BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Tom Oliver (Nottingham) DTSTART:20210929T120000Z DTEND:20210929T130000Z DTSTAMP:20260422T212555Z UID:CompAlg/1 DESCRIPTION:Title: Supervised learning of arithmetic invariants\nby Tom Oliver (Nottingha m) as part of Machine Learning Seminar\n\n\nAbstract\nWe explore the utili ty of standard supervised learning algorithms for a range of classificatio n problems in number theory. In particular\, we will consider class number s of real quadratic fields\, ranks of elliptic curves over Q\, and endomor phism types for genus 2 curves over Q. Each case is motivated by its appea rance in an open conjecture. Throughout the basic strategy is the same: we vectorize the underlying objects via the coefficients of their L-function s.\n LOCATION:https://researchseminars.org/talk/CompAlg/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexei Vernitski (Essex) DTSTART:20220701T130000Z DTEND:20220701T140000Z DTSTAMP:20260422T212555Z UID:CompAlg/2 DESCRIPTION:Title: Using machine learning to solve mathematical problems and to search for ex amples and counterexamples in pure maths research\nby Alexei Vernitski (Essex) as part of Machine Learning Seminar\n\n\nAbstract\nOur recent res earch can be generally described as applying state-of-the-art technologies of machine learning to suitable mathematical problems. As to machine lear ning\, we use both reinforcement learning and supervised learning (underpi nned by deep learning). As to mathematical problems\, we mostly concentrat e on knot theory\, for two reasons\; firstly\, we have a positive experien ce of applying another kind of artificial intelligence (automated reasonin g) to knot theory\; secondly\, examples and counter-examples in knot theor y are finite and\, typically\, not very large\, so they are convenient for the computer to work with.\n\nHere are some successful examples of our re cent work\, which I plan to talk about.\n\n1. Some recent studies used mac hine learning to untangle knots using Reidemeister moves\, but they do not describe in detail how they implemented untangling on the computer. We in vested effort into implementing untangling in one clearly defined scenario \, and were successful\, and made our computer code publicly available.\n2 . We found counterexamples showing that some recent publications claiming to give new descriptions of realisable Gauss diagrams contain an error. We trained several machine learning agents to recognise realisable Gauss dia grams and noticed that they fail to recognise correctly the same counterex amples which human mathematicians failed to spot.\n3. One problem related to (and "almost" equivalent to) recognising the trivial knot is colouring the knot diagram by elements of algebraic structures called quandles (I wi ll define them). We considered\, for some types of knot diagrams (includin g petal diagrams)\, how supervised learning copes with this problem.\n LOCATION:https://researchseminars.org/talk/CompAlg/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Anindita Maiti (Northeastern University) DTSTART:20220912T140000Z DTEND:20220912T150000Z DTSTAMP:20260422T212555Z UID:CompAlg/3 DESCRIPTION:Title: Non-perturbative Non-Lagrangian Neural Network Field Theories\nby Anin dita Maiti (Northeastern University) as part of Machine Learning Seminar\n \n\nAbstract\nEnsembles of Neural Network (NN) output functions describe f ield theories. The Neural Network Field Theories become free i.e. Gaussian in the limit of infinite width and independent parameter distributions\, due to Central Limit Theorem (CLT). Interaction terms i.e. non-Gaussianiti es in these field theories arise due to violations of CLT at finite width and / or correlated parameter distributions. In general\, non-Gaussianitie s render Neural Network Field Theories as non-perturbative and non-Lagrang ian. In this talk\, I will describe methods to study non-perturbative non- Lagrangian field theories in Neural Networks\, via a dual framework over p arameter distributions. This duality lets us study correlation functions a nd symmetries of NN field theories in the absence of an action\; further t he partition function can be approximated as a series sum over connected c orrelation functions. Thus\, Neural Networks allow us to study non-perturb ative non-Lagrangian field theories through their architectures\, and can be beneficial to both Machine Learning and physics.\n LOCATION:https://researchseminars.org/talk/CompAlg/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Manolis Tsakiris (Chinese Academy of Sciences) DTSTART:20230208T100000Z DTEND:20230208T110000Z DTSTAMP:20260422T212555Z UID:CompAlg/4 DESCRIPTION:Title: Unlabelled Principal Component Analysis\nby Manolis Tsakiris (Chinese Academy of Sciences) as part of Machine Learning Seminar\n\n\nAbstract\nTh is talk will consider the problem of recovering a matrix of bounded rank f rom a corrupted version of it\, where the corruption consists of an unknow n permutation of the matrix entries. Exploiting the theory of Groebner bas es for determinantal ideals\, recovery theorems will be given. For a speci al instance of the problem\, an algorithmic pipeline will be demonstrated\ , which employs methods for robust principal component analysis with respe ct to outliers and methods for linear regression without correspondences.