Equations\, Control and Machine Learning\nby Enri que Zuazua (FAU Erlangen-Nürnberg) as part of Mathematics of Deep Learnin g\n\n\nAbstract\nWe discuss Neural Ordinary Differential Equations (NODEs) from a control theoretical perspective to address some of the main challe nges in Machine Learning and\, in particular\, data classification and Uni versal Approximation. More precisely\, we adopt the perspective of the sim ultaneous control of systems of NODEs. For instance\, in the context of cl assification\, each item to be classified corresponds to a different initi al datum for the Cauchy problem of the NODE. And all the solutions corresp onding the data under consideration need to be driven to the corresponding target by means of the same control. We present a genuinely nonlinear and constructive method\, allowing to estimate the complexity of the control strategies we develop. The very nonlinear nature of the activation functio ns governing the nonlinear dynamics of NODEs under consideration plays a k ey role. It allows deforming half of the phase space while the other half remains invariant\, a property that classical models in mechanics do not f ulfill. This very property allows to build elementary controls inducing sp ecific dynamics and transformations whose concatenation\, along with prope rly chosen hyperplanes\, allows achieving our goals in finitely many steps . We also present the counterparts in the context of the control of neural transport equations\, establishing a link between optimal transport and d eep neural networks.\n\nThis is a joint work Domènec Ruiz-Balet.\n LOCATION:https://researchseminars.org/talk/MathDeep/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Lars Ruthotto (Emory University) DTSTART:20210518T121500Z DTEND:20210518T134500Z DTSTAMP:20260422T212528Z UID:MathDeep/5 DESCRIPTION:Title: An Introduction to Generative Modeling\nby Lars Ruthotto (Emory Unive rsity) as part of Mathematics of Deep Learning\n\n\nAbstract\nDeep generat ive models (DGM) are neural networks with many hidden layers trained to ap proximate complicated\, high-dimensional probability distributions from a finite number of samples. When trained successfully\, we can use the DGMs to estimate the likelihood of each observation and to create new samples f rom the underlying distribution. Developing DGMs has become one of the mos t hotly researched fields in artificial intelligence in recent years. The literature on DGMs has become vast and is growing rapidly.\nSome advances have even reached the public sphere\, for example\, the recent successes i n generating realistic-looking images\, voices\, or movies\; so-called dee p fakes.\n\nDespite these successes\, several mathematical and practical i ssues limit the broader use of DGMs: given a specific dataset\, it remains challenging to design and train a DGM and even more challenging to find o ut why a particular model is or is not effective. To help students contrib ute to this field\, this talk provides an introduction to DGMs and provide s a concise mathematical framework for modeling the three most popular app roaches: normalizing flows (NF)\, variational autoencoders (VAE)\, and gen erative adversarial networks (GAN). We illustrate the advantages and disad vantages of these basic approaches using numerical experiments. Our goal i s to enable and motivate the reader to contribute to this proliferating re search area. Our presentation also emphasizes relations between generative modeling and optimal transport.\n LOCATION:https://researchseminars.org/talk/MathDeep/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Jeff Calder (University of Minnesota) DTSTART:20210525T141500Z DTEND:20210525T154500Z DTSTAMP:20260422T212528Z UID:MathDeep/6 DESCRIPTION:Title: Random walks and PDEs in graph-based learning\nby Jeff Calder (Univer sity of Minnesota) as part of Mathematics of Deep Learning\n\n\nAbstract\n I will discuss some applications of random walks and PDEs in graph-based l earning\, both for theoretical analysis and algorithm development. Graph-b ased learning is a field within machine learning that uses similarities be tween datapoints to create efficient representations of high-dimensional d ata for tasks like semi-supervised classification\, clustering and dimensi on reduction. There has been considerable interest recently in semi-superv ised learning problems with very few labeled examples (e.g.