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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241113T100000
DTEND;TZID=America/New_York:20241113T230000
DTSTAMP:20260610T100231
CREATED:20241017T141250Z
LAST-MODIFIED:20241115T175125Z
UID:10003613-1731492000-1731538800@cmsa.fas.harvard.edu
SUMMARY:Frontier of Formal Theorem Proving with Large Language Models: Insights from the DeepSeek-Prover Series
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Huajian Xin\, DeepSeek \nTitle: Frontier of Formal Theorem Proving with Large Language Models: Insights from the DeepSeek-Prover Series \nAbstract: Recent advances in large language models have markedly influenced mathematical reasoning and automated theorem proving within artificial intelligence. Yet\, despite their success in natural language tasks\, these models face notable obstacles in formal theorem proving environments such as Lean and Isabelle\, where exacting derivations must adhere to strict formal specifications. Even state-of-the-art models encounter difficulty generating accurate and complex formal proofs\, revealing the unique blend of mathematical rigor required in this domain. In the DeepSeek-Prover series (V1 and V1.5)\, we have explored specialized methodologies aimed at addressing these challenges. This talk will delve into three foundational areas: the synthesis of training data through autoformalization\, reinforcement learning that utilizes feedback from proof assistants\, and test-time optimization using Monte Carlo tree search. I will also provide insights into current model capabilities\, persistent challenges\, and the future potential of large language models in automated theorem proving.
URL:https://cmsa.fas.harvard.edu/event/newtech_111324/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-11.13.24.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241106T140000
DTEND;TZID=America/New_York:20241106T150000
DTSTAMP:20260610T100231
CREATED:20241021T164918Z
LAST-MODIFIED:20241108T192620Z
UID:10003617-1730901600-1730905200@cmsa.fas.harvard.edu
SUMMARY:Is Behavior Cloning All You Need? Understanding Horizon in Imitation Learning
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Dylan Foster\, Microsoft Research \nTitle: Is Behavior Cloning All You Need? Understanding Horizon in Imitation Learning \nAbstract: Imitation learning (IL) aims to mimic the behavior of an expert in a sequential decision making task by learning from demonstrations\, and has been widely applied to robotics\, autonomous driving\, and autoregressive language generation. The simplest approach to IL\, behavior cloning (BC)\, is thought to incur sample complexity with unfavorable quadratic dependence on the problem horizon\, motivating a variety of different online algorithms that attain improved linear horizon dependence under stronger assumptions on the data and the learner’s access to the expert.In this talk\, we revisit the apparent gap between offline and online IL from a learning-theoretic perspective\, with a focus on general policy classes up to and including deep neural networks. Through a new analysis of behavior cloning with the logarithmic loss\, we will show that it is possible to achieve horizon-independent sample complexity in offline IL whenever (i) the range of the cumulative payoffs is controlled\, and (ii) an appropriate notion of supervised learning complexity for the policy class is controlled. When specialized to stationary policies\, this implies that the gap between offline and online IL is smaller than previously thought. We will then discuss implications of this result and investigate the extent to which it bears out empirically. \nBio: Dylan Foster is a principal researcher at Microsoft Research\, New York. Previously\, he was a postdoctoral fellow at MIT\, and received his PhD in computer science from Cornell University\, advised by Karthik Sridharan. His research focuses on problems at the intersection of machine learning\, AI\, interactive decision making. He has received several awards for his work\, including the best paper award at COLT (2019) and best student paper award at COLT (2018\, 2019). \n 
URL:https://cmsa.fas.harvard.edu/event/newtech_11624/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-11.6.24.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241025T103000
DTEND;TZID=America/New_York:20241025T120000
DTSTAMP:20260610T100231
CREATED:20240912T144420Z
LAST-MODIFIED:20240912T145420Z
UID:10003501-1729852200-1729857600@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_102524/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241023T140000
DTEND;TZID=America/New_York:20241023T150000
DTSTAMP:20260610T100231
CREATED:20241021T140701Z
LAST-MODIFIED:20241108T192710Z
UID:10003616-1729692000-1729695600@cmsa.fas.harvard.edu
SUMMARY:How Far Can Transformers Reason? The Globality Barrier and Inductive Scratchpad
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Aryo Lotfi (EPFL) \nTitle: How Far Can Transformers Reason? The Globality Barrier and Inductive Scratchpad \nAbstract: Can Transformers predict new syllogisms by composing established ones? More generally\, what type of targets can be learned by such models from scratch? Recent works show that Transformers can be Turing-complete in terms of expressivity\, but this does not address the learnability objective. This paper puts forward the notion of ‘globality degree’ of a target distribution to capture when weak learning is efficiently achievable by regular Transformers\, where the latter measures the least number of tokens required in addition to the tokens histogram to correlate nontrivially with the target. As shown experimentally and theoretically under additional assumptions\, distributions with high globality cannot be learned efficiently. In particular\, syllogisms cannot be composed on long chains. Furthermore\, we show that (i) an agnostic scratchpad cannot help to break the globality barrier\, (ii) an educated scratchpad can help if it breaks the globality at each step\, however not all such scratchpads can generalize to out-of-distribution (OOD) samples\, (iii) a notion of ‘inductive scratchpad’\, that composes the prior information more efficiently\, can both break the globality barrier and improve the OOD generalization. In particular\, some inductive scratchpads can achieve length generalizations of up to 6x for some arithmetic tasks depending on the input formatting.
