Harvard geometric machine learning. In this work, we show that several empirical Lear...

Harvard geometric machine learning. In this work, we show that several empirical Learn how to use decision trees, the foundational algorithm for your understanding of machine learning and artificial intelligence. Persistent homology captures intrinsic geometric and structural characteristics of the data through Betti numbers, which describe connected components (Betti-0), loops (Betti-1), and voids (Betti-2). Pure mathematical data has been compiled over the last few decades by the community and experiments in supervised, semi-supervised and unsupervised machine learning have found surprising success. Lectures will be complemented by student-led discussions of relevant papers. Great to see our research on geometric machine learning featured in this Harvard Gazette piece on math and AI. Motivated by a classical tube formula due to Weyl, we introduce a method to measure the decision boundary of a neural network through local surface volumes, providing a Explore a 55-minute conference talk from the Big Data Conference 2024 where Harvard Mathematics professor Melanie Weber delves into the geometric structures within machine learning data and their implications for neural network design. Abstract A cornerstone of machine learning is the identification and exploitation of struc-ture in high-dimensional data. This role offers an opportunity to perform research at the intersection of Geometry and Machine Learning, with a focus on studying geometric structures in data and models and how to leverage such structure for the Feb 16, 2025 · A postdoctoral position is available in the Geometric Machine Learning Group at Harvard University, led by Prof. However, for geometric PDEs whose inputs and outputs transform under changes of local frame (gauge), many existing operator-learning architectures remain representation-dependent, brittle under metric perturbations, and 15 hours ago · Harvard’s equal employment opportunity policy and non-discrimination policy help all community members participate fully in work and campus life free from harassment and discrimination. Based on these two structural differences, the critic match loss Assistant Professor Harvard University Biography I am an Assistant Professor of Applied Mathematics and of Computer Science at Harvard, where I lead the Geometric Machine Learning Group. g. From shape spaces equipped with a quotient geometry to neural networks parameterized with orthogonality constraints, researchers are poised to compute with geometric objects. In my group, we study how data—not just models—shapes the behavior and reliability I am an assistant professor in the Department of Statistics, Harvard University. . Douglas Geometric Methods for Graph Machine Learning Graph-structured data is ubiquitous in the Sciences and En-gineering; Graph ML has had a tremendous impact on scien-tific discovery, biomedical research and in the study of social networks, among others. Algebra, geometry, trigonometry, precalculus, and calculus! We would like to show you a description here but the site won’t allow us. Outside of Jan 10, 2025 · A cornerstone of machine learning is the identification and exploitation of structure in high‐dimensional data. From the 3D MRI volumes, we derive a compact set of 100 topological features that summarize the underlying topology of brain tumor structures. This course aims to bridge the gap between a Aug 4, 2025 · This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. , modeling disease progression, candidate biomarker discovery for targeted therapies, rapid Machine Learning Systems. I'm also an Associate Faculty at the Kempner Institute, and have affiliations with the Harvard Data Science Initiative. Eve Bodnia | Geometry of Machine Learning Workshop lecture Harvard CMSA • 1K views • 4 months ago This article surveyed work at the intersection of geometry and machine learning, focusing on characterizing geomet-ric structure in data and the design of algorithms and architectures that leverage such structure to learn more efficiently. Douglas (CMSA) and Mike Freedman (CMSA) […] APMTH 336 at Harvard University (Harvard) in Cambridge, Massachusetts. The main purpose of this workshop is to bring together researchers from both algebraic geometry and machine learning. So it’s significant to study non-Euclidean data with deep learning. Sep 15, 2025 · In this talk, we will delve into the inner workings of AlphaGeometry, exploring the innovative techniques that enable it to tackle intricate geometric puzzles. Choi Kempner Institute at Harvard University 150 Western Ave, Boston, MA 02134 benchoi@college. We will uncover how this AI system combines the power of neural networks with symbolic reasoning to discover elegant solutions. He is particularly invested in geometric deep learning and natural language processing, seeking to answer important questions about the geometry of data as well as the real-world implications of privacy and interpretability in LLMs. Jul 3, 2025 · Position Description: A postdoctoral position is available in the Geometric