\, 1 label per class). The widely used Laplacian regularization is ill-posed at low label rates and gives very poor classification results. In the first part of th e talk\, we will use the random walk interpretation of the graph Laplacian to precisely characterize the lowest label rate at which Laplacian regula rized semi-supervised learning is well-posed. At lower label rates\, where Laplace learning performs poorly\, we will show how our random walk analy sis leads to a new algorithm\, called Poisson learning\, that is probably more stable and informative than Laplace learning. We will conclude with s ome applications of Poisson learning to image classification and mesh segm entation of broken bone fragments of interest in anthropology.\n LOCATION:https://researchseminars.org/talk/MathDeep/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Pock (University of Graz) DTSTART:20210601T101500Z DTEND:20210601T114500Z DTSTAMP:20260422T212528Z UID:MathDeep/7 DESCRIPTION:Title: Learning with energy-based models\nby Thomas Pock (University of Graz ) as part of Mathematics of Deep Learning\n\n\nAbstract\nIn this talk\, I will show how to use learning techniques to significantly improve energy-b ased models. I will start by showing that even for the simplest models suc h as total variation\, one can greatly improve the accuracy of the numeric al approximation by learning the "best" discretization within a class of c onsistent discretizations. Then I will move forward to more expressive mod els and show how they can be learned in order to give state-of-the art per formance for image reconstruction problems\, such as denoising\, superreso lution\, MRI and CT. Finally\, I will show how energy based models for ima ge labeling such as Markov random fields can be used in the framework of d eep learning.\n LOCATION:https://researchseminars.org/talk/MathDeep/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicolas Papadakis (University of Bordeaux) DTSTART:20210608T101500Z DTEND:20210608T114500Z DTSTAMP:20260422T212528Z UID:MathDeep/8 DESCRIPTION:Title: On the learning of Wasserstein generative models\nby Nicolas Papadaki s (University of Bordeaux) as part of Mathematics of Deep Learning\n\n\nAb stract\nThe problem of WGAN (Wasserstein Generative Adversarial Network) l earning is an instance of optimization problems where one wishes to find\, among a parametric class of distributions\, the one which is closest to a target distribution in terms of an optimal transport (OT) distance. Apply ing a gradient-based algorithm for this problem requires to express the gr adient of the OT distance with respect to one of its argument\, which can be related to the solutions of the dual problem (Kantorovich potentials). The first part of this talk aims at finding conditions that ensure the exi stence of such gradient. After discussing regularity issues that may appea r with discrete target measures\, we will show that regularity problems ar e avoided when using entropy-regularized OT and/or considering the semi-di screte formulation of OT. Then\, we will see how these gradients can be ex ploited in a stable way to address some imaging problems where the target discrete measure is reasonably large. Using OT distances between multi-sca le patch distributions\, this allows to estimate a generative convolutiona l network that can synthesize an exemplar texture in a faithful and effici ent way.\nThis is a joint work with Antoine Houdard\, Arthue Leclaire and Julien Rabin.\n LOCATION:https://researchseminars.org/talk/MathDeep/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Cremers (TU Munich) DTSTART:20210615T101500Z DTEND:20210615T114500Z DTSTAMP:20260422T212528Z UID:MathDeep/9 DESCRIPTION:Title: Self-supervised Learning for 3D Shape Analysis\nby Daniel Cremers (TU Munich) as part of Mathematics of Deep Learning\n\n\nAbstract\nWhile neur al networks have swept the field of computer vision and replaced classical methods in most areas of image analysis and beyond\, extending their powe r to the domain of 3D shape analysis remains an important open challenge. In my presentation\, I will focus on the problems of shape matching\, corr espondence estimation and shape interpolation and develop suitable deep le arning approaches to tackle these challenges. In particular\, I will focus on the difficult problem of computing correspondence and interpolation fo r pairs of shapes from different classes — say a human and a horse — w here traditional isometry assumptions no longer hold.