\ n LOCATION:https://researchseminars.org/talk/CompAlg/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Guido Montufar (UCLA) DTSTART:20230222T160000Z DTEND:20230222T170000Z DTSTAMP:20260422T212555Z UID:CompAlg/5 DESCRIPTION:Title: Geometry and convergence of natural policy gradient methods\nby Guido Montufar (UCLA) as part of Machine Learning Seminar\n\n\nAbstract\nWe stud y the convergence of several natural policy gradient (NPG) methods in infi nite-horizon discounted Markov decision processes with regular policy para metrizations. For a variety of NPGs and reward functions we show that the trajectories in state-action space are solutions of gradient flows with re spect to Hessian geometries\, based on which we obtain global convergence guarantees and convergence rates. In particular\, we show linear convergen ce for unregularized and regularized NPG flows with the metrics proposed b y Kakade and Morimura and co-authors by observing that these arise from th e Hessian geometries of conditional entropy and entropy respectively. Furt her\, we obtain sublinear convergence rates for Hessian geometries arising from other convex functions like log-barriers. Finally\, we interpret the discrete-time NPG methods with regularized rewards as inexact Newton meth ods if the NPG is defined with respect to the Hessian geometry of the regu larizer. This yields local quadratic convergence rates of these methods fo r step size equal to the penalization strength. This is work with Johannes Müller.\n LOCATION:https://researchseminars.org/talk/CompAlg/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Kathlén Kohn (KTH) DTSTART:20230215T100000Z DTEND:20230215T110000Z DTSTAMP:20260422T212555Z UID:CompAlg/6 DESCRIPTION:Title: The Geometry of Linear Convolutional Networks\nby Kathlén Kohn (KTH) as part of Machine Learning Seminar\n\n\nAbstract\nWe discuss linear convo lutional neural networks (LCNs) and their critical points. We observe that the function space (i.e.\, the set of functions represented by LCNs) can be identified with polynomials that admit certain factorizations\, and we use this perspective to describe the impact of the network’s architectur e on the geometry of the function space. For instance\, for LCNs with one- dimensional convolutions having stride one and arbitrary filter sizes\, we provide a full description of the boundary of the function space. We furt her study the optimization of an objective function over such LCNs: We cha racterize the relations between critical points in function space and in p arameter space and show that there do exist spurious critical points. We c ompute an upper bound on the number of critical points in function space u sing Euclidean distance degrees and describe dynamical invariants for grad ient descent. This talk is based on joint work with Thomas Merkh\, Guido M ontúfar\, and Matthew Trager.\n LOCATION:https://researchseminars.org/talk/CompAlg/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Nick Vannieuwenhoven (KU Leuven) DTSTART:20230308T100000Z DTEND:20230308T110000Z DTSTAMP:20260422T212555Z UID:CompAlg/7 DESCRIPTION:Title: Group-invariant tensor train networks for supervised learning\nby Nick Vannieuwenhoven (KU Leuven) as part of Machine Learning Seminar\n\n\nAbst ract\nInvariance under selected transformations has recently proven to be a powerful inductive bias in several machine learning models. One class of such models are tensor train networks. In this talk\, we impose invarianc e relations on tensor train networks. We introduce a new numerical algorit hm to construct a basis of tensors that are invariant under the action of normal matrix representations of an arbitrary discrete group. This method can be up to several orders of magnitude faster than previous approaches. The group-invariant tensors are then combined into a group-invariant tenso r train network\, which can be used as a supervised machine learning model . We applied this model to a protein binding classification problem\, taki ng into account problem-specific invariances\, and obtained prediction acc uracy in line with state-of-the-art invariant deep learning approaches. Th is is joint work with Brent Sprangers.\n LOCATION:https://researchseminars.org/talk/CompAlg/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Yang-Hui He (LIMS) DTSTART:20230405T090000Z DTEND:20230405T100000Z DTSTAMP:20260422T212555Z UID:CompAlg/8 DESCRIPTION:Title: Universes as Bigdata: Physics\, Geometry and Machine-Learning\nby Yang -Hui He (LIMS) as part of Machine Learning Seminar\n\n\nAbstract\nThe sear ch for the Theory of Everything has led to superstring theory\, which then led physics\, first to algebraic/differential geometry/topology\, and the n to computational geometry\, and now to data science. With a concrete pla yground of the geometric landscape\, accumulated by the collaboration of p hysicists\, mathematicians and computer scientists over the last 4 decades \, we show how the latest techniques in machine-learning can help explore problems of interest to theoretical physics and to pure mathematics. At th e core of our programme is the question: how can AI help us with mathemati cs?