URL:https://cmsa.fas.harvard.edu/event/newtech_102324/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=application/pdf:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-10.23.24.docx-1-1.pdf
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241023T103000
DTEND;TZID=America/New_York:20241023T120000
DTSTAMP:20260610T100231
CREATED:20240911T205240Z
LAST-MODIFIED:20240911T205240Z
UID:10003495-1729679400-1729684800@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_102324/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241021T103000
DTEND;TZID=America/New_York:20241021T120000
DTSTAMP:20260610T100231
CREATED:20240911T195747Z
LAST-MODIFIED:20240911T195747Z
UID:10003482-1729506600-1729512000@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_102124/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241018T103000
DTEND;TZID=America/New_York:20241018T120000
DTSTAMP:20260610T100231
CREATED:20240912T145729Z
LAST-MODIFIED:20240912T145729Z
UID:10003503-1729247400-1729252800@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_101824/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241016T140000
DTEND;TZID=America/New_York:20241016T150000
DTSTAMP:20260610T100231
CREATED:20241010T152711Z
LAST-MODIFIED:20241108T192805Z
UID:10003612-1729087200-1729090800@cmsa.fas.harvard.edu
SUMMARY:From Word Prediction to Complex Skills: Data Flywheels for Mathematical Reasoning
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Anirudh Goyal (University of Montreal) \nTitle: From Word Prediction to Complex Skills: Data Flywheels for Mathematical Reasoning \nAbstract: This talk examines how large language models (LLMs) evolve from simple word prediction to complex skills\, with a focus on mathematical problem solving. A major driver of AI products today is the fact that new skills emerge in language models when their parameter set and training corpora are scaled up. This phenomenon is poorly understood\, and a mechanistic explanation via mathematical analysis of gradient-based training seems difficult. The first part of the talk focuses on analysing emergence using the famous (and empirical) Scaling Laws of LLMs. Then I talk about howc LLMs can verbalize these skills by assigning labels to problems and clustering them into interpretable categories. This metacognitive ability allows us to leverage skill-based prompting\, significantly improving performance on mathematical reasoning. I then present a framework that combines LLMs with human oversight to generate challenging\, out-of-distribution math questions. This process led to the creation of the MATH^2 dataset\, which enhances both model and human performance\, driving further advances in mathematical reasoning capabilities. \n 
URL:https://cmsa.fas.harvard.edu/event/newtech_101624/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-10.16.24.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241016T103000
DTEND;TZID=America/New_York:20241016T120000
DTSTAMP:20260610T100231
CREATED:20240911T205219Z
LAST-MODIFIED:20240911T205219Z
UID:10003494-1729074600-1729080000@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_101624/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241014T103000
DTEND;TZID=America/New_York:20241014T120000
DTSTAMP:20260610T100231
CREATED:20240911T195709Z
LAST-MODIFIED:20240911T195709Z
UID:10003481-1728901800-1728907200@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_101424/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241011T103000
DTEND;TZID=America/New_York:20241011T120000
DTSTAMP:20260610T100231
CREATED:20240912T144347Z
LAST-MODIFIED:20240912T144400Z
UID:10003500-1728642600-1728648000@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_101124/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241009T103000
DTEND;TZID=America/New_York:20241009T120000
DTSTAMP:20260610T100231
CREATED:20240911T205158Z
LAST-MODIFIED:20240911T205158Z
UID:10003493-1728469800-1728475200@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_10924/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241007T103000
DTEND;TZID=America/New_York:20241007T120000
DTSTAMP:20260610T100231
CREATED:20240911T195632Z
LAST-MODIFIED:20240911T195632Z
UID:10003480-1728297000-1728302400@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_10724/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241004T103000
DTEND;TZID=America/New_York:20241004T120000
DTSTAMP:20260610T100231
CREATED:20240912T145639Z
LAST-MODIFIED:20240912T145639Z
UID:10003502-1728037800-1728043200@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_10424/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241002T140000
DTEND;TZID=America/New_York:20241002T150000
DTSTAMP:20260610T100231
CREATED:20240907T180645Z
LAST-MODIFIED:20241002T195652Z
UID:10003453-1727877600-1727881200@cmsa.fas.harvard.edu
SUMMARY:Hierarchical data structures through the lenses of diffusion models
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Antonio Sclocchi\, EPFL \nTitle: Hierarchical data structures through the lenses of diffusion models \nAbstract: The success of deep learning with high-dimensional data relies on the fact that natural data are highly structured. A key aspect of this structure is hierarchical compositionality\, yet quantifying it remains a challenge. \nIn this talk\, we explore how diffusion models can serve as a tool to probe the hierarchical structure of data. We consider a context-free generative model of hierarchical data and show the distinct behaviors of high- and low-level features during a noising-denoising process. Specifically\, we find that high-level features undergo a sharp transition in reconstruction probability at a specific noise level\, while low-level features recombine into new data from different classes. This behavior of latent features leads to correlated changes in real-space variables\, resulting in a diverging correlation length at the transition. \nWe validate these predictions in experiments with real data\, using state-of-the-art diffusion models for both images and texts. Remarkably\, both modalities exhibit a growing correlation length in changing features at the transition of the noising-denoising process. \nOverall\, these results highlight the potential of hierarchical models in capturing non-trivial data structures and offer new theoretical insights for understanding generative AI.