Machine Learning Group at Harvard University, led by Prof. For neural networks, we The Geometry of Machine Learning 2026 Dates: September 8–11, 2026 Location: Harvard CMSA, Room G10, 20 Garden Street, Cambridge MA 02138 Organizers: Michael R. Sep 16, 2025 · Geometry of Machine Learning Special Lecture: Yann LeCun Date: Tuesday, Sep. Oct 26, 2024 · Geometric Deep Learning represents a significant advancement in the field of machine learning, offering new ways to model complex, non-Euclidean data. My research focuses on utilizing geometric structure in data for the design of efficient Machine Learning and Optimization methods with provable guarantees. Sep 1, 2022 · Request PDF | Geometric machine learning: research and applications | Over the last decade, deep learning has revolutionized many traditional machine learning tasks, ranging from computer vision Apr 6, 2022 · Over the last decade, deep learning has revolutionized many traditional machine learning tasks, ranging from computer vision to natural language processing. My research bridges Riemannian geometry, machine learning, and signal processing, which I use to develop interpretable and theory-grounded machine learning approaches for inverse problems, manifold learning, and data-driven modeling in the sciences. This course teaches the mathematics needed to understand how artificial intelligence (AI) works under the hood. Contribute to harvard-edge/cs249r_book development by creating an account on GitHub. AI Magazine 2025 2024 B Kiani, L Fesser, M Weber. This tutorial surveys impact areas in precision medicine (e. Although deep learning has achieved excellent performance, it does not perform as well as expected on geometric (non-Euclidean domain) data. Access on-demand learning modules, expert-led sessions, and Harvard insights that help you apply AI to real business challenges—join today for access through September 2026. harvard. The explicit incorporation of spatial regularity into the diffusion construction leads to smoother random processes that are more adapted for This work extends an established critic match loss landscape visualization method from online to off-policy reinforcement learning (RL), aiming to reveal the optimization geometry behind critic learning. This role offers an opportunity to perform research at the intersection of Geometry and Machine Learning, with a focus on studying geometric structures in data and models and how to leverage such structure for the Aug 21, 2025 · A postdoctoral position is available in the Geometric Machine Learning Group at Harvard University, led by Prof. Apr 26, 2022 · Deep Learning-based Parameter Transfer in Meteorological Data Gpu Accelerated Scalable Parallel Coordinates Plots Evaluation of Volume Representation Networks for Meteorological Ensemble Compression Efficient High-Quality Rendering of Ribbons and Twisted Lines 3D Vision and Learning for Robotic Perception and Decision-Making Oct 30, 2020 · Manifold learning is a popular and quickly-growing subfield of machine learning based on the assumption that one's observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. Whether you’re a mathematician, seasoned data scientist, or marketing professional, you’ll find The Shape of Data to be the perfect introduction to the critical interplay between Jan 10, 2025 · Melanie Weber is an Assistant Professor of Applied Mathematics and of Computer Science at Harvard University, where she leads the Geometric Machine Learning Group. Since 2017 machine-learning techniques have […] Jason is a junior concentrating in computer science and mathematics with a voracious appetite for all things machine learning. Graph representation learning has matured immensely as a field within the last few years. I am also a researcher at Microsoft Research New England. Recent work in quantum machine learning suggests that unitary evolutions and Hilbert-space embeddings can introduce useful inductive biases for learning. Euclidean data is everywhere. Harvard Geometric Machine Learning Group has 11 repositories available. This role offers an opportunity to perform research at the intersection of Geometry and Machine Learning, with a focus on studying geometric structures in data and models and how to leverage such structure for the design of efficient machine Feb 23, 2026 · Speaker: Emmanuel Abbé (EPFL, Institute of Mathematics and School of Computer and Communication Sciences) Mar 22, 2023 · We survey some recent applications of machine learning to problems in geometry and theoretical physics. An unsupervised learning algorithm to cluster hyperspectral image (HSI) data that leverages spatially regularized random walks is proposed. By analyzing vast amounts of data, machine learning algorithms can identify patterns and relationships to produce accurate predic-tions or decisions. Learn how to use decision trees, the foundational algorithm for your understanding of machine learning and artificial intelligence. About I'm an Assistant Professor of Computer Science at Harvard SEAS where I lead the Data-Centric Machine Learning (DCML) group. Harvard’s equal employment opportunity