\n LOCATION:https://researchseminars.org/talk/CompAlg/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Julia Lindberg (UT Austin) DTSTART:20230315T150000Z DTEND:20230315T160000Z DTSTAMP:20260422T212555Z UID:CompAlg/9 DESCRIPTION:Title: Estimating Gaussian mixtures using sparse polynomial moment systems\nb y Julia Lindberg (UT Austin) as part of Machine Learning Seminar\n\n\nAbst ract\nThe method of moments is a statistical technique for density estimat ion that solves a system of moment equations to estimate the parameters of an unknown distribution. A fundamental question critical to understanding identifiability asks how many moment equations are needed to get finitely many solutions and how many solutions there are. We answer this question for classes of Gaussian mixture models using the tools of polyhedral geome try. Using these results\, we present a homotopy method to perform paramet er recovery\, and therefore density estimation\, for high dimensional Gaus sian mixture models. The number of paths tracked in our method scales line arly in the dimension.\n LOCATION:https://researchseminars.org/talk/CompAlg/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Eduardo Paluzo-Hidalgo (Seville) DTSTART:20230329T140000Z DTEND:20230329T150000Z DTSTAMP:20260422T212555Z UID:CompAlg/10 DESCRIPTION:Title: An introduction to Simplicial-map Neural Networks\nby Eduardo Paluzo- Hidalgo (Seville) as part of Machine Learning Seminar\n\n\nAbstract\nIn a recently accepted project RexasiPro\, we deal with a critical environment where trustworthy is decisive. One of our approaches are simplicial-map ne ural networks (SMNNs) which are explicitly defined using simplicial maps b etween triangulations of the input and output spaces. Its combinatorial de finition lets us prove and guarantee several nice properties following tru stworthy AI principles. In "Two-hidden-layer feed-forward networks are uni versal approximators: A constructive approach"\, the first definition of S MNNs was given and its universal approximator property was proved. Later\, in "Simplicial-Map Neural Networks Robust to Adversarial Examples"\, its robustness against adversarial examples was described.\n LOCATION:https://researchseminars.org/talk/CompAlg/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Patrizio Frosini (Bologna) DTSTART:20230322T100000Z DTEND:20230322T110000Z DTSTAMP:20260422T212555Z UID:CompAlg/11 DESCRIPTION:Title: Some recent results on the theory of GENEOs and its application to Machin e Learning\nby Patrizio Frosini (Bologna) as part of Machine Learning Seminar\n\n\nAbstract\nGroup equivariant non-expansive operators (GENEOs) have been introduced a few years ago as mathematical tools for approximati ng data observers when data are represented by real-valued or vector-value d functions. The use of these operators is based on the assumption that th e interpretation of data depends on the geometric properties of the observ ers. In this talk we will illustrate some recent results in the theory of GENEOs\, showing how these operators can make available a new approach to topological data analysis and geometric deep learning.\n LOCATION:https://researchseminars.org/talk/CompAlg/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Christoph Hertrich (LSE) DTSTART:20230419T150000Z DTEND:20230419T160000Z DTSTAMP:20260422T212555Z UID:CompAlg/12 DESCRIPTION:Title: Understanding Neural Network Expressivity via Polyhedral Geometry\nby Christoph Hertrich (LSE) as part of Machine Learning Seminar\n\n\nAbstrac t\nNeural networks with rectified linear unit (ReLU) activations are one o f the standard models in modern machine learning. Despite their practical importance\, fundamental theoretical questions concerning ReLU networks re main open until today. For instance\, what is the precise set of (piecewis e linear) functions exactly representable by ReLU networks with a given de pth? Even the special case asking for the number of layers to compute a fu nction as simple as $\\max\\{0\, x_1\, x_2\, x_3\, x_4\\}$ has not been so lved yet. In this talk we will explore the relevant background to understa nd this question and report about recent progress using tropical and polyh edral geometry as well as a computer-aided approach based on mixed-integer programming. This is based on joint works with Amitabh Basu\, Marco Di Su mma\, and Martin Skutella (NeurIPS 2021)\, as well as Christian Haase and Georg Loho (ICLR 2023).