BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Isay Katsman (Yale) DTSTART:20221024T121500Z DTEND:20221024T131500Z DTSTAMP:20260404T110913Z UID:MaML/1 DESCRIPTION:Title: Riemannian Geometry in Machine Learning\nby Isay Katsman (Yale) as part of Mathematics and Machine Learning\n\n\nAbstract\nAlthough machine learning researchers have introduced a plethora of useful constructions fo r learning over Euclidean space\, numerous types of data in various applic ations benefit from\, if not necessitate\, a non-Euclidean treatment. In t his talk I cover the need for Riemannian geometric constructs to (1) build more principled generalizations of common Euclidean operations used in ge ometric machine learning models as well as to (2) enable general manifold density learning in contexts that require it. Said contexts include theore tical physics\, robotics\, and computational biology. I will cover one of my papers that fits into (1) above\, namely the ICML 2020 paper “Differe ntiating through the Fréchet Mean.” I will also cover two of my papers that fit into (2) above\, namely the NeurIPS 2020 paper “Neural Manifold ODEs” and the NeurIPS 2021 paper “Equivariant Manifold Flows.” Fina lly\, I will briefly discuss directions of relevant ongoing work.\n LOCATION:https://stable.researchseminars.org/talk/MaML/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Sebastian Fischer (LMU Munich) DTSTART:20221107T131500Z DTEND:20221107T141500Z DTSTAMP:20260404T110913Z UID:MaML/2 DESCRIPTION:Title: Benchmarking Machine Learning Methods Using OpenML and mlr3\nby Se bastian Fischer (LMU Munich) as part of Mathematics and Machine Learning\n \n\nAbstract\nBenchmark studies are an integral part of machine learning r esearch. The two main components are the datasets that are used to compare the methods and the software that supports the researcher in carrying out the experiment. OpenML is a platform for sharing datasets and machine lea rning results and is a great tool to obtain datasets.\nmlr3 is an ecosyste m of machine learning packages in the R language\, which among other thing s allows for benchmarking algorithms with ease. This presentation will sho w how OpenML and mlr3 can be used together to make benchmarking machine le arning methods as easy as possible\, by using the interface R package mlr3 oml.\n LOCATION:https://stable.researchseminars.org/talk/MaML/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Edward de Brouwer (KU Leuven) DTSTART:20221219T131500Z DTEND:20221219T141500Z DTSTAMP:20260404T110913Z UID:MaML/3 DESCRIPTION:Title: Topological Graph Neural Networks\nby Edward de Brouwer (KU Leuven ) as part of Mathematics and Machine Learning\n\n\nAbstract\nGraph neural networks (GNNs) are a powerful architecture for tackling graph learning ta sks\, yet have been shown to be oblivious to eminent substructures such as cycles. In this talk\, we introduce TOGL\, a novel layer that incorporate s global topological information of a graph using persistent homology. TOG L can be easily integrated into any type of GNN and is strictly more expre ssive (in terms the Weisfeiler–Lehman graph isomorphism test) than messa ge-passing GNNs. Augmenting GNNs with TOGL leads to improved predictive pe rformance for graph and node classification tasks\, both on synthetic data sets\, which can be classified by humans using their topology but not by ordinary GNNs\, and on real-world data.\n LOCATION:https://stable.researchseminars.org/talk/MaML/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Jim Halverson (Northeastern) DTSTART:20221121T131500Z DTEND:20221121T141500Z DTSTAMP:20260404T110913Z UID:MaML/4 DESCRIPTION:Title: Machine Learning for Pure Math\nby Jim Halverson (Northeastern) as part of Mathematics and Machine Learning\n\n\nAbstract\nProgress in machi ne learning (ML) is poised to revolutionize a variety of STEM fields. But how could these techniques — which are often stochastic\, error-prone\, and blackbox — lead to progress in pure mathematics\, which values rigor and understanding? I will exemplify how ML can be used to generate conjec tures in a Calabi-Yau singularity problem that is relevant for physics\, a nd will demonstrate how reinforcement learning can yield truth certificate s that rigorously demonstrate properties of knots. The second half of the talk will utilize ML theory instead of applied ML. Specifically\, I will d evelop a neural tangent kernel theory appropriate for flows in the space o f metrics (realized as neural networks)\, and will realize Perelman’s fo rmulation of Ricci flow as a specialization of the general theory.