Computational imaging is a rapid ly growing area that seeks to enhance the capabilities of imaging instrume nts by viewing imaging as an inverse problem. There are currently two dist inct approaches for designing computational imaging methods: model-based a nd learning-based. Model-based methods leverage analytical signal properti es and often come with theoretical guarantees and insights. Learning-based methods leverage data-driven representations for best empirical performan ce through training on large datasets. This talk presents Regularization b y Artifact Removal (RARE)\, as a framework for reconciling both viewpoints by providing a learning-based extension to the classical theory. RARE rel ies on pre-trained “artifact-removing deep neural nets” for infusing l earned prior knowledge into an inverse problem\, while maintaining a clear separation between the prior and physics-based acquisition model. Our resul ts indicate that RARE can achieve state-of-the-art performance in differen t computational imaging tasks\, while also being amenable to rigorous theo retical analysis. We will focus on the applications of RARE in biomedical imaging\, including magnetic resonance and tomographic imaging.
\n\nThis talk will be based on the following references
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\n LOCATION:https://stable.researchseminars.org/talk/MPML/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Ruth Misener (Imperial College London) DTSTART:20210618T130000Z DTEND:20210618T140000Z DTSTAMP:20260404T094311Z UID:MPML/47 DESCRIPTION:Title: Partition-based formulations for mixed-integer optimization of traine d ReLU neural networks\nby Ruth Misener (Imperial College London) as p art of Mathematics\, Physics and Machine Learning (IST\, Lisbon)\n\n\nAbst ract\nThis work develops a class of relaxations in between the big-M and c onvex hull formulations of disjunctions\, drawing advantages from both. We show that this class leads to mixed-integer formulations for trained ReLU neural networks. The approach balances model size and tightness by partit ioning node inputs into a number of groups and forming the convex hull ove r the partitions via disjunctive programming. At one extreme\, one partiti on per input recovers the convex hull of a node\, i.e.\, the tightest poss ible formulation for each node. For fewer partitions\, we develop smaller relaxations that approximate the convex hull\, and show that they outperfo rm existing formulations. Specifically\, we propose strategies for partiti oning variables based on theoretical motivations and validate these strate gies using extensive computational experiments. Furthermore\, the proposed scheme complements known algorithmic approaches\, e.g.\, optimization-bas ed bound tightening captures dependencies within a partition.\n\nThis join t work with Calvin Tsay\, Jan Kronqvist\, Alexander Thebelt is based on tw o papers: https://arxiv.org/abs/2102.04373 & https://arxiv.org/abs/2101.1 2708\n LOCATION:https://stable.researchseminars.org/talk/MPML/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Mathieu Blondel (Google Research\, Brain team\, Paris) DTSTART:20210604T130000Z DTEND:20210604T140000Z DTSTAMP:20260404T094311Z UID:MPML/48 DESCRIPTION:Title: Efficient and Modular Implicit Differentiation\nby Mathieu Blonde l (Google Research\, Brain team\, Paris) as part of Mathematics\, Physics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nAutomatic differentiati on (autodiff) has revolutionized machine learning. It allows expressing co mplex computations by composing elementary ones in creative ways and remov es the burden of computing their derivatives by hand. More recently\, diff erentiation of optimization problem solutions has attracted widespread att ention with applications such as optimization as a layer\, and in bi-level problems such as hyper-parameter optimization and meta-learning. However\ , the formulas for these derivatives often involve case-by-case tedious ma thematical derivations. In this work\, we propose a unified\, efficient an d modular approach for implicit differentiation of optimization problems. In our approach\, the user defines (in Python in the case of our implement ation) a function F capturing the optimality conditions of the problem to be differentiated. Once this is done\, we leverage autodiff of F and impli cit differentiation to automatically differentiate the optimization proble m. Our approach thus combines the benefits of implicit differentiation and autodiff. It is efficient as it can be added on top of any state-of-the-a rt solver and modular as the optimality condition specification is decoupl ed from the implicit differentiation mechanism. We show that seemingly sim ple principles allow to recover many recently proposed implicit differenti ation methods and create new ones easily. We demonstrate the ease of formu lating and solving bi-level optimization problems using our framework. We also showcase an application to the sensitivity analysis of molecular dyna mics.\n LOCATION:https://stable.researchseminars.org/talk/MPML/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuejie Chi (Carnegie Mellon University) DTSTART:20210625T130000Z DTEND:20210625T140000Z DTSTAMP:20260404T094311Z UID:MPML/49 DESCRIPTION:Title: Policy Optimization in Reinforcement Learning: A Tale of Precondition ing and Regularization\nby Yuejie Chi (Carnegie Mellon University) as part of Mathematics\, Physics and Machine Learning (IST\, Lisbon)\n\n\nAbs tract\nPolicy optimization\, which learns the policy of interest by maximi zing the value function via large-scale optimization techniques\, lies at the heart of modern reinforcement learning (RL). In addition to value maxi mization\, other practical considerations arise commonly as well\, includi ng the need of encouraging exploration\, and that of ensuring certain stru ctural properties of the learned policy due to safety\, resource and opera tional constraints. These considerations can often be accounted for by res orting to regularized RL\, which augments the target value function with a structure-promoting regularization term\, such as Shannon entropy\, Tsall is entropy\, and log-barrier functions. Focusing on an infinite-horizon di scounted Markov decision process\, this talk first shows that entropy-regu larized natural policy gradient methods converge globally at a linear conv ergence that is near independent of the dimension of the state-action spac e. Next\, a generalized policy mirror descent algorithm is proposed to acc ommodate a general class of convex regularizers beyond Shannon entropy. En couragingly\, this general algorithm inherits similar convergence guarante es\, even when the regularizer lacks strong convexity and smoothness. Our results accommodate a wide range of learning rates\, and shed light upon t he role of regularization in enabling fast convergence in RL.\n LOCATION:https://stable.researchseminars.org/talk/MPML/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Ard Louis (University of Oxford) DTSTART:20210702T130000Z DTEND:20210702T140000Z DTSTAMP:20260404T094311Z UID:MPML/50 DESCRIPTION:Title: Deep neural networks have an inbuilt Occam's razor\nby Ard Louis (University of Oxford) as part of Mathematics\, Physics and Machine Learni ng (IST\, Lisbon)\n\n\nAbstract\nOne of the most surprising properties of deep neural networks (DNNs) is that they perform best in the overparameter ized regime. We are taught early on that having more parameters than data points is a terrible idea. So why do DNNs work so well in a regime where c lassical learning theory predicts they should heavily overfit? By adapting the coding theorem from algorithmic information theory (which every physi cist should learn about!) we show that DNNs are exponentially biased at in itialisation to functions that have low descriptional (Kolmogorov) complex ity. In other words\, DNNs have an inbuilt Occam's razor\, a bias towards simple functions. We next show that stochastic gradient descent (SGD)\, th e most popular optimisation method for DNNs\, follows the same bias\, and so does not itself explain the good generalisation of DNNs. Our approach n aturally leads to a marginal-likelihood PAC-Bayes generalisation bound whi ch performs better than any other bounds on the market. Finally\, we discu ss why this bias towards simplicity allows DNNs to perform so well\, and s peculate on what this may tell us about the natural world.\n LOCATION:https://stable.researchseminars.org/talk/MPML/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Usman Khan (Tufts University) DTSTART:20210709T130000Z DTEND:20210709T140000Z DTSTAMP:20260404T094311Z UID:MPML/51 DESCRIPTION:Title: Distributed ML: Optimal algorithms for distributed stochastic non-con vex optimization\nby Usman Khan (Tufts University) as part of Mathemat ics\, Physics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nIn many e merging applications\, it is of paramount interest to learn hidden paramet ers from data. For example\, self-driving cars may use onboard cameras to identify pedestrians\, highway lanes\, or traffic signs in various light a nd weather conditions. Problems such as these can be framed as classificat ion\, regression\, or risk minimization in general\, at the heart of which lies stochastic optimization and machine learning. In many practical scen arios\, distributed and decentralized learning methods are preferable as t hey benefit from a divide-and-conquer approach towards data at the expense of local (short-range) communication. In this talk\, I will present our r ecent work that develops a novel algorithmic framework to address various aspects of decentralized stochastic first-order optimization methods for n on-convex problems. A major focus will be to characterize regimes where de centralized solutions outperform their centralized counterparts and lead t o optimal convergence guarantees. Moreover\, I will characterize certain d esirable attributes of decentralized methods in the context of linear spee dup and networkindependent convergence rates. Throughout the talk\, I will demonstrate such key aspects of the proposed methods with the help of pro vable theoretical results and numerical experiments on real data.\n LOCATION:https://stable.researchseminars.org/talk/MPML/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Simon Du (University of Washington) DTSTART:20210728T160000Z DTEND:20210728T170000Z DTSTAMP:20260404T094311Z UID:MPML/52 DESCRIPTION:Title: Provable Representation Learning\nby Simon Du (University of Wash ington) as part of Mathematics\, Physics and Machine Learning (IST\, Lisbo n)\n\n\nAbstract\nRepresentation learning has been widely used in many app lications. In this talk\, I will present our work\, which uncovers when an d why representation learning provably improves the sample efficiency\, fr om a statistical learning point of view. I will show 1) the existence of a good representation among all tasks\, and 2) the diversity of tasks are k ey conditions that permit improved statistical efficiency via multi-task r epresentation learning. These conditions provably improve the sample effic iency for functions with certain complexity measures as the representation . If time permits\, I will also talk about leveraging the theoretical insi ghts to improve practical performance.