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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210303T150000
DTEND;TZID=America/New_York:20210303T160000
DTSTAMP:20260510T013852
CREATED:20240126T084416Z
LAST-MODIFIED:20240517T194704Z
UID:10001419-1614783600-1614787200@cmsa.fas.harvard.edu
SUMMARY:Neural Theorem Proving in Lean using Proof Artifact Co-training and Language Models
DESCRIPTION:Speaker: Jason Rute\, CIBO Technologies \nTitle: Neural Theorem Proving in Lean using Proof Artifact Co-training and Language Models \nAbstract: Labeled data for imitation learning of theorem proving in large libraries of formalized mathematics is scarce as such libraries require years of concentrated effort by human specialists to be built. This is particularly challenging when applying large Transformer language models to tactic prediction\, because the scaling of performance with respect to model size is quickly disrupted in the data-scarce\, easily-overfitted regime. We propose PACT ({\bf P}roof {\bf A}rtifact {\bf C}o-{\bf T}raining)\, a general methodology for extracting abundant self-supervised data from kernel-level proof terms for co-training alongside the usual tactic prediction objective. We apply this methodology to Lean\, an interactive proof assistant which hosts some of the most sophisticated formalized mathematics to date. We instrument Lean with a neural theorem prover driven by a Transformer language model and show that PACT improves theorem proving success rate on a held-out suite of test theorems from 32% to 48%.
URL:https://cmsa.fas.harvard.edu/event/3-3-2021-new-tech-in-math/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-New-Technologies-in-Mathematics-03.03.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210224T150000
DTEND;TZID=America/New_York:20210224T160000
DTSTAMP:20260510T013852
CREATED:20240126T085540Z
LAST-MODIFIED:20240517T194101Z
UID:10001422-1614178800-1614182400@cmsa.fas.harvard.edu
SUMMARY:A Mathematical Language
DESCRIPTION:  \nSpeaker: Thomas Hales\, Univ. of Pittsburgh Dept. of Mathematics \nTitle: A Mathematical Language \nAbstract: A controlled natural language for mathematics is an artificial language that is designed in an explicit way with precise computer-readable syntax and semantics.  It is based on a single natural language (which for us is English) and can be broadly understood by mathematically literate English speakers.  This talk will describe the design of a controlled natural language for mathematics that has been influenced by the Lean theorem prover\, by TeX\, and by earlier controlled natural languages. The semantics are provided by dependent type theory.
URL:https://cmsa.fas.harvard.edu/event/2-24-2021-new-technologies-in-mathematics/
LOCATION:MA
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-New-Technologies-in-Mathematics-02.24.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210210T150000
DTEND;TZID=America/New_York:20210210T160000
DTSTAMP:20260510T013852
CREATED:20240126T092338Z
LAST-MODIFIED:20240515T195824Z
UID:10001434-1612969200-1612972800@cmsa.fas.harvard.edu
SUMMARY:A Mathematical Exploration of Why Language Models Help Solve Downstream Tasks
DESCRIPTION:Speaker: Nikunj Saunshi\, Dept. of Computer Science\, Princeton University \nTitle: A Mathematical Exploration of Why Language Models Help Solve Downstream Tasks \nAbstract: Autoregressive language models pretrained on large corpora have been successful at solving downstream tasks\, even with zero-shot usage. However\, there is little theoretical justification for their success. This paper considers the following questions: (1) Why should learning the distribution of natural language help with downstream classification tasks? (2) Why do features learned using language modeling help solve downstream tasks with linear classifiers? For (1)\, we hypothesize\, and verify empirically\, that classification tasks of interest can be reformulated as next word prediction tasks\, thus making language modeling a meaningful pretraining task. For (2)\, we analyze properties of the cross-entropy objective to show that eps-optimal language models in cross-entropy (log-perplexity) learn features that are O(sqrt{eps}) good on such linear classification tasks\, thus demonstrating mathematically that doing well on language modeling can be beneficial for downstream tasks. We perform experiments to verify assumptions and validate our theoretical results. Our theoretical insights motivate a simple alternative to the cross-entropy objective that performs well on some linear classification tasks. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/2-10-2021-new-tech-in-math/