\n LOCATION:https://researchseminars.org/talk/CompAlg/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Vasco Portilheiro (UCL) DTSTART:20230412T150000Z DTEND:20230412T160000Z DTSTAMP:20260422T212555Z UID:CompAlg/13 DESCRIPTION:Title: Barriers to Learning Symmetries\nby Vasco Portilheiro (UCL) as part o f Machine Learning Seminar\n\n\nAbstract\nGiven the success of equivariant models\, there has been increasing interest in models which can learn a s ymmetry from data\, rather than it being imposed a priori. We present work which formalizes a tradeoff between (a) the simultaneous learnability of symmetries and equivariant functions\, and (b) universal approximation of equivariant functions. The work is motivated by an experiment which modifi es the Equivariant Multilayer Perceptron (EMLP) of Finzi et al. (2021) in an attempt to learn a group together with an equivariant function. Additio nally\, the tradeoff is shown to not exist for group-convolutional network s.\n LOCATION:https://researchseminars.org/talk/CompAlg/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Bastian Rieck (Munich) DTSTART:20230426T090000Z DTEND:20230426T100000Z DTSTAMP:20260422T212555Z UID:CompAlg/14 DESCRIPTION:Title: Curvature for Graph Learning\nby Bastian Rieck (Munich) as part of Ma chine Learning Seminar\n\n\nAbstract\nCurvature bridges geometry and topol ogy\, using local information to derive global statements. While well-know n in a differential topology context\, it was recently extended to the dom ain of graphs. In fact\, graphs give rise to various notions of curvature\ , which differ in expressive power and purpose. We will give a brief overv iew of curvature in graphs\, define some relevant concepts\, and show thei r utility for data science and machine learning applications. In particula r\, we shall discuss two applications: first\, the use of curvature to dis tinguish between different models for synthesising new graphs from some un known distribution\; second\, a novel framework for defining curvature for hypergraphs\, whose structural properties require a more generic setting. We will also describe new applications that are specifically geared towar ds a treatment by curvature\, thus underlining the utility of this concept for data science.\n LOCATION:https://researchseminars.org/talk/CompAlg/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Taejin Paik (Seoul National University) DTSTART:20230524T090000Z DTEND:20230524T100000Z DTSTAMP:20260422T212555Z UID:CompAlg/15 DESCRIPTION:Title: Isometry-Invariant and Subdivision-Invariant Representations of Embedded Simplicial Complexes\nby Taejin Paik (Seoul National University) as pa rt of Machine Learning Seminar\n\n\nAbstract\nGeometric objects such as me shes and graphs are commonly used in various applications\, but analyzing them can be challenging due to their complex structures. Traditional appro aches may not be robust to transformations like subdivision or isometry\, leading to inconsistent results. Here is a novel approach to address these limitations by using only topological and geometric data to analyze simpl icial complexes in a subdivision-invariant and isometry-invariant way. Thi s approach involves using a graph neural network to create an $O(3)$-equiv ariant operator and the Euler curve transform to generate sufficient stati stics that describe the properties of the object.\n LOCATION:https://researchseminars.org/talk/CompAlg/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Platt (KCL) DTSTART:20230503T090000Z DTEND:20230503T100000Z DTSTAMP:20260422T212555Z UID:CompAlg/16 DESCRIPTION:Title: Group invariant machine learning by fundamental domain projections\nb y Daniel Platt (KCL) as part of Machine Learning Seminar\n\n\nAbstract\nIn many applications one wants to learn a function that is invariant under a group action. For example\, classifying images of digits\, no matter how they are rotated. There exist many approaches in the literature to do this . I will mention two approaches that are very useful in many applications\ , but struggle if the group is big or acts in a complicated way. I will th en explain our approach which does not have these two problems. The approa ch works by finding some "canonical representative" of each input element. In the example of images of digits\, one may rotate the digit so that the brightest quarter is in the top-left\, which would define a "canonical re presentative". In the general case\, one has to define what that means. Ou r approach is useful if the group is big\, and I will present experiments on the Complete Intersection Calabi-Yau and Kreuzer-Skarke datasets to sho w this. Our approach is useless if the group is small\, and the case of ro tated images of digits is an example of this. This is joint work with Benj amin Aslan and David Sheard.