\n LOCATION:https://stable.researchseminars.org/talk/MPML/52/ END:VEVENT BEGIN:VEVENT SUMMARY:J. Nathan Kutz (University of Washington) DTSTART:20210916T160000Z DTEND:20210916T170000Z DTSTAMP:20260404T094311Z UID:MPML/53 DESCRIPTION:Title: Deep learning for the discovery of parsimonious physics models\nb y J. Nathan Kutz (University of Washington) as part of Mathematics\, Physi cs and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nA major challenge in the study of dynamical systems is that of model discovery: turning data i nto reduced order models that are not just predictive\, but provide insigh t into the nature of the underlying dynamical system that generated the da ta. We introduce a number of data-driven strategies for discovering nonlin ear multiscale dynamical systems and their embeddings from data. We consid er two canonical cases: (i) systems for which we have full measurements of the governing variables\, and (ii) systems for which we have incomplete m easurements. For systems with full state measurements\, we show that the r ecent sparse identification of nonlinear dynamical systems (SINDy) method can discover governing equations with relatively little data and introduce a sampling method that allows SINDy to scale efficiently to problems with multiple time scales\, noise and parametric dependencies. For systems w ith incomplete observations\, we show that the Hankel alternative view of Koopman (HAVOK) method\, based on time-delay embedding coordinates and the dynamic mode decomposition\, can be used to obtain a linear models and Ko opman invariant measurement systems that nearly perfectly captures the dyn amics of nonlinear quasiperiodic systems. Neural networks are used in targ eted ways to aid in the model reduction process. Together\, these approach es provide a suite of mathematical strategies for reducing the data requir ed to discover and model nonlinear multiscale systems.\n LOCATION:https://stable.researchseminars.org/talk/MPML/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Leong Chuan Kwek (Nanyang Technological University\, Singapore) DTSTART:20210923T090000Z DTEND:20210923T100000Z DTSTAMP:20260404T094311Z UID:MPML/54 DESCRIPTION:Title: Machine Learning and Quantum Technology\nby Leong Chuan Kwek (Nan yang Technological University\, Singapore) as part of Mathematics\, Physic s and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nThe rise of machine l earning in recent times has remarkably transformed science and society. Th e goal of machine learning is to get computers to act without being explic itly programmed. Machine learning with deep reinforcement learning (RL) wa s recently recognized as a powerful tool to engineer dynamics in quantum s ystem. Also\, recently there has been some interest to exploit and leverag e the limited available quantum resources for performing classically chall enging tasks with noisy intermediate-scale quantum (NISQ) computers. Here\ , we discuss some of our recent work on the applications of machine learni ng to quantum systems.\n LOCATION:https://stable.researchseminars.org/talk/MPML/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Constantino Tsallis (Group of Statistical Physics\, CBPF and Santa Fe Institute) DTSTART:20211021T160000Z DTEND:20211021T170000Z DTSTAMP:20260404T094311Z UID:MPML/55 DESCRIPTION:Title: Statistical mechanics for complex systems\nby Constantino Tsallis (Group of Statistical Physics\, CBPF and Santa Fe Institute) as part of M athematics\, Physics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nTo gether with Newtonian mechanics\, Maxwell electromagnetism\, Einstein rela tivity and quantum mechanics\, Boltzmann-Gibbs (BG) statistical mechanics constitutes one of the pillars of contemporary theoretical physics\, with uncountable applications in science and technology. This theory applies fo rmidably well to a plethora of physical systems. Still\, it fails in the r ealm of complex systems\, characterized by generically strong space-time e ntanglement of their elements. On the basis of a nonadditive entropy (defi ned by an index q\, which recovers\, for q=1\, the celebrated Boltzmann-Gi bbs-von Neumann-Shannon entropy)\, it is possible to generalize the BG the ory. We will briefly review the foundations and applications in natural\, artificial and social systems.\n\nA Bibliography is available at http://ts allis.cat.cbpf.br/biblio.htm\n LOCATION:https://stable.researchseminars.org/talk/MPML/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Volkan Cevher (Laboratory for Information and Inference Systems – LIONS\, EPFL) DTSTART:20210930T160000Z DTEND:20210930T170000Z DTSTAMP:20260404T094311Z UID:MPML/56 DESCRIPTION:Title: Optimization Challenges in Adversarial Machine Learning\nby Volka n Cevher (Laboratory for Information and Inference Systems – LIONS\, EPF L) as part of Mathematics\, Physics and Machine Learning (IST\, Lisbon)\n\ n\nAbstract\nThanks to neural networks (NNs)\, faster computation\, and ma ssive datasets\, machine learning (ML) is under increasing pressure to pro vide automated solutions to even harder real-world tasks beyond human perf ormance with ever faster response times due to potentially huge technologi cal and societal benefits. Unsurprisingly\, the NN learning formulations p resent a fundamental challenge to the back-end learning algorithms despite their scalability\, in particular due to the existence of traps in the no n-convex optimization landscape\, such as saddle points\, that can prevent algorithms from obtaining “good” solutions.\n\nIn this talk\, we desc ribe our recent research that has demonstrated that the non-convex optimiz ation dogma is false by showing that scalable stochastic optimization algo rithms can avoid traps and rapidly obtain locally optimal solutions. Coupl ed with the progress in representation learning\, such as over-parameteriz ed neural networks\, such local solutions can be globally optimal.\n\nUnfo rtunately\, this talk will also demonstrate that the central min-max optim ization problems in ML\, such as generative adversarial networks (GANs)\, robust reinforcement learning (RL)\, and\ndistributionally robust ML\, con tain spurious attractors that do not include any stationary points of the original learning formulation. Indeed\, we will describe how algorithms ar e subject to a grander challenge\, including unavoidable convergence failu res\, which could explain the stagnation in their progress despite the imp ressive earlier demonstrations.\n LOCATION:https://stable.researchseminars.org/talk/MPML/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Clément Hongler (EPFL) DTSTART:20211014T160000Z DTEND:20211014T170000Z DTSTAMP:20260404T094311Z UID:MPML/57 DESCRIPTION:Title: Neural Tangent Kernel\nby Clément Hongler (EPFL) as part of Math ematics\, Physics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nThe N eural Tangent Kernel is a new way to understand the gradient descent in de ep neural networks\, connecting them with kernel methods. In this talk\, I 'll introduce this formalism and give a number of results on the Neural Ta ngent Kernel and explain how they give us insight into the dynamics of neu ral networks during training and into their generalization features.\n\nBa sed off joint works with Arthur Jacot and Franck Gabriel.\n LOCATION:https://stable.researchseminars.org/talk/MPML/57/ END:VEVENT BEGIN:VEVENT SUMMARY:George Em Karniadakis (Brown University) DTSTART:20211104T170000Z DTEND:20211104T180000Z DTSTAMP:20260404T094311Z UID:MPML/58 DESCRIPTION:Title: Operator regression via DeepOnet: Theory\, Algorithms and Application s\nby George Em Karniadakis (Brown University) as part of Mathematics\ , Physics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nWe will revie w physics-informed neural network and summarize available theoretical resu lts. We will also introduce new NNs that learn functionals and nonlinear o perators from functions and corresponding responses for system identificat ion. The universal approximation theorem of operators is suggestive of the potential of NNs in learning from scattered data any continuous operator or complex system. We first generalize the theorem to deep neural networks \, and subsequently we apply it to design a new composite NN with small ge neralization error\, the deep operator network (DeepONet)\, consisting of a NN for encoding the discrete input function space (branch net) and anoth er NN for encoding the domain of the output functions (trunk net). We demo nstrate that DeepONet can learn various explicit operators\, e.g.\, integr als\, Laplace transforms and fractional Laplacians\, as well as implicit o perators that represent deterministic and stochastic differential equation s. More generally\, DeepOnet can learn multiscale operators spanning acros s many scales and trained by diverse sources of data simultaneously.\n LOCATION:https://stable.researchseminars.org/talk/MPML/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Arbel (INRIA Grenoble Rhône-Alpes) DTSTART:20211111T170000Z DTEND:20211111T180000Z DTSTAMP:20260404T094311Z UID:MPML/59 DESCRIPTION:Title: Annealed Flow Transport Monte Carlo\nby Michael Arbel (INRIA Gren oble Rhône-Alpes) as part of Mathematics\, Physics and Machine Learning ( IST\, Lisbon)\n\n\nAbstract\nAnnealed Importance Sampling (AIS) and its Se quential Monte Carlo (SMC) extensions are state-of-the-art methods for est imating normalizing constants of probability distributions. We propose her e a novel Monte Carlo algorithm\, Annealed Flow Transport (AFT)\, that bui lds upon AIS and SMC and combines them with normalizing flows (NF) for imp roved performance. This method transports a set of particles using not onl y importance sampling (IS)\, Markov chain Monte Carlo (MCMC) and resamplin g steps - as in SMC\, but also relies on NF which are learned sequentially to push particles towards the successive annealed targets. We provide lim it theorems for the resulting Monte Carlo estimates of the normalizing con stant and expectations with respect to the target distribution. Additional ly\, we show that a continuous-time scaling limit of the population versio n of AFT is given by a Feynman--Kac measure which simplifies to the law of a controlled diffusion for expressive NF. We demonstrate experimentally t he benefits and limitations of our methodology on a variety of application s.