policy and non-discrimination policy help all community members participate fully in work and campus life free from harassment and discrimination. My research interests span Applied Probability, Statistics, and Machine Learning. Mar 5, 2025 · Compact Ricci-flat Calabi-Yau and holonomy G2 manifolds appear in string and M-theory respectively as descriptions of the extra spatial dimensions that arise in the theories. This course will give an overview of this emerging research area and its mathematical foundation, with a focus on recent literature and open problems. Graph machine learning approaches, also known as geometric deep learning, or graph neural networks has become widely used in biomedical applications. Browse the latest Mathematics courses from Harvard University. Sep 17, 2025 · A postdoctoral position is available in the Geometric Machine Learning Group at Harvard University, led by Prof. M Weber. Learn more… This advanced machine learning book highlights many algorithms from a geometric perspective and introduces tools in network science, metric geometry, and topological data analysis through practical application. Sep 15, 2025 · Home Calendar The Geometry of Machine Learning The Geometry of Machine Learning 2025 SEP 15 Date Monday, Sep 15, 2025 (All day) - Thursday, Sep 18, 2025 (All day) This course teaches the mathematics needed to understand how artificial intelligence (AI) works under the hood. Follow their code on GitHub. Thank you for supporting our work! Aug 29, 2022 · Melanie Weber, Assistant Professor of Applied Mathematics and Computer Science, explores the interaction of geometry and machine learning to develop better algorithms, especially when data and resources are limited. While classical approaches assume that data lies in a high‐dimensional Euclidean Geometric Methods for Graph Machine Learning Graph-structured data is ubiquitous in the Sciences and En-gineering; Graph ML has had a tremendous impact on scien-tific discovery, biomedical research and in the study of social networks, among others. Interactive online math videos, lessons, and tutoring. NTT Research and Harvard scientists use machine learning to enhance biohybrid ray development, advancing technology in medical and scientific fields. These tutorials aim to: Introduce the concept of graph neural networks (GNNs). Course site: https://locator. Emphasis is placed on BibMe™ Plus 3-day free trial* Citation style APA only MLA, APA, Chicago, Harvard & 7,000 more Ad-free experience Plagiarism detection Expert help with your papers The HarvardX Professional Certificate in Python for Data Science and Machine Learning provides learners with hands-on experience in popular libraries and methodologies, positioning them to thrive in a market with diverse opportunities. Data Science: Building Machine Learning Models Build a movie recommendation system and learn the science behind one of the most popular and successful data science techniques. Learn about the prevalence of geometric patterns in machine learning, particularly focusing on fundamental symmetries like permutation-invariance in graphs and We will cover a range of topics at the intersection of geometry and machine learning including basic differential geometry, graph representation learning, manifold learning, graph neural networks, machine learning on manifolds, and geometric deep learning. While classical approaches assume that data lies in a high-dimensional Euclidean space, geometric machine learning methods are designed for non-Euclidean data, including graphs, strings, and matrices, or data characterized by symmetries inherent in the underlying system. Browse the latest courses from Harvard University Master how to use AI in your everyday work and drive impact at your organization. Throughout the thesis, we will nd that understanding the underlying mathematical structure of machine learning algorithms enables us to interpret, improve, and extend upon them. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships but also geometric properties including cell volumes, volumes of faces where cells meet, and dihedral angles between adjacent cells. Graph Pooling via Ricci Flow Transactions on Machine Learning Research 2024 B Kiani, J Wang, M Weber. Oct 1, 2023 · Recently, there has been a surge of interest in exploiting geometric structure in data and models in Machine Learning. The Geometry of Machine Learning 2026 Dates: September 8–11, 2026 Location: Harvard CMSA, Room G10, 20 Garden Street, Cambridge MA 02138 Organizers: Michael R. The main difference arises from the crucial use of non-linearity in […] Geometry of Machine Learning Special Lecture 9/16/2025Speaker: Yann LeCun, NYU & METATitle: Self-Supervised Learning, JEPA, World Models, and the future of AI Sep 16, 2025 · Geometry of Machine Learning Special Lecture: Yann LeCun Title: Self-Supervised Learning, JEPA, World Models, and the future of AI Date: Tuesday, Sep. I am an Assistant Professor of Applied Mathematics and of Computer Science at Harvard, where I lead the Geometric Machine Learning Group. edu/course/colgsas-220762/2022/spring/20263 In parallel to these