\n LOCATION:https://stable.researchseminars.org/talk/MaML/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Davies (Deep Mind) DTSTART:20221212T120000Z DTEND:20221212T130000Z DTSTAMP:20260404T110913Z UID:MaML/5 DESCRIPTION:Title: Machine Learning with Mathematicians\nby Alex Davies (Deep Mind) a s part of Mathematics and Machine Learning\n\n\nAbstract\nCan machine lear ning be a useful tool for research mathematicians? There are many examples of mathematicians pioneering new technologies to aid our understanding of the mathematical world: using very early computers to help formulate the Birch and Swinnerton-Dyer conjecture and using computer aid to prove the f our colour theorem are among the most notable. Up until now\, there hasn ’t been significant use of machine learning in the field and it hasn’t been clear where it might be useful for the questions that mathematicians care about. In this talk\, we will discuss how working together with top mathematicians to use machine learning to achieve two new results – prov ing a new connection between the hyperbolic and geometric structure of kno ts\, and conjecturing a resolution to a 50-year problem in representation theory\, the combinatorial invariance conjecture. Through these examples\, we demonstrate a way that machine learning can be used by mathematicians to help guide the development of surprising and beautiful new conjectures. \n LOCATION:https://stable.researchseminars.org/talk/MaML/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Noemi Montobbio (IIT) DTSTART:20230109T131500Z DTEND:20230109T141500Z DTSTAMP:20260404T110913Z UID:MaML/6 DESCRIPTION:Title: Emergence of Lie Symmetries in Functional Architectures Learned by CNN s\nby Noemi Montobbio (IIT) as part of Mathematics and Machine Learnin g\n\n\nAbstract\nConvolutional Neural Networks (CNNs) are a powerful tool providing outstanding performances on image classification tasks\, based o n an architecture designed in analogy with information processing in biolo gical visual systems. The functional architectures of the early visual pat hways have often been described in terms of geometric invariances\, and se veral studies have leveraged this framework to investigate the analogies b etween CNN models and biological mechanisms. Remarkably\, upon learning on natural images\, the translation-invariant filters of the first layer of a CNN have been shown to develop as approximate Gabor functions\, resembli ng the orientation-selective receptive profiles found in the primary visua l cortex (V1). With a similar approach\, we modified a standard CNN archit ecture to insert computational blocks compatible with specific biological processing stages\, and studied the spontaneous development of approximate geometric invariances after training the network on natural images. In pa rticular\, inserting a pre-filtering step mimicking the Lateral Geniculate Nucleus (LGN) led to the emergence of a radially symmetric profile well a pproximated by a Laplacian of Gaussian\, which is a well-known model of re ceptive profiles of LGN cells. Moreover\, we introduced a lateral connecti vity kernel acting on the feature space of the first network layer. We the n studied the learned connectivity as a function of relative tuning of fir st-layer filters\, thus re-mapping it into the roto-translation space. Thi s analysis revealed orientation-specific patterns\, which we compared qual itatively and quantitatively with established group-based models of V1 hor izontal connectivity.\n LOCATION:https://stable.researchseminars.org/talk/MaML/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Anna Seigal (Harvard) DTSTART:20230123T141500Z DTEND:20230123T151500Z DTSTAMP:20260404T110913Z UID:MaML/7 DESCRIPTION:by Anna Seigal (Harvard) as part of Mathematics and Machine Le arning\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/MaML/7/ END:VEVENT END:VCALENDAR