\n LOCATION:https://stable.researchseminars.org/talk/MPML/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Soledad Villar (Mathematical Institute for Data Science at Johns H opkins University) DTSTART:20211202T170000Z DTEND:20211202T180000Z DTSTAMP:20260404T094311Z UID:MPML/60 DESCRIPTION:Title: Equivariant machine learning structure like classical physics\nby Soledad Villar (Mathematical Institute for Data Science at Johns Hopkins University) as part of Mathematics\, Physics and Machine Learning (IST\, L isbon)\n\n\nAbstract\nThere has been enormous progress in the last few yea rs in designing neural networks that respect the fundamental symmetries an d coordinate freedoms of physical law. Some of these frameworks make use o f irreducible representations\, some make use of high-order tensor objects \, and some apply symmetry-enforcing constraints. Different physical laws obey different combinations of fundamental symmetries\, but a large fracti on (possibly all) of classical physics is equivariant to translation\, rot ation\, reflection (parity)\, boost (relativity)\, and permutations. Here we show that it is simple to parameterize universally approximating polyno mial functions that are equivariant under these symmetries\, or under the Euclidean\, Lorentz\, and Poincare groups\, at any dimensionality d. The k ey observation is that nonlinear O(d)-equivariant (and related-group-equiv ariant) functions can be expressed in terms of a lightweight collection of scalars---scalar products and scalar contractions of the scalar\, vector\ , and tensor inputs. These results demonstrate theoretically that gauge-in variant deep learning models for classical physics with good scaling for l arge problems are feasible right now.\n LOCATION:https://stable.researchseminars.org/talk/MPML/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Pier Luigi Dragotti (Department of Electrical and Electronic Engin eering\, Imperial College\, London) DTSTART:20211209T170000Z DTEND:20211209T180000Z DTSTAMP:20260404T094311Z UID:MPML/61 DESCRIPTION:Title: Computational Imaging for Art investigation and for Neuroscience\ nby Pier Luigi Dragotti (Department of Electrical and Electronic Engineeri ng\, Imperial College\, London) as part of Mathematics\, Physics and Machi ne Learning (IST\, Lisbon)\n\n\nAbstract\nThe revolution in sensing\, with the emergence of many new imagingtechniques\, offers the possibility of g aining unprecedented access tothe physical world\, but this revolution can only bear fruit through the skilful interplay between the physical and co mputational worlds. This is the domain of computational imaging which advo cates that\, to develop effective imaging systems\, it will be necessary t o go beyond the traditional decoupled imaging pipeline where device physic s\, image processing and the end-user application are considered separatel y. Instead\, we need to rethink imaging as an integrated sensing and infer ence model. In this talk we cover two research areas where computational i maging is likely to have an impact.\n\nWe first focus on the heritage sect or which is experiencing a digital revolution driven in part by the increa sing use of non-invasive\, non-destructive imaging techniques. These new i maging methods provide a way to capture information about an entire painti ng and can give us information about features at or below the surface of t he painting. We focus on Macro X-Ray Fluorescence (XRF) scanning which is a technique for the mapping of chemical elements in paintings. After descr ibing in broad terms the working of this device\, a method that can proces s XRF scanning data from paintings is introduced. The method is based on c onnecting the problem of extracting elemental maps in XRF data to Prony's method\, a technique broadly used in engineering to estimate frequencies o f a sum of sinusoids. The results presented show the ability of our method to detect and separate weak signals related to hidden chemical elements i n the paintings. We then discuss results on the Leonardo's "The Virgin of the Rocks" and show that our algorithm is able to reveal\, more clearly th an ever before\, the hidden drawings of a previous composition that Leonar do then abandoned for the painting that we can now see.\n\nIn the second p art of the talk\, we focus on two-photon microscopy and neuroscience. To u nderstand how networks of neurons process information\, it is essential to monitor their activity in living tissue. Multi-photon microscopy is unpar alleled in its ability to image cellular activity and neural circuits\, de ep in living tissue\, at single-cell resolution. However\, in order to ach ieve step changes in our understanding of brain function\, large-scale ima ging studies of neural populations are needed and this can be achieved onl y by developing computational tools that can enhance the quality of the da ta acquired and can scan 3-D volumes quickly. In this talk we introduce li ght-field microscopy and present a method to localize neurons in 3-D. The method is based on the use of proper sparsity priors\, novel optimization strategies and machine learning.\n\n\nThis is joint work with A. Foust\, P . Song\, C. Howe\, H. Verinaz\, J. Huang and Y.Su from Imperial College Lo ndon\, and C. Higgitt and N. Daly from The National Gallery in London\n LOCATION:https://stable.researchseminars.org/talk/MPML/61/ END:VEVENT BEGIN:VEVENT SUMMARY:Suman Ravuri (DeepMind) DTSTART:20211125T170000Z DTEND:20211125T180000Z DTSTAMP:20260404T094311Z UID:MPML/62 DESCRIPTION:Title: Skilful precipitation nowcasting using deep generative models of rada r\nby Suman Ravuri (DeepMind) as part of Mathematics\, Physics and Mac hine Learning (IST\, Lisbon)\n\n\nAbstract\nPrecipitation nowcasting\, the high-resolution forecasting of precipitation up to two hours ahead\, supp orts the real-world socioeconomic needs of many sectors reliant on weather -dependent decision-making. State-of-the-art operational nowcasting method s typically advect precipitation fields with radar-based wind estimates\, and struggle to capture important non-linear events such as convective ini tiations. Recently introduced deep learning methods use radar to directly predict future rain rates\, free of physical constraints. While they accur ately predict low-intensity rainfall\, their operational utility is limite d because their lack of constraints produces blurry nowcasts at longer lea d times\, yielding poor performance on rarer medium-to-heavy rain events. Here we present a deep generative model for the probabilistic nowcasting o f precipitation from radar that addresses these challenges. Using statisti cal\, economic and cognitive measures\, we show that our method provides i mproved forecast quality\, forecast consistency and forecast value. Our mo del produces realistic and spatiotemporally consistent predictions over re gions up to 1\,536 km × 1\,280 km and with lead times from 5–90 min ahead. Using a systematic evaluation by more than 50 expert meteoro logists\, we show that our generative model ranked first for its accuracy and usefulness in 89% of cases against two competitive methods. When verif ied quantitatively\, these nowcasts are skillful without resorting to blur ring. We show that generative nowcasting can provide probabilistic predict ions that improve forecast value and support operational utility\, and at resolutions and lead times where alternative methods struggle.\n LOCATION:https://stable.researchseminars.org/talk/MPML/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Dan Roberts (MIT\, Center for Theoretical Physics) DTSTART:20220113T170000Z DTEND:20220113T180000Z DTSTAMP:20260404T094311Z UID:MPML/63 DESCRIPTION:Title: The Principles of Deep Learning Theory\nby Dan Roberts (MIT\, Cen ter for Theoretical Physics) as part of Mathematics\, Physics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nDeep learning is an exciting approa ch to modern artificial intelligence based on artificial neural networks. The goal of this talk is to provide a blueprint — using tools from physi cs — for theoretically analyzing deep neural networks of practical relev ance. This task will encompass both understanding the statistics of initia lized deep networks and determining the training dynamics of such an ensem ble when learning from data.\n\nThis talk is based on a book\, "The Principles of Deep Learning Theor y\," co-authored with Sho Yaida and based on research also in collabor ation with Boris Hanin. It will be published next year by Cambridge Univer sity Press.\n LOCATION:https://stable.researchseminars.org/talk/MPML/63/ END:VEVENT BEGIN:VEVENT SUMMARY:Anders Hansen (Faculty of Mathematics and Department of Applied Ma thematics and Theoretical Physics\, University of Cambridge) DTSTART:20220120T170000Z DTEND:20220120T180000Z DTSTAMP:20260404T094311Z UID:MPML/64 DESCRIPTION:Title: Why things don’t work — On the extended Smale's 9th and 18th prob lems (the limits of AI) and methodological barriers\nby Anders Hansen (Faculty of Mathematics and Department of Applied Mathematics and Theoreti cal Physics\, University of Cambridge) as part of Mathematics\, Physics an d Machine Learning (IST\, Lisbon)\n\n\nAbstract\nThe alchemists wanted to create gold\, Hilbert wanted an algorithm to solve Diophantine equations\, researchers want to make deep learning robust in AI\, MATLAB wants (but f ails) to detect when it provides wrong solutions to linear programs etc. W hy does one not succeed in so many of these fundamental cases? The reason is typically methodological barriers. The history of science is full of me thodological barriers — reasons for why we never succeed in reaching cer tain goals. In many cases\, this is due to the foundations of mathematics. We will present a new program on methodological barriers and foundations of mathematics\, where — in this talk — we will focus on two basic pro blems: (1) The instability problem in deep learning: Why do researchers fa il to produce stable neural networks in basic classification and computer vision problems that can easily be handled by humans — when one can prov e that there exist stable and accurate neural networks? Moreover\, AI algo rithms can typically not detect when they are wrong\, which becomes a seri ous issue when striving to create trustworthy AI. The problem is more gene ral\, as for example MATLAB's linprog routine is incapable of certifying c orrect solutions of basic linear programs. Thus\, we’ll address the foll owing question: (2) Why are algorithms (in AI and computations in general) incapable of determining when they are wrong? These questions are deeply connected to the extended Smale’s 9th and 18th problems on the list of m athematical problems for the 21st century.\n LOCATION:https://stable.researchseminars.org/talk/MPML/64/ END:VEVENT BEGIN:VEVENT SUMMARY:Joosep Pata (National Institute of Chemical Physics and Biophysics \, Estonia) DTSTART:20220203T170000Z DTEND:20220203T180000Z DTSTAMP:20260404T094311Z UID:MPML/65 DESCRIPTION:Title: Machine learning for data reconstruction at the LHC\nby Joosep Pa ta (National Institute of Chemical Physics and Biophysics\, Estonia) as pa rt of Mathematics\, Physics and Machine Learning (IST\, Lisbon)\n\n\nAbstr act\nPhysics analyses at the CERN experiments rely on detector hits being interpreted or reconstructed as particle candidates. The data reconstructi on systems are built on decades of physics and detector knowledge and must operate reliably on petabytes of data in diverse computing centers spread around the world. In the recent years\, machine learning (ML) is playing an increasingly important role at the LHC experiments for reconstructing a nd interpreting the data\, from calibrating the detector readouts to the f inal interpretation for complex signal processes. We will discuss the vari ous aspects of ML at the LHC experiments\, focusing on data reconstruction and particle identification approaches using modern machine learning meth ods such as graph neural networks. We will bring a concrete detailed examp le from machine learned particle flow (MLPF)\, an R&D effort to develop a fully optimizable particle flow reconstruction across detector subsystems in CMS.