\n LOCATION:https://researchseminars.org/talk/CompAlg/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Vasco Brattka (Bundeswehr München) DTSTART:20230614T090000Z DTEND:20230614T100000Z DTSTAMP:20260422T212555Z UID:CompAlg/17 DESCRIPTION:Title: On the Complexity of Computing Gödel Numbers\nby Vasco Brattka (Bund eswehr München) as part of Machine Learning Seminar\n\n\nAbstract\nGiven a computable sequence of natural numbers\, it is a natural task to find a Gödel number of a program that generates this sequence. It is easy to see that this problem is neither continuous nor computable. In algorithmic le arning theory this problem is well studied from several perspectives and o ne question studied there is for which sequences this problem is at least learnable in the limit. Here we study the problem on all computable sequen ces and we classify the Weihrauch complexity of it. For this purpose we ca n\, among other methods\, utilize the amalgamation technique known from le arning theory. As a benchmark for the classification we use closed and com pact choice problems and their jumps on natural numbers\, and we argue tha t these problems correspond to induction and boundedness principles\, as t hey are known from the Kirby-Paris hierarchy in reverse mathematics. We pr ovide a topological as well as a computability-theoretic classification\, which reveal some significant differences.\n LOCATION:https://researchseminars.org/talk/CompAlg/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Edward Pearce-Crump (Imperial) DTSTART:20230621T090000Z DTEND:20230621T100000Z DTSTAMP:20260422T212555Z UID:CompAlg/18 DESCRIPTION:Title: Exploring group equivariant neural networks using set partition diagrams< /a>\nby Edward Pearce-Crump (Imperial) as part of Machine Learning Seminar \n\n\nAbstract\nWhat do jellyfish and an 11th century Japanese novel have to do with neural networks? In recent years\, much attention has been give n to developing neural network architectures that can efficiently learn fr om data with underlying symmetries. These architectures ensure that the le arned functions maintain a certain geometric property called group equivar iance\, which determines how the output changes based on a change to the i nput under the action of a symmetry group. In this talk\, we will describe a number of new group equivariant neural network architectures that are b uilt using tensor power spaces of $\\mathbb{R}^n$ as their layers. We will show that the learnable\, linear functions between these layers can be ch aracterised by certain subsets of set partition diagrams. This talk will b e based on several papers that are to appear in ICML 2023.\n LOCATION:https://researchseminars.org/talk/CompAlg/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Alvaro Torras Casas (Cardiff) DTSTART:20230531T090000Z DTEND:20230531T100000Z DTSTAMP:20260422T212555Z UID:CompAlg/19 DESCRIPTION:Title: Dataset comparison using persistent homology morphisms\nby Alvaro Tor ras Casas (Cardiff) as part of Machine Learning Seminar\n\n\nAbstract\nPer sistent homology summarizes geometrical information of data by means of a barcode. Given a pair of datasets\, $X$ and $Y$\, one might obtain their r espective barcodes $B(X)$ and $B(Y)$. Thanks to stability results\, if $X$ and $Y$ are similar enough one deduces that the barcodes $B(X)$ and $B(Y) $ are also close enough\; however\, the converse is not true in general. I n this talk we consider the case when there is a known relation between $X $ and $Y$ encoded by a morphism between persistence modules. For example\, this is the case when $Y$ is a finite subset of euclidean space and $X$ i s a sample taken from $Y$. As in linear algebra\, a morphism between persi stence modules is understood by a choice of a pair of bases together with the associated matrix. I will explain how to use this matrix to get barcod es for images\, kernels and cokernels. Additionally\, I will explain how t o compute an induced block function that relates the barcodes $B(X)$ and $ B(Y)$. I will finish the talk revising some applications of this theory as well as future research directions.\n LOCATION:https://researchseminars.org/talk/CompAlg/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Gebhart (Minnesota) DTSTART:20230705T150000Z DTEND:20230705T160000Z DTSTAMP:20260422T212555Z UID:CompAlg/20 DESCRIPTION:Title: Specifying Local Constraints in Representation Learning with Cellular She aves\nby Thomas Gebhart (Minnesota) as part of Machine Learning Semina r\n\n\nAbstract\nMany machine learning algorithms constrain their learned representations by imparting inductive biases based on local smoothness as sumptions. While these constraints are often natural and effective\, there are situations in which their simplicity is mis-aligned with the represen tation structure required by the task\, leading to a lack of expressivity and pathological behaviors like representational oversmoothing or inconsis tency. Without a broader theoretical framework for reasoning about local r epresentational constraints\, it is difficult to conceptualize and move be yond such representational misalignments. In this talk\, we will see that cellular sheaf theory offers an ideal algebro-topological framework for bo th reasoning about and implementing machine learning models on data which are subject to such local-to-global constraints over a topological space. We will introduce cellular sheaves from a categorical perspective\, observ ing the relationship between their definition as a limit object and the co nsistency objectives underlying representation learning. We will then turn to a discussion of sheaf (co)homology as a semi-computable tool for imple menting these categorical concepts. Finally\, we will observe two practica l applications of these ideas in the form of sheaf neural networks\, a gen eralization of graph neural networks for processing sheaf-valued signals\; and knowledge sheaves\, a sheaf-theoretic reformulation of knowledge grap h embedding.