LOCATION:MA
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-New-Technologies-in-Mathematics-02.10.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210127T150000
DTEND;TZID=America/New_York:20210127T160000
DTSTAMP:20260510T013853
CREATED:20240126T092449Z
LAST-MODIFIED:20240515T191649Z
UID:10001435-1611759600-1611763200@cmsa.fas.harvard.edu
SUMMARY:Knowledge graph representation: From recent models towards a theoretical understanding
DESCRIPTION:Speaker: Carl Allen and Ivana Balažević – University of Edinburgh School of Informatics \nTitle: Knowledge graph representation: From recent models towards a theoretical understanding \nAbstract: Knowledge graphs (KGs)\, or knowledge bases\, are large repositories of facts in the form of triples (subject\, relation\, object)\, e.g. (Edinburgh\, capital_of\, Scotland). Many models have been developed to succinctly represent KGs such that known facts can be recalled (question answering) and\, more impressively\, previously unknown facts can be inferred (link prediction). Subject and object entities are typically represented as vectors in R^d and relations as mappings (e.g. linear transformations) between them. Such representation can be interpreted as positioning entities in a space such that relations are implied by their relative locations. In this talk we give an overview of knowledge graph representation including select recent models; and\, by drawing a connection to word embeddings\, explain a theoretical model for how semantic relationships can correspond to geometric structure.
URL:https://cmsa.fas.harvard.edu/event/1-27-2021-new-tech-in-math-seminar/
LOCATION:MA
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-New-Technologies-in-Mathematics-01.27.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210120T150000
DTEND;TZID=America/New_York:20210120T160000
DTSTAMP:20260510T013853
CREATED:20240126T093733Z
LAST-MODIFIED:20240515T191339Z
UID:10001440-1611154800-1611158400@cmsa.fas.harvard.edu
SUMMARY:Language Modeling for Mathematical Reasoning
DESCRIPTION:Speaker: Christian Szegedy \nTitle: Language Modeling for Mathematical Reasoning \nAbstract: In this talk\, I will summarize the current state of the art of transformer based language models and give examples on non-trivial reasoning task language models can solve in higher order logic reasoning. I will also discuss how to inject injective bias into transformer networks via pretraining on very simple synthetic tasks and representing graph structures for transformer networks. \n 
URL:https://cmsa.fas.harvard.edu/event/1-20-2021-new-tech-in-math/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-New-Technologies-in-Mathematics-01.20.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210113T150000
DTEND;TZID=America/New_York:20210113T160000
DTSTAMP:20260510T013853
CREATED:20240126T093843Z
LAST-MODIFIED:20240517T201031Z
UID:10001441-1610550000-1610553600@cmsa.fas.harvard.edu
SUMMARY:AI and Theorem Proving
DESCRIPTION:Speaker: Josef Urban\, Czech Technical University \nTitle: AI and Theorem Proving \nAbstract: The talk will discuss the main approaches that combine machine learning with automated theorem proving and automated formalization. This includes learning to choose relevant facts for “hammer” systems\, guiding the proof search of tableaux and superposition automated provers by interleaving learning and proving (reinforcement learning) over large ITP libraries\, guiding the application of tactics in interactive tactical systems\, and various forms of lemmatization and conjecturing. I will also show some demos of the systems\, and discuss autoformalization approaches such as learning probabilistic grammars from aligned informal/formal corpora\, combining them with semantic pruning\, and using neural methods to learn direct translation from Latex to formal mathematics.