\n LOCATION:https://stable.researchseminars.org/talk/MPML/65/ END:VEVENT BEGIN:VEVENT SUMMARY:Jan Kieseler (European Organization for Nuclear Research (CERN)) DTSTART:20220303T170000Z DTEND:20220303T180000Z DTSTAMP:20260404T094311Z UID:MPML/66 DESCRIPTION:Title: The MODE project\nby Jan Kieseler (European Organization for Nucl ear Research (CERN)) as part of Mathematics\, Physics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nThe effective design of instruments that re ly on the interaction of radiation with matter for their operation is a co mplex task. Furthermore\, the underlying physics processes are intrinsical ly stochastic in nature and open a vast space of possible choices for the physical characteristics of the instrument. While even large scale detecto rs such as e.g. at the LHC are built using surrogates for the ultimate phy sics objective\, the MODE Collaboration (an acronym for Machine-learning O ptimized Design of Experiments) aims at developing tools also based on dee p learning techniques to achieve end-to-end optimization of the design of instruments via a fully differentiable pipeline capable of exploring the P areto-optimal frontier of the utility function for future particle collide r experiments and related detectors. The construction of such a differenti able model requires inclusion of information-extraction procedures\, inclu ding data collection\, detector response\, pattern recognition\, and other existing constraints such as cost. This talk will give an introduction to the goals of the newly founded MODE collaboration and highlight some of t he already existing ingredients.\n LOCATION:https://stable.researchseminars.org/talk/MPML/66/ END:VEVENT BEGIN:VEVENT SUMMARY:Fernando E. Rosas (Faculty of Medicine\, Department of Brain Scien ces\, Imperial College) DTSTART:20220324T170000Z DTEND:20220324T180000Z DTSTAMP:20260404T094311Z UID:MPML/67 DESCRIPTION:Title: Towards a deeper understanding of high-order interdependencies in com plex systems\nby Fernando E. Rosas (Faculty of Medicine\, Department o f Brain Sciences\, Imperial College) as part of Mathematics\, Physics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nWe live in an increasingly interconnected world and\, unfortunately\, our understanding of interdepen dency is still limited. As a matter of fact\, while bivariated relationshi ps are at the core of most of our data analysis methods\, there is still n o principled theory to account for the different types of interactions tha t can occur between three or more variables. This talk explores the vast a nd largely unexplored territory of multivariate complexity\, and discusses information-theoretic approaches that have been introduced to fill this i mportant knowledge gap.\n\nThe first part of the talk is devoted to synerg istic phenomena\, which correspond to statistical regularities that affect the whole but not the parts. We explain how synergy can be effectively ca ptured by information-theoretic measures inspired in the nature of high br ain functions\, and how these measures allow us to map complex interdepend encies into hypergraphs. The second part of the talk focuses on a new theo ry of what constitutes causal emergence\, and how it can be measured from time series data. This theory enables a formal\, quantitative account of d ownward causation\, and introduces “causal decoupling” as a complement ary modality of emergence. Importantly\, this not only establishes concept ual tools to frame conjectures about emergence rigorously\, but also provi des practical procedures to test them on data. We illustrate the considere d analysis tools on different case studies\, including cellular automata\, baroque music\, flocking models\, and neuroimaging datasets.\n LOCATION:https://stable.researchseminars.org/talk/MPML/67/ END:VEVENT BEGIN:VEVENT SUMMARY:Josef Urban (Czech Institute of of Informatics\, Robotics and Cybe rnetics (CIIRC)) DTSTART:20220331T160000Z DTEND:20220331T170000Z DTSTAMP:20260404T094311Z UID:MPML/68 DESCRIPTION:Title: Machine Learning and Theorem Proving\nby Josef Urban (Czech Insti tute of of Informatics\, Robotics and Cybernetics (CIIRC)) as part of Math ematics\, Physics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nThe t alk will describe several ways in which machine learning is combined with theorem proving today over large corpora of formal proof. If time permits\ , I will also show some demos of the systems and mention related topics su ch as ML-guided conjecturing and autoformalization.\n LOCATION:https://stable.researchseminars.org/talk/MPML/68/ END:VEVENT BEGIN:VEVENT SUMMARY:André F. T. Martins (Instituto Superior Técnico) DTSTART:20220224T163000Z DTEND:20220224T173000Z DTSTAMP:20260404T094311Z UID:MPML/69 DESCRIPTION:Title: From Sparse Modeling to Sparse Communication\nby André F. T. Mar tins (Instituto Superior Técnico) as part of Mathematics\, Physics and Ma chine Learning (IST\, Lisbon)\n\n\nAbstract\nNeural networks and other mac hine learning models compute continuous representations\, while humans com municate mostly through discrete symbols. Reconciling these two forms of c ommunication is desirable for generating human-readable interpretations or learning discrete latent variable models\, while maintaining end-to-end d ifferentiability.\n\nIn the first part of the talk\, I will describe how s parse modeling techniques can be extended and adapted for facilitating spa rse communication in neural models. The building block is a family of spar se transformations called alpha-entmax\, a drop-in replacement for softmax \, which contains sparsemax as a particular case. Entmax transformations a re differentiable and (unlike softmax) they can return sparse probability distributions\, useful to build interpretable attention mechanisms. Varian ts of these sparse transformations have been applied with success to machi ne translation\, natural language inference\, visual question answering\, and other tasks.\n\nIn the second part\, I will introduce mixed random var iables\, which are in-between the discrete and continuous worlds. We build rigorous theoretical foundations for these hybrids\, via a new “direct sum” base measure defined on the face lattice of the probability simplex . From this measure\, we introduce new entropy and Kullback-Leibler diverg ence functions that subsume the discrete and differential cases and have i nterpretations in terms of code optimality. Our framework suggests two str ategies for representing and sampling mixed random variables\, an extrinsi c (“sample-and-project”) and an intrinsic one (based on face stratific ation).\n\nIn the third part\, I will show how sparse transformations can also be used to design new loss functions\, replacing the cross-entropy lo ss. To this end\, I will introduce the family of Fenchel-Young losses\, re vealing connections between generalized entropy regularizers and separatio n margin. I will illustrate with applications in natural language generati on\, morphology\, and machine translation.\n\nThis work was funded by the DeepSPIN ERC project - https://deep-spin.github.io\n LOCATION:https://stable.researchseminars.org/talk/MPML/69/ END:VEVENT BEGIN:VEVENT SUMMARY:Dmitry Krotov (Watson AI Lab and IBM Research in Cambridge) DTSTART:20220414T160000Z DTEND:20220414T170000Z DTSTAMP:20260404T094311Z UID:MPML/70 DESCRIPTION:Title: Modern Hopfield Networks in AI and Neurobiology\nby Dmitry Krotov (Watson AI Lab and IBM Research in Cambridge) as part of Mathematics\, Ph ysics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nModern Hopfiel d Networks or Dense Associative Memories are recurrent neural networks wit h fixed point attractor states that are described by an energy function. I n contrast to conventional Hopfield Networks\, their modern versions have a very large memory storage capacity\, which makes them appealing tools fo r many problems in machine learning and cognitive and neuro-sciences. In t his talk I will introduce an intuition and a mathematical formulation of t his class of models\, and will give examples of problems in AI that can be tackled using these new ideas. I will also explain how different individu al models of this class (e.g. hierarchical memories\, attention mechanism in transformers\, etc.) arise from their general mathematical formulation with the Lagrangian functions.
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\n LOCATION:https://stable.researchseminars.org/talk/MPML/70/ END:VEVENT BEGIN:VEVENT SUMMARY:Emtiyaz Khan (RIKEN-AIP\, Tokyo and OIST\, Okinawa\, Japan) DTSTART:20220428T090000Z DTEND:20220428T100000Z DTSTAMP:20260404T094311Z UID:MPML/71 DESCRIPTION:Title: The Bayesian Learning Rule for Adaptive AI\nby Emtiyaz Khan (RIKE N-AIP\, Tokyo and OIST\, Okinawa\, Japan) as part of Mathematics\, Physics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nHumans and animals hav e a natural ability to autonomously learn and quickly adapt to their surro undings. How can we design AI systems that do the same? In this talk\, I w ill present Bayesian principles to bridge such gaps between humans and AI. I will show that a wide variety of machine-learning algorithms are instan ces of a single learning-rule called the Bayesian learning rule. The rule unravels a dual perspective yielding new adaptive mechanisms for machine-l earning based AI systems. My hope is to convince the audience that Bayesia n principles are indispensable for an AI that learns as efficiently as we do.\n\nReference: M.E. Khan\, H. Rue\, The Bayesian Le arning Rule [arXiv] [Tweet]