URL:https://cmsa.fas.harvard.edu/event/newtech_10224/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-10.2.24.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241002T103000
DTEND;TZID=America/New_York:20241002T120000
DTSTAMP:20260610T100231
CREATED:20240911T205114Z
LAST-MODIFIED:20240911T205114Z
UID:10003492-1727865000-1727870400@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_10224/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240930T153000
DTEND;TZID=America/New_York:20240930T173000
DTSTAMP:20260610T100231
CREATED:20240912T152420Z
LAST-MODIFIED:20250328T150047Z
UID:10003504-1727710200-1727717400@cmsa.fas.harvard.edu
SUMMARY:Machine Learning in Science Education Panel Discussion
DESCRIPTION:Machine Learning in Science Education Panel Discussion\nMonday\, Sep. 30\, 2024\n3:30-5:30 pm ET \nMachine Learning is rapidly influencing many spheres of human activity. As part of the CMSA Mathematics and Machine Learning Program\, this panel discussion will explore current and future uses of Machine Learning in science education. Panelists will make brief presentations\, which will be followed by discussion and audience questions. \nGregory Kestin (Harvard University)\n AI-Supported Activities: Design Principles and Impact on Student Learning \nLogan McCarty (Harvard University)\nSurveying the Landscape: Teaching and Learning with AI \nAlexis Ross (Massachusetts Institute of Technology)\nAdaptive Teaching towards Misconceptions with LLMs \nIlia Sucholutsky (New York University)\n Why should machines have human-like  representations? Towards  student-centric AI tutors \n  \nOrganizers: \n\nDan Freed (Harvard University and CMSA)\nMichael Douglas (CMSA)
URL:https://cmsa.fas.harvard.edu/event/teachingmachinelearning_93024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,MML Meeting,Special Lectures
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/ML_9.30.24_Machine-Learning-in-Science-Education.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240930T103000
DTEND;TZID=America/New_York:20240930T120000
DTSTAMP:20260610T100231
CREATED:20240911T160033Z
LAST-MODIFIED:20240911T162524Z
UID:10003479-1727692200-1727697600@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_93024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240927T103000
DTEND;TZID=America/New_York:20240927T120000
DTSTAMP:20260610T100231
CREATED:20240912T144322Z
LAST-MODIFIED:20240912T144322Z
UID:10003499-1727433000-1727438400@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_92724/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240925T140000
DTEND;TZID=America/New_York:20240925T150000
DTSTAMP:20260610T100231
CREATED:20240907T180716Z
LAST-MODIFIED:20241002T144226Z
UID:10003454-1727272800-1727276400@cmsa.fas.harvard.edu
SUMMARY:Infinite Limits and Scaling Laws for Deep Neural Networks
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Blake Bordelon \nTitle: Infinite Limits and Scaling Laws for Deep Neural Networks \nAbstract: Scaling up the size and training horizon of deep learning models has enabled breakthroughs in computer vision and natural language processing. Empirical evidence suggests that these neural network models are described by regular scaling laws where performance of finite parameter models improves as model size increases\, eventually approaching a limit described by the performance of an infinite parameter model. In this talk\, we will first examine certain infinite parameter limits of deep neural networks which preserve representation learning and then describe how quickly finite models converge to these limits. Using dynamical mean field theory methods\, we provide an asymptotic description of the learning dynamics of randomly initialized infinite width and depth networks. Next\, we will empirically investigate how close the training dynamics of finite networks are to these idealized limits. Lastly\, we will provide a theoretical model of neural scaling laws which describes how generalization depends on three computational resources: training time\, model size and data quantity. This theory allows analysis of compute optimal scaling strategies and predicts how model size and training time should be scaled together in terms of spectral properties of the limiting kernel. The theory also predicts how representation learning can improve neural scaling laws in certain regimes. For very hard tasks\, the theory predicts that representation learning can approximately double the training-time exponent compared to the static kernel limit.