\n LOCATION:https://researchseminars.org/talk/MathDeep/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Yixing Huang (FAU Erlangen-Nürnberg) DTSTART:20210622T101500Z DTEND:20210622T114500Z DTSTAMP:20260422T212528Z UID:MathDeep/10 DESCRIPTION:Title: Deep Learning for Computed Tomography Image Reconstruction from Insuffic ient Data\nby Yixing Huang (FAU Erlangen-Nürnberg) as part of Mathema tics of Deep Learning\n\n\nAbstract\nComputed tomography (CT) image recons truction from insufficient data is a severely ill-posed inverse problem. C onventional methods solely have very limited performance to address this p roblem. Deep learning has achieved impressive results in solving various i nverse problems. \nHowever\, the robustness of deep learning methods is st ill a concern for clinical applications due to the following two challenge s: a) With limited access to sufficient training data\, a learned deep lea rning model may not generalize well to unseen data\; b) Deep learning mode ls are sensitive to noise. Therefore\, the quality of images processed by neural networks only may be inadequate. In this talk\, we investigate the robustness of deep learning in CT image reconstruction first. Since learni ng-based images with incorrect structures are likely not consistent with m easured projection data\, we propose a data consistent reconstruction (DCR ) method to improve their image quality\, which combines the advantages of conventional methods and deep learning: \nFirst\, a prior image is genera ted by deep learning. Afterwards\, unmeasured data are inpainted by forwar d projection of the prior image. \nFinally\, a final image is reconstructe d by a conventional method\, integrating data consistency for measured dat a and learned prior information for missing data. The DCR method is demons trated in two\nscenarios: image reconstruction from limited-angle data and truncated data.\n LOCATION:https://researchseminars.org/talk/MathDeep/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Carola-Bibiane Schönlieb (University of Cambridge) DTSTART:20210629T101500Z DTEND:20210629T114500Z DTSTAMP:20260422T212528Z UID:MathDeep/11 DESCRIPTION:Title: Deeply learned regularisation for inverse problems\nby Carola-Bibian e Schönlieb (University of Cambridge) as part of Mathematics of Deep Lear ning\n\n\nAbstract\nInverse problems are about the reconstruction of an un known physical quantity from indirect measurements. In imaging\, they appe ar in a variety of places\, from medical imaging\, for instance MRI or CT\ , to remote sensing\, for instance Radar\, to material sciences and molecu lar biology\, for instance electron microscopy. Here\, imaging is a tool f or looking inside specimen\, resolving structures beyond the scale visible to the naked eye\, and to quantify them. It is a mean for diagnosis\, pre diction and discovery.\nMost inverse problems of interest are ill-posed an d require appropriate mathematical treatment for recovering meaningful sol utions. Classically\, inversion approaches are derived almost conclusively in a knowledge driven manner\, constituting handcrafted mathematical mode ls. Examples include variational regularization methods with Tikhonov regu larisation\, the total variation and several sparsity-promoting regularize rs such as the L1 norm of Wavelet coefficients of the solution. While such handcrafted approaches deliver mathematically rigorous and computationall y robust solutions to inverse problems\, they are also limited by our abil ity to model solution properties accurately and to realise these approache s in a computationally efficient manner.\nRecently\, a new paradigm has be en introduced to the regularisation of inverse problems\, which derives re gularised solutions to inverse problems in a data driven way. Here\, the i nversion approach is not mathematically modelled in the classical sense\, but modelled by highly over-parametrised models\, typically deep neural ne tworks\, that are adapted to the inverse problems at hand by appropriately selected (and usually plenty of) training data. Current approaches that f ollow this new paradigm distinguish themselves through solution accuracies paired with computational efficieny that were previously unconceivable.\n In this talk I will provide a glimpse into such deep learning approaches a nd some of their mathematical properties. I will finish with open problems and future research perspectives.