URL:https://cmsa.fas.harvard.edu/event/1-13-2021-new-technologies-in-mathematics/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-New-Technologies-in-Mathematics-01.13.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201209T150000
DTEND;TZID=America/New_York:20201209T160000
DTSTAMP:20260510T013853
CREATED:20240127T015429Z
LAST-MODIFIED:20240515T200218Z
UID:10001466-1607526000-1607529600@cmsa.fas.harvard.edu
SUMMARY:Machine learning and su(3) structures on six manifolds
DESCRIPTION:Speaker: James Gray – Virginia Tech \nTitle: Machine learning and su(3) structures on six manifolds \nAbstract: In this talk we will discuss the application of Machine Learning techniques to obtain numerical approximations to various metrics of SU(3) structure on six manifolds. More precisely\, we will be interested in SU(3) structures whose torsion classes make them suitable backgrounds for various string compactifications. A variety of aspects of this topic will be covered. These will include learning moduli dependent Ricci-Flat metrics on Calabi-Yau threefolds and obtaining numerical approximations to torsional SU(3) structures. \n 
URL:https://cmsa.fas.harvard.edu/event/12-9-2020-new-tech-in-math/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-New-Technologies-in-Mathematics-12.09.20.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201118T150000
DTEND;TZID=America/New_York:20201118T160000
DTSTAMP:20260510T013853
CREATED:20240127T020145Z
LAST-MODIFIED:20240515T200420Z
UID:10001472-1605711600-1605715200@cmsa.fas.harvard.edu
SUMMARY:Universes as Big Data\, or Machine-Learning Mathematical Structures
DESCRIPTION:Speaker: Yang-Hui He\, Oxford University\, City University of London and Nankai University \nTitle: Universes as Big Data\, or Machine-Learning Mathematical Structures \nAbstract: We review how historically the problem of string phenomenology lead theoretical physics first to algebraic/differetial geometry\, and then to computational geometry\, and now to data science and AI. With the concrete playground of the Calabi-Yau landscape\, accumulated by the collaboration of physicists\, mathematicians and computer scientists over the last 4 decades\, we show how the latest techniques in machine-learning can help explore problems of physical and mathematical interest\, from geometry\, to group theory\, to combinatorics and number theory. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/11-18-2020-new-tech-in-math/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-New-Technologies-in-Mathematics-11.18.20.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201111T150000
DTEND;TZID=America/New_York:20201111T160000
DTSTAMP:20260510T013853
CREATED:20240127T021159Z
LAST-MODIFIED:20240515T200604Z
UID:10001480-1605106800-1605110400@cmsa.fas.harvard.edu
SUMMARY:Towards AI for mathematical modeling of complex biological systems: Machine-learned model reduction\, spatial graph dynamics\, and symbolic mathematics
DESCRIPTION:Speaker: Eric Mjolsness\, Departments of Computer Science and Mathematics\, UC Irvine \nTitle: Towards AI for mathematical modeling of complex biological systems: Machine-learned model reduction\, spatial graph dynamics\, and symbolic mathematics \nAbstract: The complexity of biological systems (among others) makes demands on the complexity of the mathematical modeling enterprise that could be satisfied with mathematical artificially intelligence of both symbolic and numerical flavors. Technologies that I think will be fruitful in this regard include (1) the use of machine learning to bridge spatiotemporal scales\, which I will illustrate with the “Dynamic Boltzmann Distribution” method for learning model reduction of stochastic spatial biochemical networks and the “Graph Prolongation Convolutional Network” approach to course-graining the biophysics of microtubules; (2) a meta-language for stochastic spatial graph dynamics\, “Dynamical Graph Grammars”\, that can represent structure-changing processes including microtubule dynamics and that has an underlying combinatorial theory related to operator algebras; and (3) an integrative conceptual architecture of typed symbolic modeling languages and structure-preserving maps between them\, including model reduction and implementation maps. \n  \n  \n 
URL:https://cmsa.fas.harvard.edu/event/11-11-2020-new-technologies-in-mathematics/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-New-Technologies-in-Mathematics-11.11.20-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201104T150000
DTEND;TZID=America/New_York:20201104T160000
DTSTAMP:20260510T013853
CREATED:20240127T021940Z
LAST-MODIFIED:20240515T200835Z
UID:10001486-1604502000-1604505600@cmsa.fas.harvard.edu
SUMMARY:Some exactly solvable models for machine learning via Statistical physics
DESCRIPTION:Speaker: Florent Krzakala\, EPFL \nTitle: Some exactly solvable models for machine learning via Statistical physics \nAbstract: The increasing dimensionality of data in the modern machine learning age presents new challenges and opportunities. The high dimensional settings allow one to use powerful asymptotic methods from probability theory and statistical physics to obtain precise characterizations and develop new algorithmic approaches. Statistical mechanics approaches\, in particular\, are very well suited for such problems. Will give examples of recent works in our group that build on powerful methods of statistical physics of disordered systems to analyze some relevant questions in machine learning and neural networks\, including overparameterization\, kernel methods\, and the behavior gradient descent algorithm in a high dimensional non-convex landscape.