\n LOCATION:https://stable.researchseminars.org/talk/MPML/71/ END:VEVENT BEGIN:VEVENT SUMMARY:Rianne van den Berg (Microsoft Research Amsterdam) DTSTART:20220421T160000Z DTEND:20220421T170000Z DTSTAMP:20260404T094311Z UID:MPML/72 DESCRIPTION:Title: Generative models for discrete random variables\nby Rianne van de n Berg (Microsoft Research Amsterdam) as part of Mathematics\, Physics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nn this talk I will discuss how different classes of generative models can be adapted to handle discr ete random variables\, and how this can be used to connect generative mode ls to downstream tasks such as lossless compression. I will start by discu ssing normalizing flow models\, and the challenges that arise when convert ing these models that are typically designed for real-valued random variab les to discrete random variables. Next\, I will demonstrate how denoising diffusion models with discrete state spaces have a rich design space in te rms of the noising process\, and how this influences the performance of th e learned denoising model. Finally\, I will show how denoising diffusion m odels can be connected to autoregressive models\, and introduce an autoreg ressive model with a random generation order.\n LOCATION:https://stable.researchseminars.org/talk/MPML/72/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrea L. Bertozzi (University of California Los Angeles) DTSTART:20220505T160000Z DTEND:20220505T170000Z DTSTAMP:20260404T094311Z UID:MPML/73 DESCRIPTION:Title: Graph based models in semi-supervised and unsupervised learning\n by Andrea L. Bertozzi (University of California Los Angeles) as part of Ma thematics\, Physics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nSim ilarity graphs provide a structure for analyzing high dimensional data. These undirected weighted graphs provide structure for identifying inherent clusters in datasets and many methods exist to sort through such data building on the graph laplacian matrix. One way to think about suc h problems is in terms of penalized cut problems. These can be expressed in terms of the graph total variation which has a well-known analogue in Euclidean space. We show how to use ideas from geometric methods for PDE s to develop efficient and high performing methods for semi-supervised and unsupervised learning. These methods also extend to active learning and to modularity optimization for community detection on networks.\n LOCATION:https://stable.researchseminars.org/talk/MPML/73/ END:VEVENT BEGIN:VEVENT SUMMARY:Stanley Osher (Department of Mathematics\, University of Californi a\, Los Angeles) DTSTART:20220519T160000Z DTEND:20220519T170000Z DTSTAMP:20260404T094311Z UID:MPML/74 DESCRIPTION:Title: Conservation laws and generalized optimal transport\nby Stanley O sher (Department of Mathematics\, University of California\, Los Angeles) as part of Mathematics\, Physics and Machine Learning (IST\, Lisbon)\n\n\n Abstract\nIn this talk\, we connect Lax’s entropy-entropy flux in conser vation laws with optimal transport type metric spaces. Following this conn ection\, we further design variational discretizations for conservation la ws and mean field control of conservation laws. In particular\, we design unconditionally stable time discretization methods that are easy to implem ent.\n\nOn joint work with Siting Liu\, UCLA and Wuchen Li\, University of South Carolina.\n LOCATION:https://stable.researchseminars.org/talk/MPML/74/ END:VEVENT BEGIN:VEVENT SUMMARY:Anja Butter (ITP\, University of Heidelberg) DTSTART:20220602T160000Z DTEND:20220602T170000Z DTSTAMP:20260404T094311Z UID:MPML/75 DESCRIPTION:Title: Machine Learning and LHC Event Generation\nby Anja Butter (ITP\, University of Heidelberg) as part of Mathematics\, Physics and Machine Lea rning (IST\, Lisbon)\n\n\nAbstract\nFirst-principle simulations are at the heart of the high-energy physics research program. They link the vast dat a output of multi-purpose detectors with fundamental theory predictions an d interpretation. In the coming LHC runs\, these simulations will face unp recedented precision requirements to match the experimental accuracy. New ideas and tools based on neural networks have been developed at the interf ace of particle physics and machine learning. They can improve the speed a nd precision of forward simulations and handle the complexity of collision data. Such networks can be employed within established simulation tools o r as part of a new framework. Since neural networks can be inverted\, they open new avenues in LHC analyses.\n LOCATION:https://stable.researchseminars.org/talk/MPML/75/ END:VEVENT BEGIN:VEVENT SUMMARY:Paulo Tabuada (UCLA) DTSTART:20220609T160000Z DTEND:20220609T170000Z DTSTAMP:20260404T094311Z UID:MPML/77 DESCRIPTION:Title: Deep neural networks\, universal approximation\, and geometric contro l\nby Paulo Tabuada (UCLA) as part of Mathematics\, Physics and Machin e Learning (IST\, Lisbon)\n\n\nAbstract\nDeep neural networks have drastic ally changed the landscape of several engineering areas such as computer v ision and natural language processing. Notwithstanding the widespread succ ess of deep networks in these\, and many other areas\, it is still not wel l understood why deep neural networks work so well. In particular\, the qu estion of which functions can be learned by deep neural networks has remai ned unanswered.\nIn this talk we give an answer to this question for deep residual neural networks\, a class of deep networks that can be interprete d as the time discretization of nonlinear control systems. We will show th at the ability of these networks to memorize training data can be expresse d through the control theoretic notion of controllability which can be pro ved using geometric control techniques. We then add an additional ingredie nt\, monotonicity\, to conclude that deep residual networks can approximat e\, to arbitrary accuracy with respect to the uniform norm\, any continuou s function on a compact subset of n-dimensional Euclidean space by using a t most n+1 neurons per layer. We will conclude the talk by showing how the se results pave the way for the use of deep networks in the perception pip eline of autonomous systems while providing formal (and probability free) guarantees of stability and robustness.\n LOCATION:https://stable.researchseminars.org/talk/MPML/77/ END:VEVENT BEGIN:VEVENT SUMMARY:Petar Veličković (DeepMind and University of Cambridge) DTSTART:20220929T160000Z DTEND:20220929T170000Z DTSTAMP:20260404T094311Z UID:MPML/78 DESCRIPTION:Title: Geometric Deep Learning: Grids\, Graphs\, Groups\, Geodesics and Gaug es\nby Petar Veličković (DeepMind and University of Cambridge) as pa rt of Mathematics\, Physics and Machine Learning (IST\, Lisbon)\n\n\nAbstr act\nThe last decade has witnessed an experimental revolution in data scie nce and machine learning\, epitomised by deep learning methods. Indeed\, m any high-dimensional learning tasks previously thought to be beyond reach –such as computer vision\, playing Go\, or protein folding – are in fa ct feasible with appropriate computational scale. Remarkably\, the essence of deep learning is built from two simple algorithmic principles: first\, the notion of representation or feature learning\, whereby adapted\, ofte n hierarchical\, features capture the appropriate notion of regularity for each task\, and second\, learning by local gradient-descent type methods\ , typically implemented as backpropagation.\n\nWhile learning generic func tions in high dimensions is a cursed estimation problem\, most tasks of in terest are not generic\, and come with essential pre-defined regularities arising from the underlying low-dimensionality and structure of the physic al world. This talk is concerned with exposing these regularities through unified geometric principles that can be applied throughout a wide spectru m of applications.\n\nSuch a 'geometric unification' endeavour in the spir it of Felix Klein's Erlangen Program serves a dual purpose: on one hand\, it provides a common mathematical framework to study the most successful n eural network architectures\, such as CNNs\, RNNs\, GNNs\, and Transformer s. On the other hand\, it gives a constructive procedure to incorporate pr ior physical knowledge into neural architectures and provide principled wa y to build future architectures yet to be invented.\n LOCATION:https://stable.researchseminars.org/talk/MPML/78/ END:VEVENT BEGIN:VEVENT SUMMARY:Yongji Wang (Department of Geosciences\, Princeton University) DTSTART:20220526T160000Z DTEND:20220526T170000Z DTSTAMP:20260404T094311Z UID:MPML/79 DESCRIPTION:Title: Physics-informed neural networks for solving 3-D Euler equation\n by Yongji Wang (Department of Geosciences\, Princeton University) as part of Mathematics\, Physics and Machine Learning (IST\, Lisbon)\n\n\nAbstract \nOne of the most challenging open questions in mathematical fluid dynamic s is whether an inviscid incompressible fluid\, described by the 3-dimensi onal Euler equations\, with initially smooth velocity and finite energy ca n develop singularities in finite time. This long-standing open problem is closely related to one of the seven Millennium Prize Problems which consi ders the problem the viscous analogue to the Euler equations (the Navier-S tokes equations). In this talk\, I will describe how we leverage the power of deep learning\, using deep neural networks with equation constraints\, namely physics-informed neural networks (PINNs)\, to find a smooth self-s imilar blow-up solution for the 3-dimensional Euler equations in the prese nce of a cylindrical boundary. To the best of our knowledge\, the solution represents the first example of a truly 2-D or higher dimensional backwar ds self-similar solution. This new numerical framework based on PINNs is s hown to be robust and readily adaptable to other fluid equations\, which s heds new light to the century-old mystery of capital importance in the fie ld of mathematical fluid dynamics.\n LOCATION:https://stable.researchseminars.org/talk/MPML/79/ END:VEVENT BEGIN:VEVENT SUMMARY:John Baez (U.C. Riverside) DTSTART:20220616T170000Z DTEND:20220616T180000Z DTSTAMP:20260404T094311Z UID:MPML/80 DESCRIPTION:Title: Shannon Entropy from Category Theory\nby John Baez (U.C. Riversid e) as part of Mathematics\, Physics and Machine Learning (IST\, Lisbon)\n\ n\nAbstract\nShannon entropy is a powerful concept. But what properties si ngle out Shannon entropy as special? Instead of focusing on the entropy of a probability measure on a finite set\, it can help to focus on the "info rmation loss"\, or change in entropy\, associated with a measure-preservin g function. Shannon entropy then gives the only concept of information los s that is functorial\, convex-linear and continuous.\n\nThis is joint work with Tom Leinster and Tobias Fritz.\n LOCATION:https://stable.researchseminars.org/talk/MPML/80/ END:VEVENT BEGIN:VEVENT SUMMARY:Dario Izzo (European Space Agency) DTSTART:20220630T160000Z DTEND:20220630T170000Z DTSTAMP:20260404T094311Z UID:MPML/81 DESCRIPTION:Title: Geodesy of irregular small bodies via neural density fields: geodesyN ets\nby Dario Izzo (European Space Agency) as part of Mathematics\, Ph ysics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nThe problem of de termining the density distribution of celestial bodies from the induced gr avitational pull is of great importance in astrophysics as well as space e ngineering (thinking of situations where spacecraft need to perform orbita l and surface proximity operations). Knowledge of a body density distribut ion provides also great insights on the body's origin and composition. In practice\, the state-of-the-art approaches for modelling the gravity field of extended bodies are spherical harmonics models\, mascon models and pol yhedral gravity models. All of these\, however\, while being widely studie d and developed since the early works from Laplace\, introduce requirement s such as knowledge of a shape model\, assumption of a homogeneous interna l density\, being outside the\nBrillouin sphere\, etc...\n\n\nIn this talk \, we introduce and explain Neural Density Fields\, a new approach to repr esent the density of extended bodies and learn its accurate form inverting data from gravitational accelerations\, orbits or the gravity potential. The resulting deep learning model\, called geodesyNets is able to compete with classical approaches while solving most of their limitations. We als o introduce eclipseNets\, a deep learning model based on related ideas and able to learn the eclipse shadow cones of irregular bodies\, thus allowin g highly precise propagation and stability studies.