\n LOCATION:https://researchseminars.org/talk/CompAlg/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Challenger Mishra (Cambridge) DTSTART:20230712T090000Z DTEND:20230712T100000Z DTSTAMP:20260422T212555Z UID:CompAlg/21 DESCRIPTION:Title: Mathematical conjecture generation and Machine Intelligence\nby Chall enger Mishra (Cambridge) as part of Machine Learning Seminar\n\n\nAbstract \nConjectures hold a special status in mathematics. Good conjectures epito mise milestones in mathematical discovery\, and have historically inspired new mathematics and shaped progress in theoretical physics. Hilbert’s l ist of 23 problems and André Weil’s conjectures oversaw major developme nts in mathematics for decades. Crafting conjectures can often be understo od as a problem in pattern recognition\, for which Machine Learning (ML) i s tailor-made. In this talk\, I will propose a framework that allows a pri ncipled study of a space of mathematical conjectures. Using this framework and exploiting domain knowledge and machine learning\, we generate a numb er of conjectures in number theory and group theory. I will present eviden ce in support of some of the resulting conjectures and present a new theor em. I will lay out a vision for this endeavour\, and conclude by posing so me general questions about the pipeline.\n LOCATION:https://researchseminars.org/talk/CompAlg/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Le Quoc Tung (ENS Lyon) DTSTART:20230726T090000Z DTEND:20230726T100000Z DTSTAMP:20260422T212555Z UID:CompAlg/22 DESCRIPTION:Title: Algorithmic and theoretical aspects of sparse deep neural networks\nb y Le Quoc Tung (ENS Lyon) as part of Machine Learning Seminar\n\n\nAbstrac t\nSparse deep neural networks offer a compelling practical opportunity to reduce the cost of training\, inference and storage\, which are growing e xponentially in the state of the art of deep learning. In this presentatio n\, we will introduce an approach to study sparse deep neural networks thr ough the lens of another related problem: sparse matrix factorization\, i. e.\, the problem of approximating a (dense) matrix by the product of (mult iple) sparse factors. In particular\, we identify and investigate in detai l some theoretical and algorithmic aspects of a variant of sparse matrix f actorization named fixed support matrix factorization (FSMF) in which the set of non-zero entries of sparse factors are known. Several fundamental q uestions of sparse deep neural networks such as the existence of optimal s olutions of the training problem or topological properties of its function space can be addressed using the results of (FSMF). In addition\, by appl ying the results of (FSMF)\, we also study butterfly parametrization\, an approach that consists of replacing (large) weight matrices with the produ cts of extremely sparse and structured ones in sparse deep neural networks .\n LOCATION:https://researchseminars.org/talk/CompAlg/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Honglu Fan (Geneva) DTSTART:20230802T090000Z DTEND:20230802T100000Z DTSTAMP:20260422T212555Z UID:CompAlg/23 DESCRIPTION:Title: Local uniformization\, Hilbert scheme of points and reinforcement learnin g\nby Honglu Fan (Geneva) as part of Machine Learning Seminar\n\n\nAbs tract\nIn this talk\, I will give a brief tour about how local uniformizat ion\, the Hilbert scheme of points\, and reinforcement learning come toget her in a joint work (arXiv:2307.00252 [cs.LG]) with Gergely Berczi and Min gcong Zeng.\n LOCATION:https://researchseminars.org/talk/CompAlg/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Charlotte Aten (Denver) DTSTART:20230906T140000Z DTEND:20230906T150000Z DTSTAMP:20260422T212555Z UID:CompAlg/24 DESCRIPTION:Title: Discrete neural nets and polymorphic learning\nby Charlotte Aten (Den ver) as part of Machine Learning Seminar\n\n\nAbstract\nClassical neural n etwork learning techniques have primarily been focused on optimization in a continuous setting. Early results in the area showed that many activatio n functions could be used to build neural nets that represent any function \, but of course this also allows for overfitting. In an effort to amelior ate this deficiency\, one seeks to reduce the search space of possible fun ctions to a special class which preserves some relevant structure. I will propose a solution to this problem of a quite general nature\, which is to use polymorphisms of a relevant discrete relational structure as activati on functions. I will give some concrete examples of this\, then hint that this specific case is actually of broader applicability than one might gue ss.