URL:https://cmsa.fas.harvard.edu/event/11-4-2020-new-technologies-in-math/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-New-Technologies-in-Mathematics-11.04.20.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201028T150000
DTEND;TZID=America/New_York:20201028T160000
DTSTAMP:20260510T013853
CREATED:20240127T031359Z
LAST-MODIFIED:20240515T201157Z
UID:10001502-1603897200-1603900800@cmsa.fas.harvard.edu
SUMMARY:Generalization bounds for rational self-supervised learning algorithms\, or "Understanding generalizations requires rethinking deep learning"
DESCRIPTION:Speakers: Boaz Barak and Yamini Bansal\, Harvard University Dept. of Computer Science \nTitle: Generalization bounds for rational self-supervised learning algorithms\, or “Understanding generalizations requires rethinking deep learning” \nAbstract: The generalization gap of a learning algorithm is the expected difference between its performance on the training data and its performance on fresh unseen test samples. Modern deep learning algorithms typically have large generalization gaps\, as they use more parameters than the size of their training set. Moreover the best known rigorous bounds on their generalization gap are often vacuous. In this talk we will see a new upper bound on the generalization gap of classifiers that are obtained by first using self-supervision to learn a complex representation of the (label free) training data\, and then fitting a simple (e.g.\, linear) classifier to the labels. Such classifiers have become increasingly popular in recent years\, as they offer several practical advantages and have been shown to approach state-of-art results. We show that (under the assumptions described below) the generalization gap of such classifiers tends to zero as long as the complexity of the simple classifier is asymptotically smaller than the number of training samples. We stress that our bound is independent of the complexity of the representation that can use an arbitrarily large number of parameters. Our bound assuming that the learning algorithm satisfies certain noise-robustness (adding small amount of label noise causes small degradation in performance) and rationality (getting the wrong label is not better than getting no label at all) conditions that widely (and sometimes provably) hold across many standard architectures. We complement this result with an empirical study\, demonstrating that our bound is non-vacuous for many popular representation-learning based classifiers on CIFAR-10 and ImageNet\, including SimCLR\, AMDIM and BigBiGAN. The talk will not assume any specific background in machine learning\, and should be accessible to a general mathematical audience. Joint work with Gal Kaplun. \n 
URL:https://cmsa.fas.harvard.edu/event/10-28-2020-new-technologies-in-mathematics-seminar/
LOCATION:MA
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-New-Technologies-in-Mathematics-10.28.20.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201014T150000
DTEND;TZID=America/New_York:20201014T160000
DTSTAMP:20260510T013853
CREATED:20240201T021720Z
LAST-MODIFIED:20240515T192014Z
UID:10001522-1602687600-1602691200@cmsa.fas.harvard.edu
SUMMARY:Triple Descent and a Fine-Grained Bias-Variance Decomposition
DESCRIPTION:Speaker: Jeffrey Pennington\, Google Brain \nTitle: Triple Descent and a Fine-Grained Bias-Variance Decomposition \nAbstract: Classical learning theory suggests that the optimal generalization performance of a machine learning model should occur at an intermediate model complexity\, striking a balance between simpler models that exhibit high bias and more complex models that exhibit high variance of the predictive function. However\, such a simple trade-off does not adequately describe the behavior of many modern deep learning models\, which simultaneously attain low bias and low variance in the heavily overparameterized regime. Recent efforts to explain this phenomenon theoretically have focused on simple settings\, such as linear regression or kernel regression with unstructured random features\, which are too coarse to reveal important nuances of actual neural networks. In this talk\, I will describe a precise high-dimensional asymptotic analysis of Neural Tangent Kernel regression that reveals some of these nuances\, including non-monotonic behavior deep in the overparameterized regime. I will also present a novel bias-variance decomposition that unambiguously attributes these surprising observations to particular sources of randomness in the training procedure.