\n LOCATION:https://researchseminars.org/talk/MathDeep/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Andreas Bärmann/Kevin Aigner (FAU Erlangen-Nürnberg) DTSTART:20210706T101500Z DTEND:20210706T114500Z DTSTAMP:20260422T212528Z UID:MathDeep/12 DESCRIPTION:Title: Online Learning for Optimization Problems with Unknown or Uncertain Cost Functions\nby Andreas Bärmann/Kevin Aigner (FAU Erlangen-Nürnberg) as part of Mathematics of Deep Learning\n\n\nAbstract\nThe first part of t he talk begins by recapitulating several basic algorithms and results in o nline learning\, in particular the multiplicative weights method and onlin e gradient descent. Based on these algorithms\, we demonstrate how to lear n the objective function of a decision-maker while only observing the prob lem input data and the decision-maker’s corresponding decisions over mul tiple rounds. Our approach works for linear objectives over arbitrary feas ible sets for which we have a linear optimization oracle. The two exact al gorithms we present – based on multiplicative weights updates and online gradient descent respectively – converge at a rate of $O(1/\\sqrt T)$ a nd thus allow taking decisions which are essentially as good as those of t he observed decision-maker already after relatively few observations. We s how the effectiveness and possible applications of our methods in a broad computational study. This is joint work with Alexander Martin\, Sebastian Pokutta and Oskar Schneider.\n\nIn the second part of the talk\, we consid er the robust treatment of stochastic optimization problems involving rand om vectors with unknown discrete probability distributions. With this prob lem class\, we demonstrate the basic concepts of data-driven optimization under uncertainty. Furthermore\, we introduce a new iterative approach tha t uses scenario observations to learn more about the uncertainty over time . This means our solutions become less and less conservative\, interpolati ng between distributionally robust and stochastic optimization. We achieve this by solving the distributionally robust optimization problem over tim e via an online-learning approach while iteratively updating the ambiguity sets. We provide a regret bound for the quality of the obtained solutions that converges at a rate of $O(\\log T/T)$ and illustrate the effectivene ss of our procedure by numerical experiments. Our proposed algorithm is ab le to solve the online learning problem significantly faster than equivale nt reformulations. This is joint work with Kristin Braun\, Frauke Liers\, Sebastian Pokutta\, Oskar Schneider\, Kartikey Sharma and Sebastian Tschup pik.\n LOCATION:https://researchseminars.org/talk/MathDeep/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Anne Koelewijn (FAU Erlangen-Nürnberg) DTSTART:20210713T101500Z DTEND:20210713T114500Z DTSTAMP:20260422T212528Z UID:MathDeep/13 DESCRIPTION:Title: Biomechanics meets Deep Learning\nby Anne Koelewijn (FAU Erlangen-N ürnberg) as part of Mathematics of Deep Learning\n\n\nAbstract\nBiomechan ics is the study of human movement. Until recently\, artificial intelligen ce (AI) or deep learning was hardly used in biomechanics research\, but in stead it was mainly based on physical models and experiments. However\, re cently deep learning has also become increasingly important in the field o f biomechanics. This talk will discuss different ways how biomechanics and deep learning can be combined to improve research outcomes in movement an alysis. In the first part of the talk\, we start with a general introducti on into movement analysis\, and discuss more traditional methods that are used in the field. Mainly\, we will cover how gait simulations can be crea ted by solving trajectory optimization problems\, since here many benefits of adding AI/deep learning can be identified. In the second part of the t alk\, we will discuss the combination of biomechanics and deep learning. F irst\, we will discuss different ways to improve biomechanics models with deep learning\, and highlight one example regarding energy expenditure mod els. Finally\, we will discuss how gait simulations can be used to improve outcomes of deep learning models\, by creating larger datasets.\n LOCATION:https://researchseminars.org/talk/MathDeep/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Jevgenija Rudzusika (KTH Stockholm) DTSTART:20210720T101500Z DTEND:20210720T114500Z DTSTAMP:20260422T212528Z UID:MathDeep/14 DESCRIPTION:Title: Accelerated Forward-Backward Optimization using Deep Learning\nby Je vgenija Rudzusika (KTH Stockholm) as part of Mathematics of Deep Learning\ n\n\nAbstract\nWe propose several deep-learning accelerated optimization s olvers with convergence guarantees. We use ideas from the analysis of acce lerated forward-backward schemes like FISTA\, but instead of the classical approach of proving convergence for a choice of parameters\, such as a st ep-size\, we show convergence whenever the update is chosen in a specific set. Rather than picking a point in this set using some predefined method\ , we train a deep neural network to pick the best update. Finally\, we sho w that the method is applicable to several cases of smooth and non-smooth optimization and show superior results to established accelerated solvers. \n LOCATION:https://researchseminars.org/talk/MathDeep/14/ END:VEVENT END:VCALENDAR