developments, machine learning problems such as exploring optimisation landscapes of deep learning and training various machine learning algorithms can be posed as algebraic geometry problems. In Jan 10, 2025 · Melanie Weber is an Assistant Professor of Applied Mathematics and of Computer Science at Harvard University, where she leads the Geometric Machine Learning Group. Melanie Weber. Douglas Geometric Machine Learning and Applications in the Sciences Presenter: Melanie Weber (Harvard University) Title: Geometric Machine Learning and Applications in the Sciences Date/Time: Tuesday, June 18th, 9:30 - 11:00 AM Abstract: Many machine learning and data science applications involve data with geometric structure, such as graphs, strings, and matrices, or data with symmetries that arise Jan 10, 2025 · A cornerstone of machine learning is the identification and exploitation of structure in high‐dimensional data. This study presents the first validated ML model for predicting EBW success rate prior to execution, using real manufacturing data from the International Thermonuclear Machine-learning forecasts indicate a critical transition period of four to five years, during which timely maintenance is essential to bridge the gap between brushwood-beam decay and root-system maturation, thereby ensuring long-term slope stability. This thesis presents a mathematical perspective on manifold learning, delving into the intersection of kernel learning, spectral graph theory, and differential geometry. Multispectral satellite imagery poses significant challenges for deep learning models due to the high dimensionality of spectral data and the presence of structured correlations across channels. We study geometric structure in data and models and how to leverage such information for the design of efficient machine learning algorithms with provable guarantees. It emphasized the potential of these approaches to improve In order to understand modern semi-supervised learning methods, we develop an toolkit of mathematical methods in spectral graph theory and Riemannian geometry. tlt. This study presents the first validated ML model for predicting EBW success rate prior to execution, using real manufacturing data from the International Thermonuclear Jan 10, 2025 · Melanie Weber is an Assistant Professor of Applied Mathematics and of Computer Science at Harvard University, where she leads the Geometric Machine Learning Group. Sep 15, 2025 · The Geometry of Machine Learning Dates: September 15–18, 2025 Location: Harvard CMSA, Room G10, 20 Garden Street, Cambridge MA 02138 Directions to CMSA Despite the extraordinary progress in large language models, mathematicians suspect that other dimensions of intelligence must be defined and simulated to complete the picture. The structure, annotation, normalization, and interpretation of genome scale assays. The Learning solution operators of partial differential equations (PDEs) from data has emerged as a promising route to fast surrogate models in multi-query scientific workflows. Discuss the theoretical motivation behind For classification tasks, the performance of a deep neural network is determined by the structure of its decision boundary, whose geometry directly affects essential properties of the model, including accuracy and robustness. Geometric Machine Learning Data spaces with geometric structures arise in many fields in machine learning. We propose a high-efficiency, two-stage machine learning framework designed to identify high-performance NANF designs using minimal training data. Geometric Machine Learning. 16, 2025 Time: 5:00 pm ET Location: Harvard Science Center, Hall C & via Zoom Webinar Registration required. We would like to show you a description here but the site won’t allow us. These include the CMSA Postdoctoral Fellowship, the George F. Carrier Postdoctoral Fellowship, the Kempner Research Fellowship, and the Harvard Data Science Postdoctoral Fellowship. edu 3 days ago · Where: Science Center 232 Speaker: Frank Lu (Harvard) Read more HARVARD-MIT ALGEBRAIC GEOMETRY A modest extension of Reider’s Theorem on ample divisors on a surface When: March 24, 2026 3:00 pm - 4:00 pm Graph machine learning provides a powerful toolbox to learn representations from any arbitrary graph structure and use learned representations for a variety of downstream tasks. While classical approaches assume that data lies in a high‐dimensional Euclidean space, geometric machine learning methods are designed for non‐Euclidean data, including graphs, strings, and matrices, or data characterized by symmetries inherent in the underlying system. It’s a subset of artificial intelligence that involves creating algorithms capable of making predictions or decisions based on data. Group Photos Faculty Postdocs and Graduate Students Behrooz Tahmasebi Area: Geometric Deep Learning Thien Le Area: Graph Machine Learning Willem Diepeveen Area: Geometric Representation Learning, Optimization on Manifolds Abduhla Ali Area: AI for Science Tianyu Zhao Area: Graph Machine Learning Student Researchers Ben Choi Area: Geometry of Foundation Models Camilo Brown-Pinilla Area: Geometry