\n LOCATION:https://stable.researchseminars.org/talk/MPML/81/ END:VEVENT BEGIN:VEVENT SUMMARY:Audrey Durand (IID\, Université Laval\, Canada) DTSTART:20220707T160000Z DTEND:20220707T170000Z DTSTAMP:20260404T094311Z UID:MPML/82 DESCRIPTION:Title: Interactive learning for Neurosciences - Between Simulation and Reali ty\nby Audrey Durand (IID\, Université Laval\, Canada) as part of Mat hematics\, Physics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nLear ning a behaviour to conduct a given task can be achieved by interacting wi th the the environment. This is the crux of reinforcement learning (RL)\, where an (automated) agent learns to solve a problem through an iterative trial-and-error process. More specifically\, an RL agent can interact with the environment and learn from these interactions by observing a feedback on the goal task. Therefore\, these methods typically require to be able to intervene on the environment and make (possibly a very large number of) mistakes. Although this can be a limiting factor in some applications\, s imple RL settings\, such as bandit settings\, can still host a variety of problems for interactively learning behaviours. In other situations\, simu lation might be the key.\n\nIn this talk\, we will show that RL can be use d to formulate and tackle data acquisition (imaging) problems in neuroscie nces. We will see how bandit methods can be used to optimize super-resolut ion imaging by learning on real devices through an actual empirical proces s. We will also see how simulation can be leveraged to learn more sequenti al decision making strategies. These applications highlight the potential of RL to support expert users on difficult task and enable new discoveries .\n LOCATION:https://stable.researchseminars.org/talk/MPML/82/ END:VEVENT BEGIN:VEVENT SUMMARY:Joseph Bakarji (University of Washington) DTSTART:20220714T160000Z DTEND:20220714T170000Z DTSTAMP:20260404T094311Z UID:MPML/83 DESCRIPTION:Title: Dimensionally Consistent Learning with Buckingham Pi\nby Joseph B akarji (University of Washington) as part of Mathematics\, Physics and Mac hine Learning (IST\, Lisbon)\n\n\nAbstract\nDimensional analysis is a robu st technique for extracting insights and finding symmetries in physical sy stems\, especially when the governing equations are not known. The Bucking ham Pi theorem provides a procedure for finding a set of dimensionless gro ups from given measurements\, although this set is not unique. We propose an automated approach using the symmetric and self-similar structure of av ailable measurement data to discover the dimensionless groups that best co llapse this data to a lower dimensional space according to an optimal fit. We develop three data-driven techniques that use the Buckingham Pi theore m as a constraint: (i) a constrained optimization problem with a nonparame tric function\, (ii) a deep learning algorithm (BuckiNet) that projects th e input parameter space to a lower dimension in the first layer\, and (iii ) a sparse identification of nonlinear dynamics (SINDy) to discover dimens ionless equations whose coefficients parameterize the dynamics. I discuss the accuracy and robustness of these methods when applied to known nonline ar systems.\n LOCATION:https://stable.researchseminars.org/talk/MPML/83/ END:VEVENT BEGIN:VEVENT SUMMARY:Inês Hipólito (Humboldt-Universität) DTSTART:20220908T160000Z DTEND:20220908T170000Z DTSTAMP:20260404T094311Z UID:MPML/84 DESCRIPTION:Title: The Free Energy Principle in the Edge of Chaos\nby Inês Hipólit o (Humboldt-Universität) as part of Mathematics\, Physics and Machine Lea rning (IST\, Lisbon)\n\n\nAbstract\nLiving beings do an extraordinary thin g. By being alive they are resisting the second law of thermodynamics. Thi s law stipulates that open\, living systems tend to dissipation by the inc rease of entropy or chaos. From minimal cognitive organisms like plants to more complex organisms equipped with nervous systems\, all living systems adjust and adapt to their environments\, thereby resisting the second law . Impressively\, while all animals cognitively enact and survive their loc al environments\, more complex systems do so also by actively constructing their local environments\, thereby not only defying the second law\, but also (evolution) selective properties. Because all living beings defy the second law by adjusting and engaging with the environment\, a prominent qu estion is how do living organisms persist while engaging in adaptive excha nges with their complex environments? In this talk I will offer an overvie w of how the Free Energy Principle (FEP) offers a principled solution to t his problem. The FEP prescribes that living systems maintain themselves by remaining in non-equilibrium steady states by restricting themselves to a limited number of states\; it has been widely applied to explain neurocog nitive function and embodied action\, develop artificial intelligence and inspire psychopathology models.\n LOCATION:https://stable.researchseminars.org/talk/MPML/84/ END:VEVENT BEGIN:VEVENT SUMMARY:Robert Nowak (University of Wisconsin-Madison) DTSTART:20221027T160000Z DTEND:20221027T170000Z DTSTAMP:20260404T094311Z UID:MPML/85 DESCRIPTION:Title: The Neural Balance Theorem and its Consequences\nby Robert Nowak (University of Wisconsin-Madison) as part of Mathematics\, Physics and Mac hine Learning (IST\, Lisbon)\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/MPML/85/ END:VEVENT BEGIN:VEVENT SUMMARY:Frederico Fiuza (SLAC) DTSTART:20221103T170000Z DTEND:20221103T180000Z DTSTAMP:20260404T094311Z UID:MPML/86 DESCRIPTION:Title: Accelerating the understanding of nonlinear dynamical systems using m achine learning\nby Frederico Fiuza (SLAC) as part of Mathematics\, Ph ysics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nThe description o f nonlinear\, multi-scale dynamics is a common challenge in a wide range o f physical systems and research fields — from weather forecast to contro lled nuclear fusion. The development of reduced models that balance betwee n accuracy and complexity is critical to advancing theoretical comprehensi on and enabling holistic computational descriptions of these problems. I w ill discuss how techniques from statistical and machine learning are offer ing new ways of inferring reduced physics models from the increasingly abu ndant data of nonlinear dynamics produced by experiments\, observations\, and simulations. In particular\, I will focus on how sparse regression tec hniques can be used to infer interpretable plasma physics models (in the f orm of nonlinear partial differential equations) directly from the data of first-principles fully-kinetic simulations. The potential of this approac h is demonstrated by recovering the fundamental hierarchy of plasma physic s models based solely on particle-based simulation data of complex plasma dynamics. I will discuss how this data-driven methodology provides a promi sing tool to accelerate the development of reduced theoretical models of n onlinear dynamical systems and to design computationally efficient algorit hms for multi-scale simulations.\n LOCATION:https://stable.researchseminars.org/talk/MPML/86/ END:VEVENT BEGIN:VEVENT SUMMARY:Markus Reichstein (MPI for Biogeochemistry) DTSTART:20221124T170000Z DTEND:20221124T180000Z DTSTAMP:20260404T094311Z UID:MPML/87 DESCRIPTION:Title: Integrating Machine Learning with System Modelling and Observations f or a better understanding of the Earth System\nby Markus Reichstein (M PI for Biogeochemistry) as part of Mathematics\, Physics and Machine Learn ing (IST\, Lisbon)\n\n\nAbstract\nThe Earth is a complex dynamic networked system. Machine learning\, i.e. derivation of computational models from d ata\, has already made important contributions to predict and understand c omponents of the Earth system\, specifically in climate\, remote sensing a nd environmental sciences. For instance\, classifications of land cover ty pes\, prediction of land-atmosphere and ocean-atmosphere exchange\, or det ection of extreme events have greatly benefited from these approaches. Suc h data-driven information has already changed how Earth system models are evaluated and further developed. However\, many studies have not yet suffi ciently addressed and exploited dynamic aspects of systems\, such as memor y effects for prediction and effects of spatial context\, e.g. for classif ication and change detection. In particular new developments in deep learn ing offer great potential to overcome these limitations. Yet\, a key chall enge and opportunity is to integrate (physical-biological) system modeling approaches with machine learning into hybrid modeling approaches\, which combines physical consistency and machine learning versatility. A couple o f examples are given with focus on the terrestrial biosphere\, where the c ombination of system-based and machine-learning-based modelling helps our understanding of aspects of the Earth system.\n LOCATION:https://stable.researchseminars.org/talk/MPML/87/ END:VEVENT BEGIN:VEVENT SUMMARY:Bruno Loureiro (École Polytechnique Fédérale de Lausanne (EPFL) ) DTSTART:20221215T170000Z DTEND:20221215T180000Z DTSTAMP:20260404T094311Z UID:MPML/88 DESCRIPTION:Title: Phase diagram of Stochastic Gradient Descent in high-dimensional two- layer neural networks\nby Bruno Loureiro (École Polytechnique Fédér ale de Lausanne (EPFL)) as part of Mathematics\, Physics and Machine Learn ing (IST\, Lisbon)\n\n\nAbstract\nDespite the non-convex optimization land scape\, over-parametrized shallow networks are able to achieve global conv ergence under gradient descent. The picture can be radically different for narrow networks\, which tend to get stuck in badly-generalizing local min ima. Here we investigate the cross-over between these two regimes in the h igh-dimensional setting\, and in particular investigate the connection bet ween the so-called mean-field/hydrodynamic regime and the seminal approach of Saad & Solla. Focusing on the case of Gaussian data\, we study the int erplay between the learning rate\, the time scale\, and the number of hidd en units in the high-dimensional dynamics of stochastic gradient descent ( SGD). Our work builds on a deterministic description of SGD in high-dimens ions from statistical physics\, which we extend and for which we provide r igorous convergence rates.\n LOCATION:https://stable.researchseminars.org/talk/MPML/88/ END:VEVENT BEGIN:VEVENT SUMMARY:Diogo Gomes (KAUST) DTSTART:20221014T083000Z DTEND:20221014T110000Z DTSTAMP:20260404T094311Z UID:MPML/89 DESCRIPTION:Title: From Calculus of Variations to Reinforcement Learning (Lectures 1 & 2 )\nby Diogo Gomes (KAUST) as part of Mathematics\, Physics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nThis course begins with a brief in troduction to classical calculus of variations and its applications to cla ssical problems such as geodesic trajectories and the brachistochrone prob lem. Then\, we examine Hamilton-Jacobi equations\, the role of convexity a nd the classical verification theorem. Next\, we illustrate the lack of cl assical solutions and motivate the definition of viscosity solutions. The course ends with a brief description of the reinforcement learning problem and its connection with Hamilton-Jacobi equations.