URL:https://cmsa.fas.harvard.edu/event/10-14-2020-new-technologies-seminar/
LOCATION:MA
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-New-Technologies-in-Mathematics-10.14.20.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20200923T150000
DTEND;TZID=America/New_York:20200923T160000
DTSTAMP:20260510T013853
CREATED:20240209T014918Z
LAST-MODIFIED:20240515T201416Z
UID:10001784-1600873200-1600876800@cmsa.fas.harvard.edu
SUMMARY:Self-induced regularization from linear regression to neural networks
DESCRIPTION:Speaker: Andrea Montanari\, Departments of Electrical Engineering and Statistics\, Stanford \nTitle: Self-induced regularization from linear regression to neural networks \nAbstract: Modern machine learning methods –most noticeably multi-layer neural networks– require to fit highly non-linear models comprising tens of thousands to millions of parameters. Despite this\, little attention is paid to the regularization mechanism to control model’s complexity. Indeed\, the resulting models are often so complex as to achieve vanishing training error: they interpolate the data. Despite this\, these models generalize well to unseen data : they have small test error. I will discuss several examples of this phenomenon\, beginning with a simple linear regression model\, and ending with two-layers neural networks in the so-called lazy regime. For these examples precise asymptotics could be determined mathematically\, using tools from random matrix theory. I will try to extract a unifying picture. A common feature is the fact that a complex unregularized nonlinear model becomes essentially equivalent to a simpler model\, which is however regularized in a non-trivial way. [Based on joint papers with: Behrooz Ghorbani\, Song Mei\, Theodor Misiakiewicz\, Feng Ruan\, Youngtak Sohn\, Jun Yan\, Yiqiao Zhong] \n  \n 
URL:https://cmsa.fas.harvard.edu/event/9-23-2020-new-tech-in-mathematics-seminar/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-New-Technologies-in-Mathematics-09.23.20.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20200916T150000
DTEND;TZID=America/New_York:20200916T160000
DTSTAMP:20260510T013853
CREATED:20240209T021453Z
LAST-MODIFIED:20240515T183741Z
UID:10001799-1600268400-1600272000@cmsa.fas.harvard.edu
SUMMARY:Graph Representation Learning: Recent Advances and Open Challenges
DESCRIPTION:Speaker: William Hamilton\, McGill University and MILA \nTitle: Graph Representation Learning: Recent Advances and Open Challenges \nAbstract: Graph-structured data is ubiquitous throughout the natural and social sciences\, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial if we want systems that can learn\, reason\, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning\, most prominently in the development of graph neural networks (GNNs). Advances in GNNs have led to state-of-the-art results in numerous domains\, including chemical synthesis\, 3D-vision\, recommender systems\, question answering\, and social network analysis. In the first part of this talk I will provide an overview and summary of recent progress in this fast-growing area\, highlighting foundational methods and theoretical motivations. In the second part of this talk I will discuss fundamental limitations of the current GNN paradigm and propose open challenges for the theoretical advancement of the field. \n 
URL:https://cmsa.fas.harvard.edu/event/9-16-2020-new-technologies-seminar/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-New-Technologies-in-Mathematics-09.16.20-1.png
END:VEVENT
END:VCALENDAR