\n LOCATION:https://researchseminars.org/talk/CompAlg/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Felix Schremmer (Hong Kong) DTSTART:20231018T090000Z DTEND:20231018T100000Z DTSTAMP:20260422T212555Z UID:CompAlg/25 DESCRIPTION:Title: Machine learning assisted exploration for affine Deligne-Lusztig varietie s\nby Felix Schremmer (Hong Kong) as part of Machine Learning Seminar\ n\n\nAbstract\nIn this interdisciplinary study\, we describe a procedure t o assist and accelerate research in pure mathematics by using machine lear ning. We study affine Deligne-Lusztig varieties\, certain geometric object s related to a number of mathematical questions\, by carefully developing a number of machine learning models. This iterated pipeline yields well in terpretable and highly accurate models\, thus producing strongly supported mathematical conjectures. We explain how this method could have dramatica lly accelerated the research in the past. A completely new mathematical th eorem\, found by our ML-assisted method and proved using the classical mat hematical tools of the field\, concludes this study. This is joint work wi th Bin Dong\, Pengfei Jin\, Xuhua He and Qingchao Yu.\n LOCATION:https://researchseminars.org/talk/CompAlg/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Bruno Gavranović (Strathclyde) DTSTART:20230920T090000Z DTEND:20230920T100000Z DTSTAMP:20260422T212555Z UID:CompAlg/26 DESCRIPTION:Title: Fundamental Components of Deep Learning: A category-theoretic approach\nby Bruno Gavranović (Strathclyde) as part of Machine Learning Seminar\ n\n\nAbstract\nDeep learning\, despite its remarkable achievements\, is st ill a young field. Like the early stages of many scientific disciplines\, it is permeated by ad-hoc design decisions. From the intricacies of the im plementation of backpropagation\, through new and poorly understood phenom ena such as double descent\, scaling laws or in-context learning\, to a gr owing zoo of neural network architectures - there are few unifying princip les in deep learning\, and no uniform and compositional mathematical found ation. In this talk I'll present a novel perspective on deep learning by u tilising the mathematical framework of category theory. I'll identify two main conceptual components of neural networks\, report on progress made th roughout last years by the research community in formalising them\, and sh ow how they've been used to describe backpropagation\, architectures\, and supervised learning in general\, shedding a new light on the existing fie ld.\n LOCATION:https://researchseminars.org/talk/CompAlg/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Rahul Sarkar (Stanford) DTSTART:20230927T140000Z DTEND:20230927T150000Z DTSTAMP:20260422T212555Z UID:CompAlg/27 DESCRIPTION:Title: A framework for generating inequality conjectures\nby Rahul Sarkar (S tanford) as part of Machine Learning Seminar\n\n\nAbstract\nIn this talk\, I'll present some recent and ongoing work\, where we propose a systematic approach to finding abstract patterns in mathematical data\, in order to generate conjectures about mathematical inequalities. We focus on strict i nequalities of type $f < g$ and associate them with a Banach manifold. We develop a structural understanding of this conjecture space by studying li near automorphisms of this manifold. Next\, we propose an algorithmic pipe line to generate novel conjecture. As proof of concept\, we give a toy alg orithm to generate conjectures about the prime counting function and diame ters of Cayley graphs of non-abelian simple groups. Some of these conjectu res were proved while others remain unproven.\n LOCATION:https://researchseminars.org/talk/CompAlg/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Martina Scolamiero (KTH) DTSTART:20231108T100000Z DTEND:20231108T110000Z DTSTAMP:20260422T212555Z UID:CompAlg/28 DESCRIPTION:Title: Machine Learning with Topological Data Analysis features\nby Martina Scolamiero (KTH) as part of Machine Learning Seminar\n\n\nAbstract\nIn Top ological Data Analysis\, Persistent Homology has been widely used to extra ct features from data. Such features are then used for clustering\, visual ization and classification. In this talk I will describe how we define Lip schitz continuous persistence features starting from pseudo metrics to com pare topological representations of data. Special emphasis will be on the variety of different features that can be constructed in this way and how they can be used in machine learning pipelines. Joint work with the TDA gr oup at KTH.\n LOCATION:https://researchseminars.org/talk/CompAlg/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Agnese Barbensi (Queensland) DTSTART:20231122T100000Z DTEND:20231122T110000Z DTSTAMP:20260422T212555Z UID:CompAlg/29 DESCRIPTION:Title: Persistent homology\, hypergraphs and geometric cycle matching\nby Ag nese Barbensi (Queensland) as part of Machine Learning Seminar\n\n\nAbstra ct\nTopological data analysis has been demonstrated to be a powerful tool to describe topological signatures in real-life data\, and to extract comp lex patterns arising in natural systems. An important challenge in topolog ical data analysis is to find robust ways of computing and analysing persi stent generators\, and to match significant topological signals across dis tinct systems. In this talk\, I will present some recent work dealing with these problems. Our method is based on an interpretation of persistent ho mology summaries with network theoretical tools\, combined with statistica l and optimal transport techniques.