\n LOCATION:https://stable.researchseminars.org/talk/MPML/89/ END:VEVENT BEGIN:VEVENT SUMMARY:José Miguel Urbano (KAUST) DTSTART:20221014T133000Z DTEND:20221014T160000Z DTSTAMP:20260404T094311Z UID:MPML/90 DESCRIPTION:Title: Semi-Supervised Learning and the infinite-Laplacian (Lectures 1 & 2)< /a>\nby José Miguel Urbano (KAUST) as part of Mathematics\, Physics and M achine Learning (IST\, Lisbon)\n\n\nAbstract\nMotivated by a recent applic ation in Semi-Supervised Learning (SSL)\, the minicourse is a brief introd uction to the analysis of infinity-harmonic functions. We will discuss the Lipschitz extension problem\, its solution via MacShane-Whitney extension s and its several drawbacks\, leading to the notion of AMLE (Absolutely Mi nimising Lipschitz Extension). We then explore the equivalence between bei ng absolutely minimising Lipschitz\, enjoying comparison with cones and so lving the infinity-Laplace equation in the viscosity sense.\n LOCATION:https://stable.researchseminars.org/talk/MPML/90/ END:VEVENT BEGIN:VEVENT SUMMARY:João Sacramento (ETH Zürich) DTSTART:20221110T170000Z DTEND:20221110T180000Z DTSTAMP:20260404T094311Z UID:MPML/91 DESCRIPTION:Title: The least-control principle for learning at equilibrium\nby João Sacramento (ETH Zürich) as part of Mathematics\, Physics and Machine Lea rning (IST\, Lisbon)\n\n\nAbstract\nA large number of models of interest i n both neuroscience and machine learning can be expressed as dynamical sys tems at equilibrium. This class of systems includes deep neural networks\, equilibrium recurrent neural networks\, and meta-learning. In this talk I will present a new principle for learning equilibria with a temporally - and spatially - local rule. Our principle casts learning as a least-contro l problem\, where we first introduce an optimal controller to lead the sys tem towards a solution state\, and then define learning as reducing the am ount of control needed to reach such a state. We show that incorporating l earning signals within a dynamics as an optimal control enables transmitti ng activity-dependent credit assignment information\, avoids storing inter mediate states in memory\, and does not rely on infinitesimal learning sig nals. In practice\, our principle leads to strong performance matching tha t of leading gradient-based learning methods when applied to an array of b enchmarking experiments. Our results shed light on how the brain might lea rn and offer new ways of approaching a broad class of machine learning pro blems.\n LOCATION:https://stable.researchseminars.org/talk/MPML/91/ END:VEVENT BEGIN:VEVENT SUMMARY:Tom Goldstein (University of Maryland) DTSTART:20221117T170000Z DTEND:20221117T180000Z DTSTAMP:20260404T094311Z UID:MPML/92 DESCRIPTION:Title: Building (and breaking) neural networks that think fast and slow\ nby Tom Goldstein (University of Maryland) as part of Mathematics\, Physic s and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nMost neural networks are built to solve simple patternmatching tasks\, a process that is often known as “fast” thinking. In this talk\, I’ll use adversarial method s to explore the robustness of neural networks. I’ll also discuss whethe r vulnerabilities of AI systems that have been observed in academic labs c an pose real security threats to industrial systems. Then\, I’ll present methods for constructing neural networks that exhibit “slow” thinking abilities akin to human logical reasoning. Rather than learning simple pa ttern matching rules\, these networks have the ability to synthesize algor ithmic reasoning processes and solve difficult discrete search and plannin g problems that cannot be solved by conventional AI systems. Interestingly \, these reasoning systems naturally exhibit error correction and robustne ss properties that make them more difficult to break than their fast think ing counterparts.\n LOCATION:https://stable.researchseminars.org/talk/MPML/92/ END:VEVENT BEGIN:VEVENT SUMMARY:Yang-Hui He (London Institute for Mathematical Sciences & Merton C ollege\, Oxford University) DTSTART:20230202T170000Z DTEND:20230202T180000Z DTSTAMP:20260404T094311Z UID:MPML/93 DESCRIPTION:Title: COLLOQUIUM: Universes as Bigdata: Physics\, Geometry and Machine-Lear ning\nby Yang-Hui He (London Institute for Mathematical Sciences & Mer ton College\, Oxford University) as part of Mathematics\, Physics and Mach ine Learning (IST\, Lisbon)\n\n\nAbstract\nThe search for the Theory of Ev erything has led to superstring theory\, which then led physics\, first to algebraic/differential geometry/topology\, and then to computational geom etry\, and now to data science. With a concrete playground of the geometri c landscape\, accumulated by the collaboration of physicists\, mathematici ans and computer scientists over the last 4 decades\, we show how the late st techniques in machine-learning can help explore problems of interest to theoretical physics and to pure mathematics. At the core of our programme is the question: how can AI help us with mathematics?\n LOCATION:https://stable.researchseminars.org/talk/MPML/93/ END:VEVENT BEGIN:VEVENT SUMMARY:Sebastian Engelke (University of Geneva) DTSTART:20230112T170000Z DTEND:20230112T180000Z DTSTAMP:20260404T094311Z UID:MPML/94 DESCRIPTION:Title: Machine learning beyond the data range: extreme quantile regression\nby Sebastian Engelke (University of Geneva) as part of Mathematics\, P hysics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nMachine learning methods perform well in prediction tasks within the range of the training data. When interest is in quantiles of the response that go beyond the ob served records\, these methods typically break down. Extreme value theory provides the mathematical foundation for estimation of such extreme quanti les. A common approach is to approximate the exceedances over a high thres hold by the generalized Pareto distribution. For conditional extreme quant iles\, one may model the parameters of this distribution as functions of t he predictors. Up to now\, the existing methods are either not flexible en ough or do not generalize well in higher dimensions. We develop new approa ches for extreme quantile regression that estimate the parameters of the g eneralized Pareto distribution with tree-based methods and recurrent neura l networks. Our estimators outperform classical machine learning methods a nd methods from extreme value theory in simulations studies. We illustrate how the recurrent neural network model can be used for effective forecast ing of flood risk.\n LOCATION:https://stable.researchseminars.org/talk/MPML/94/ END:VEVENT BEGIN:VEVENT SUMMARY:Alhussein Fawzi (DeepMind) DTSTART:20230119T170000Z DTEND:20230119T180000Z DTSTAMP:20260404T094311Z UID:MPML/95 DESCRIPTION:Title: Discovering faster matrix multiplication algorithms with deep reinfor cement learning\nby Alhussein Fawzi (DeepMind) as part of Mathematics\ , Physics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nImproving the efficiency of algorithms for fundamental computational tasks such as matr ix multiplication can have widespread impact\, as it affects the overall s peed of a large amount of computations. The automatic discovery of algorit hms using machine learning offers the prospect of reaching beyond human in tuition and outperforming the current best human-designed algorithms. In t his talk I'll present AlphaTensor\, our reinforcement learning agent based on AlphaZero for discovering efficient and provably correct algorithms fo r the multiplication of arbitrary matrices. AlphaTensor discovered algorit hms that outperform the state-of-the-art complexity for many matrix sizes. Particularly relevant is the case of 4 × 4 matrices in a finite field\, where AlphaTensor's algorithm improves on Strassen's two-level algorithm f or the first time since its discovery 50 years ago. I'll present our probl em formulation as a single-player game\, the key ingredients that enable t ackling such difficult mathematical problems using reinforcement learning\ , and the flexibility of the AlphaTensor framework.\n LOCATION:https://stable.researchseminars.org/talk/MPML/95/ END:VEVENT BEGIN:VEVENT SUMMARY:Sara A. Solla (Northwestern University) DTSTART:20230302T170000Z DTEND:20230302T180000Z DTSTAMP:20260404T094311Z UID:MPML/96 DESCRIPTION:Title: Low Dimensional Manifolds for Neural Dynamics\nby Sara A. Solla ( Northwestern University) as part of Mathematics\, Physics and Machine Lear ning (IST\, Lisbon)\n\n\nAbstract\nThe ability to simultaneously record th e activity from tens to hundreds to thousands of neurons has allowed us to analyze the computational role of population activity as opposed to singl e neuron activity. Recent work on a variety of cortical areas suggests tha t neural function may be built on the activation of population-wide activi ty patterns\, the neural modes\, rather than on the independent modulation of individual neural activity. These neural modes\, the dominant covariat ion patterns within the neural population\, define a low dimensional neura l manifold that captures most of the variance in the recorded neural activ ity. We refer to the time-dependent activation of the neural modes as thei r latent dynamics and argue that latent cortical dynamics within the manif old are the fundamental and stable building blocks of neural population ac tivity.\n LOCATION:https://stable.researchseminars.org/talk/MPML/96/ END:VEVENT BEGIN:VEVENT SUMMARY:Andreas Döpp (Ludwig-Maximilians-Universität München) DTSTART:20230601T160000Z DTEND:20230601T170000Z DTSTAMP:20260404T094311Z UID:MPML/97 DESCRIPTION:Title: Machine-learning strategies in laser-plasma physics\nby Andreas D öpp (Ludwig-Maximilians-Universität München) as part of Mathematics\, P hysics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nThe field of laser-plasma physics has experienced significant advancements in the past few decades\, owing to the increasing power and accessibility of high-powe r lasers. Initially\, research in this area was limited to single-shot exp eriments with minimal exploration of parameters. However\, recent technolo gical advancements have enabled the collection of a wealth of data through both experimental and simulation-based approaches.
\n\nIn this semi nar talk\, I will present a range of machine learning techniques that we h ave developed for applications in laser-plasma physics [1]. The first part of my talk will focus on Bayesian optimization\, where I will showcase ou r latest findings on multi-objective and multi-fidelity optimization of la ser-plasma accelerators and neural networks [2-4].
\n\nIn the second part of the talk\, I will discuss machine learning solutions for tackling complex inverse problems\, such as image deblurring or extracting 3D info rmation from 2D sensors [5-6]. Specifically\, I will discuss various adapt ations of established convolutional network architectures\, such as the U- Net\, as well as novel physics-informed retrieval methods like deep algori thm unrolling. These techniques have shown promising results in overcoming the challenges posed by these intricate inverse problems.