APMTH 220 at Harvard University (Harvard) in Cambridge, Massachusetts. Harvard also offers various independent postdoctoral fellowships suitable for candidates interested in working with us on Geometric Machine Learning. The workshop explored the intersection of Foundation Models and Geometric Machine Learning, highlighting how alternative geometric embedding spaces like hyperbolic and spherical geometries could overcome the limitations of traditional Euclidean foundation models. Markov diffusions are defined on the space of HSI spectra with transitions constrained to near spatial neighbors. In Oct 13, 2020 · Quiver theory and machine learning share a common ground, namely, they both concern about linear representations of directed graphs. Sep 3, 2024 · Recent milestones in machine learning for mathematics include data-driven discovery of theorems in knot theory and representation theory, the discovery and proof of new singular solutions of the Euler equations, new counterexamples and lower bounds in graph theory, and more. Off-policy RL differs from stepwise online actor-critic learning in its replay-based data flow and target computation. Our research supports geometric modeling in machine learning by developing new methods and an open-source software The Geometry of Machine Learning 2026 Dates: September 8–11, 2026 Location: Harvard CMSA, Room G10, 20 Garden Street, Cambridge MA 02138 Organizers: Michael R. Geometric Machine Learning on EEG Signals Benjamin J. The Geometric Machine Learning Group at Harvard University studies how to identify geometry structure in data and models and how to leverage such structure for the design of efficient machine learning algorithms with provable guarantees. Recently, many studies on extending deep learning approaches for graphs and manifolds have merged Learn to use machine learning in Python in this introductory course on artificial intelligence. In-person registration* Zoom Webinar […] Discrete notions of curvature not only allow for characterizing data geometry, but have many applications in graph machine learning. This course aims to bridge the gap between a The Geometry of Machine Learning Dates: September 15–18, 2025 Location: Harvard CMSA, Room G10, 20 Garden Street, Cambridge MA 02138 Despite the extraordinary progress in Machine Learning Accelerated Molecular Dynamics Neural Equivariant Interatomic Potentials NequIP showed for the first time that geometric equivariance leads to interatomic potentials with remarkable accuracy and an unprecedented data efficiency [1]. Machine Learning (ML) is increasingly used in advanced manufacturing, yet its application to predictive weld quality assurance remains limited, particularly for high-precision techniques such as electron beam welding (EBW). Unitary Convolutions for Learning on Graphs and Groups NeurIPS 2024 Spotlight A Feng, M Weber. Recently, there has been a surge of interest in exploiting geometric structure in data and models in machine learning. We will cover a range of topics at the intersection of Geometry and Machine Learning including Basic Differential Geometry We would like to show you a description here but the site won’t allow us. 16, 2025 Time: 5:00 pm ET Location: Harvard Science […] In this context, the emergence of geometric deep learning has filled the above technical gaps and realized the effective combination of deep learning tech-nology and non-Euclidean data, which consists of manifolds and graphs. Machine learning is the technology behind these amazing feats. As machine learning becomes more ubiquitous and the software libraries easier to use, developers may become unaware of the underlying design decisions, and therefore the limitations and possible biases, of machine learning algorithms. Apr 26, 2022 · Deep Learning-based Parameter Transfer in Meteorological Data Gpu Accelerated Scalable Parallel Coordinates Plots Evaluation of Volume Representation Networks for Meteorological Ensemble Compression Efficient High-Quality Rendering of Ribbons and Twisted Lines 3D Vision and Learning for Robotic Perception and Decision-Making We would like to show you a description here but the site won’t allow us. By incorporating geometric principles such as symmetry, invariance, and equivariance, GDL models can achieve better performance on a wide range of tasks, from 3D object recognition to drug discovery. We thus advocate the programme of machine learning mathematical structures, and formulating Sep 18, 2023 · We received a grant from the Harvard Data Science Initiative’s Competitive Research Fund to support our research on learning under symmetry. This role offers an opportunity to perform research at the intersection of Geometry and Machine Learning, with a focus on studying geometric structures in data and models and how to leverage such structure for the Hollow-core fibers offer superior loss and latency characteristics compared to solid-core alternatives, yet the geometric complexity of nested antiresonance nodeless fibers (NANFs) makes traditional optimization computationally prohibitive. dfsfibr uhtyhhj uxyr quqppr dznit ulppjxc dfqg idmcri dsnpum frac