\n LOCATION:https://researchseminars.org/talk/CompAlg/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Kyu-Hwan Lee (Connecticut) DTSTART:20231206T150000Z DTEND:20231206T160000Z DTSTAMP:20260422T212555Z UID:CompAlg/30 DESCRIPTION:Title: Data-scientific study of Kronecker coefficients\nby Kyu-Hwan Lee (Con necticut) as part of Machine Learning Seminar\n\n\nAbstract\nThe Kronecker coefficients are the decomposition multiplicities of the tensor product o f two irreducible representations of the symmetric group. Unlike the Littl ewood--Richardson coefficients\, which are the analogues for the general l inear group\, there is no known combinatorial description of the Kronecker coefficients\, and it is an NP-hard problem to decide whether a given Kro necker coefficient is zero or not. In this talk\, we take a data-scientifi c approach to study whether Kronecker coefficients are zero or not. We sho w that standard machine-learning classifiers may be trained to predict whe ther a given Kronecker coefficient is zero or not. Motivated by principal component analysis and kernel methods\, we also define loadings of partiti ons and use them to describe a sufficient condition for Kronecker coeffici ents to be nonzero.\n LOCATION:https://researchseminars.org/talk/CompAlg/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Shailesh Lal (BIMSA) DTSTART:20240320T100000Z DTEND:20240320T110000Z DTSTAMP:20260422T212555Z UID:CompAlg/31 DESCRIPTION:Title: Neural Network solvers for the Yang-Baxter Equation\nby Shailesh Lal (BIMSA) as part of Machine Learning Seminar\n\n\nAbstract\nWe develop a no vel neural network architecture that learns solutions to the Yang Baxter e quation for R matrices of difference form. This method already enables us to learn all solution classes of the 2d Yang Baxter equation. We propose a nd test paradigms for exploring the landscape of Yang Baxter equation solu tion space aided by these methods. Further\, we shall also comment on the application of these methods to generating new solutions of the Yang Baxte r equation. The talk is based on joint work with Suvajit Majumder and Evge ny Sobko available in part in arXiv:2304.07247.\n LOCATION:https://researchseminars.org/talk/CompAlg/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniele Angella (Università di Firenze) DTSTART:20240313T100000Z DTEND:20240313T110000Z DTSTAMP:20260422T212555Z UID:CompAlg/32 DESCRIPTION:Title: Constructing and Machine Learning Calabi-Yau Five-Folds\nby Daniele A ngella (Università di Firenze) as part of Machine Learning Seminar\n\n\nA bstract\nThe significance of Calabi-Yau manifolds transcends both Complex Geometry and String Theory. One possible approach to constructing Calabi-Y au manifolds involves intersecting hypersurfaces within the product of pro jective spaces\, defined by polynomials of a specific degree. We show a me thod to construct all possible complete intersections Calabi-Yau five-fol ds within a product of four or less complex projective spaces\, with up to four constraints. This results in a comprehensive set of 27\,068 distinct spaces. For approximately half of these constructions\, excluding the pro duct spaces\, we can compute the cohomological data\, yielding 2\,375 dist inct Hodge diamonds. We present distributions of the invariants and engage in a comparative analysis with their lower-dimensional counterparts. Supe rvised machine learning techniques are applied to the cohomological data. The Hodge number $h^{1\,1}$ can be learnt with high efficiency\; however\, accuracy diminishes for other Hodge numbers due to the extensive ranges o f potential values. The talk is a joint collaboration with Rashid Alawadhi \, Andrea Leonardo\, and Tancredi Schettini Gherardini.\n LOCATION:https://researchseminars.org/talk/CompAlg/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Ellie Heyes (City\, University of London) DTSTART:20240417T090000Z DTEND:20240417T100000Z DTSTAMP:20260422T212555Z UID:CompAlg/33 DESCRIPTION:Title: Generating Calabi–Yau Manifolds with Machine Learning\nby Ellie Hey es (City\, University of London) as part of Machine Learning Seminar\n\n\n Abstract\nCalabi–Yau n-folds can be obtained as hypersurfaces in toric v arieties built from (n+1)-dimensional reflexive polytopes. Calabi–Yau 3- folds are of particular interest in string theory as they reduce 10-dimens ional superstring theory to 4-dimensional quantum field theories with N=1 supersymmetry. We generate Calabi–Yau 3-folds by generating 4-dimensiona l reflexive polytopes and their triangulations using genetic algorithms an d reinforcement learning respectively. We show how\, by modifying the fitn ess function of the genetic algorithm\, one can generate Calabi–Yau mani folds with specific properties that give rise to certain string models of particular interest.\n LOCATION:https://researchseminars.org/talk/CompAlg/33/ END:VEVENT END:VCALENDAR