\n\n[1] Data-driven Science and Machine Lear
ning Methods in Laser-Plasma Physics
\nhttps://arxiv.org/abs/2212.00026
[2] Expected h
ypervolume improvement for simultaneous multi-objective and multi-fidelity
optimization
\nhttps://ar
xiv.org/abs/2112.13901
[3] Multi-objective and multi-fidelit
y Bayesian optimization of laser-plasma acceleration
\nhttps://arxiv.org/abs/2210.03484
[5] Measuring spatio-temporal couplings using modal spatio-spectra
l wavefront retrieval
\nht
tps://arxiv.org/abs/2303.01360
[6] Hyperspectral Compressive
Wavefront Sensing
\nhttps
://arxiv.org/abs/2303.03555
\;
\n LOCATION:https://stable.researchseminars.org/talk/MPML/97/ END:VEVENT BEGIN:VEVENT SUMMARY:Ben Edelman (Harvard University) DTSTART:20230209T170000Z DTEND:20230209T180000Z DTSTAMP:20260404T094311Z UID:MPML/98 DESCRIPTION:Title: Studies in feature learning through the lens of sparse boolean functi ons\nby Ben Edelman (Harvard University) as part of Mathematics\, Phys ics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nHow do deep neural networks learn to construct useful features? Why do self-attention-based n etworks such as transformers perform so well on combinatorial tasks such a s language learning? Why do some capabilities of networks emerge "disconti nuously" as the computational resources used for training are scaled up? W e will present perspectives on these questions through the lens of a parti cular class of simple synthetic tasks: learning sparse boolean functions. In part one\, we will show that the hypothesis class of one-layer transfor mers can learn these functions in a statistically efficient manner. This l eads to a view of each layer of a transformer as creating new "variables" out of sparse combinations of the previous layer's outputs. In part two\, we will focus on the classic task of learning sparse parities\, which is s tatistically easy but computationally difficult. We will demonstrate that SGD on various neural networks (transformers\, MLPs\, etc.) successfully l earns sparse parities\, with computational efficiency that is close to kno wn lower bounds. Moreover\, the training curves display no apparent progre ss for a long time\, and then quickly drop late in training. We show that despite this apparent delayed breakthrough in performance\, hidden progres s is actually being made throughout the course of training.\n\nBased on jo int work with Surbhi Goel\, Sham Kakade\, Cyril Zhang\, Boaz Barak\, and E ran Malach:\n\nhttps://arxiv.org/abs/2110.10090\n\nhttps://arxiv.org/abs/2 207.08799\n LOCATION:https://stable.researchseminars.org/talk/MPML/98/ END:VEVENT BEGIN:VEVENT SUMMARY:Valentin De Bortoli (Center for Sciences of Data\, ENS Ulm\, Paris ) DTSTART:20230316T170000Z DTEND:20230316T180000Z DTSTAMP:20260404T094311Z UID:MPML/99 DESCRIPTION:Title: Diffusion models\, theory and methodology\nby Valentin De Bortoli (Center for Sciences of Data\, ENS Ulm\, Paris) as part of Mathematics\, Physics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nGenerative mode ling is the task of drawing new samples from an underlying distribution kn own only via an empirical measure. There exists a myriad of models to tack le this problem with applications in image and speech processing\, medical imaging\, forecasting and protein modeling to cite a few. Among these met hods diffusion models are a new powerful class of generative models that e xhibit remarkable empirical performance. They consist of a ``noising'' sta ge\, whereby a diffusion is used to gradually add Gaussian noise to data\, and a generative model\, which entails a ``denoising'' process defined by approximating the time-reversal of the diffusion. In this talk we discuss three aspects of diffusion models. First\, we will dive into the methodol ogy behind diffusion models. Second\, we will present some of their theore tical guarantees with an emphasis on their behavior under the so-called ma nifold hypothesis. Such theoretical guarantees are non-vacuous and provide insight on the empirical behavior of these models. Finally\, I will prese nt an extension of diffusion models to the Optimal Transport setting and i ntroduce Diffusion Schrodinger Bridges.\n LOCATION:https://stable.researchseminars.org/talk/MPML/99/ END:VEVENT BEGIN:VEVENT SUMMARY:Memming Park (Champalimaud Foundation) DTSTART:20230323T170000Z DTEND:20230323T180000Z DTSTAMP:20260404T094311Z UID:MPML/100 DESCRIPTION:Title: On learning signals in recurrent networks\nby Memming Park (Cham palimaud Foundation) as part of Mathematics\, Physics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nNeural dynamical systems with stable attrac tor structures such as point attractors and continuous attractors are wide ly hypothesized to underlie meaningful temporal behavior that requires wor king memory. However\, perhaps counterintuitively\, having good working me mory is not sufficient for supporting useful learning signals that are nec essary to adapt to changes in the temporal structure of the environment. W e show that in addition to the well-known continuous attractors\, the peri odic and quasi-periodic attractors are also fundamentally capable of suppo rting learning arbitrarily long temporal relationships. Due to the fine tu ning problem of the continuous attractors and the lack of\ntemporal fluctu ations\, we believe the less explored quasi-periodic attractors are unique ly qualified for learning to produce temporally structured behavior. Our t heory has wide implications for the design of artificial learning systems\ , and makes predictions on the observable signatures of biological neural dynamics that can support temporal dependence learning. Based on our theor y\, we developed a new initialization scheme for artificial recurrent neur al networks which outperforms standard methods for tasks that require lear ning temporal dynamics. Finally\, we speculate on their biological impleme ntations and make predictions on neuronal dynamics.\n LOCATION:https://stable.researchseminars.org/talk/MPML/100/ END:VEVENT BEGIN:VEVENT SUMMARY:Rongjie Lai (Rensselaer Polytechnic Institute) DTSTART:20230420T160000Z DTEND:20230420T170000Z DTSTAMP:20260404T094311Z UID:MPML/101 DESCRIPTION:Title: Learning Manifold-Structured Data using Deep Neural Networks: Theory and Applications\nby Rongjie Lai (Rensselaer Polytechnic Institute) a s part of Mathematics\, Physics and Machine Learning (IST\, Lisbon)\n\n\nA bstract\nDeep artificial neural networks have made great success in many p roblems in science and engineering. In this talk\, I will discuss our rece nt efforts to develop DNNs capable of learning non-trivial geometry inform ation hidden in data. In the first part\, I will discuss our work on advoc ating the use of a multi-chart latent space for better data representation . Inspired by differential geometry\, we propose a Chart Auto-Encoder (CAE ) and prove a universal approximation theorem on its representation capabi lity. CAE admits desirable manifold properties that conventional auto-enco ders with a flat latent space fail to obey. We further establish statistic al guarantees on the generalization error for trained CAE models and show their robustness to noise. Our numerical experiments also demonstrate sati sfactory performance on data with complicated geometry and topology. If ti me permits\, I will discuss our work on defining convolution on manifolds via parallel transport. This geometric way of defining parallel transport convolution (PTC) provides a natural combination of modeling and learning on manifolds. PTC allows for the construction of compactly supported filte rs and is also robust to manifold deformations. I will demonstrate its app lications to shape analysis and point clouds processing using PTC-nets. Th is talk is based on a series of joint work with my students and collaborat ors.\n LOCATION:https://stable.researchseminars.org/talk/MPML/101/ END:VEVENT BEGIN:VEVENT SUMMARY:Gonçalo Correia (IST and Priberam Labs) DTSTART:20230309T170000Z DTEND:20230309T180000Z DTSTAMP:20260404T094311Z UID:MPML/102 DESCRIPTION:Title: Learnable Sparsity and Weak Supervision for Data-Efficient\, Transpa rent\, and Compact Neural Models\nby Gonçalo Correia (IST and Pribera m Labs) as part of Mathematics\, Physics and Machine Learning (IST\, Lisbo n)\n\n\nAbstract\nNeural network models have become ubiquitous in Machine Learning literature. These models are compositions of differentiable build ing blocks that result in dense representations of the underlying data. To obtain good representations\, conventional neural models require many tra ining data points. Moreover\, those representations\, albeit capable of ob taining a high performance on many tasks\, are largely uninterpretable. Th ese models are often overparameterized and give out representations that d o not compactly represent the data. To address these issues\, we find solu tions in sparsity and various forms of weak supervision. For data-efficien cy\, we leverage transfer learning as a form of weak supervision. The prop osed model can perform similarly to models trained on millions of data poi nts on a sequence-to-sequence generation task\, even though we only train it on a few thousand. For transparency\, we propose a probability normaliz ing function that can learn its sparsity. The model learns the sparsity it needs differentiably and thus adapts it to the data according to the neur al component's role in the overall structure. We show that the proposed mo del improves the interpretability of a popular neural machine translation architecture when compared to conventional probability normalizing functio ns. Finally\, for compactness\, we uncover a way to obtain exact gradients of discrete and structured latent variable models efficiently. The discre te nodes in these models can compactly represent implicit clusters and str uctures in the data\, but training them was often complex and prone to fai lure since it required approximations that rely on sampling or relaxations . We propose to train these models with exact gradients by parameterizing discrete distributions with sparse functions\, both unstructured and struc tured. We obtain good performance on three latent variable model applicati ons while still achieving the practicality of the approximations mentioned above. Through these novel contributions\, we challenge the conventional wisdom that neural models cannot exhibit data-efficiency\, transparency\, or compactness.\n LOCATION:https://stable.researchseminars.org/talk/MPML/102/ END:VEVENT BEGIN:VEVENT SUMMARY:Diogo Gomes (KAUST) DTSTART:20230504T160000Z DTEND:20230504T170000Z DTSTAMP:20260404T094311Z UID:MPML/103 DESCRIPTION:Title: Mathematics for data science and AI - curriculum design\, experience s\, and lessons learned\nby Diogo Gomes (KAUST) as part of Mathematics \, Physics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nIn this talk \, we will explore the importance of mathematical foundations for AI and d ata science and the design of an academic curriculum for graduate students . While traditional mathematics for AI and data science has focused on cor e techniques like linear algebra\, basic probability\, and optimization me thods (e.g.\, gradient and stochastic gradient descent)\, several advanced mathematical techniques are now essential to understanding modern data sc ience. These include ideas from the calculus of variations in spaces of ra ndom variables\, functional analytic methods\, ergodic theory\, control th eory methods in reinforcement learning\, and metrics in spaces of probabil ity measures. We will discuss the author's experience designing an applied mathematics curriculum on data science and draw on the author's experienc e and lessons learned in teaching an advanced course on the mathematical f oundations of data science. This talk aims to promote discussion and excha nge of ideas on how mathematicians can play an important role in AI and da ta science and better equip our students to excel in this field.\n LOCATION:https://stable.researchseminars.org/talk/MPML/103/ END:VEVENT BEGIN:VEVENT SUMMARY:Harry Desmond (University of Portsmouth) DTSTART:20230511T160000Z DTEND:20230511T170000Z DTSTAMP:20260404T094311Z UID:MPML/104 DESCRIPTION:Title: Exhaustive Symbolic Regression (or how to find the best function for your data)\nby Harry Desmond (University of Portsmouth) as part of Ma thematics\, Physics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nSym bolic regression aims to find optimal functional representation of dataset s\, with broad applications across science. This is traditionally done usi ng a "genetic algorithm" which stochastically searches function space usin g an evolution-inspired method for generating new trial functions. Motivat ed by the uncertainties inherent in this approach -- and its failure on se emingly simple test cases -- I will describe a new method which exhaustive ly searches and evaluates function space. Coupled to a model selection pri nciple based on minimum description length\, Exhaustive Symbolic Regressio n is guaranteed to find the simple equations that optimally balance simpli city with accuracy on any dataset. I will describe how the method works an d showcase it on Hubble rate measurements and dynamical galaxy data.\n\nBa sed on work with Deaglan Bartlett and Pedro G. Ferreira:
Causal representation learning (CRL) aims at learning causal factors and t
heir causal relations from high-dimensional observations\, e.g. images. In
general\, this is an ill-posed problem\, but under certain assumptions or
with the help of additional information or interventions\, we are able to
guarantee that the representations we learn are corresponding to some tru
e underlying causal factors up to some equivalence class.
\nIn this t
alk I will first present CITRIS (https://proceed
ings.mlr.press/v162/lippe22a/lippe22a.pdf)\, a variational autoencoder
framework for causal representation learning from temporal sequences of i
mages\, in systems in which we can perform interventions. CITRIS exploits
temporality and observing intervention targets to identify scalar and mult
idimensional causal factors\, such as 3D rotation angles. In experiments o
n 3D rendered image sequences\, CITRIS outperforms previous methods on rec
overing the underlying causal variables. Moreover\, using pretrained autoe
ncoders\, CITRIS can even generalize to unseen instantiations of causal fa
ctors.
\n
\nWhile CRL is an exciting and promising new field of
research\, the assumptions required by CITRIS and other current CRL method
s can be difficult to satisfy in many settings. Moreover\, in many practic
al cases learning representations that are not guaranteed to be fully caus
al\, but exploit some ideas from causality\, can still be extremely useful
. As examples\, I will describe some of our work on exploiting these "caus
ality-inspired" representations for adapting policies across domains in RL
(https://openreview.net/forum?id=8H5bpVwvt5) and to nonst
ationary environments (https://openreview.net/forum?id=VQ9fog
N1q6e)\, and how learning a factored graphical representations (even i
f not necessarily causal) can be beneficial in these (and possibly other)
settings.