URL:https://cmsa.fas.harvard.edu/event/newtech_92524/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-9.25.24.docx-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240925T103000
DTEND;TZID=America/New_York:20240925T120000
DTSTAMP:20260610T100231
CREATED:20240911T204040Z
LAST-MODIFIED:20240911T204040Z
UID:10003491-1727260200-1727265600@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_92524/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240923T103000
DTEND;TZID=America/New_York:20240923T120000
DTSTAMP:20260610T100231
CREATED:20240911T153551Z
LAST-MODIFIED:20240912T154245Z
UID:10003478-1727087400-1727092800@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_92324/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240920T103000
DTEND;TZID=America/New_York:20240920T120000
DTSTAMP:20260610T100231
CREATED:20240912T144302Z
LAST-MODIFIED:20240912T144302Z
UID:10003498-1726828200-1726833600@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_92024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240918T103000
DTEND;TZID=America/New_York:20240918T120000
DTSTAMP:20260610T100231
CREATED:20240910T135135Z
LAST-MODIFIED:20240911T203928Z
UID:10003476-1726655400-1726660800@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_91824/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240916T103000
DTEND;TZID=America/New_York:20240916T120000
DTSTAMP:20260610T100231
CREATED:20240911T153307Z
LAST-MODIFIED:20240911T165549Z
UID:10003477-1726482600-1726488000@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_91624/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240913T103000
DTEND;TZID=America/New_York:20240913T120000
DTSTAMP:20260610T100231
CREATED:20240911T210525Z
LAST-MODIFIED:20240911T210525Z
UID:10003497-1726223400-1726228800@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_91324/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240911T103000
DTEND;TZID=America/New_York:20240911T120000
DTSTAMP:20260610T100231
CREATED:20240907T155038Z
LAST-MODIFIED:20240911T210751Z
UID:10003444-1726050600-1726056000@cmsa.fas.harvard.edu
SUMMARY:Math and Machine Learning Program Discussion
DESCRIPTION:Math and Machine Learning Program Discussion \n 
URL:https://cmsa.fas.harvard.edu/event/mml_meeting_91124/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:MML Meeting
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240903T090000
DTEND;TZID=America/New_York:20241101T170000
DTSTAMP:20260610T100231
CREATED:20240105T033600Z
LAST-MODIFIED:20250305T175957Z
UID:10001112-1725354000-1730480400@cmsa.fas.harvard.edu
SUMMARY:Mathematics and Machine Learning Program
DESCRIPTION:Mathematics and Machine Learning Program \nDates: September 3 – November 1\, 2024 \nLocation: Harvard CMSA\, 20 Garden Street\, Cambridge\, MA 0213 \nMachine learning and AI are increasingly important tools in all fields of research. 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. Rigorous numerical methods and interactive theorem proving are playing an important part in obtaining these results. Conversely\, much of the spectacular progress in AI has a surprising simplicity at its core. Surely there are remarkable mathematical structures behind this\, yet to be elucidated. \nThe program will begin and end with two week-long workshops\, and will feature focus weeks on number theory\, knot theory\, graph theory\, rigorous numerics in PDE\, and interactive theorem proving\, as well as a course on geometric aspects of deep learning.\n\n  \nSeptember 3–5\, 2024: Opening Workshop: AI for Mathematicians\, with Leon Bottou\, François Charton\, David McAllester\, Adam Wagner and Geordie Williamson.   A series of six lectures covering logic and theorem proving\, AI methods\, theory of machine learning\, two lectures on case studies in math-AI\, and a lecture and discussion on open problems and the ethics of AI in science.\nOpening Workshop Youtube Playlist \n\nSeptember 6–7\, 2024: Big Data Conference \n  \nSeptember 9–13\, 2024: Applying Machine Learning to Math\, with François Charton and Geordie Williamson\nPublic Lecture September 12\, 2024: Geordie Williamson\, University of Sydney: Can AI help with hard mathematics? (Youtube link)\nThe focus of this week will be on practical examples and techniques for the mathematics researcher keen to explore or deepen their use of AI techniques. We will have talks showcasing easily stated problems\, on which machine learning techniques can be employed profitably. These provide excellent toy examples for generating intuition. We will also have expert talks on some of the technical subtleties which arise. There are several instances where the accepted heuristics emerging from the study of large language models (LLM) and image recognition don’t appear to apply on mathematics problems\, and we will try to highlight these subtleties.\nApplying Machine Learning to Math Youtube Playlist \n  \nSeptember 16–20\, 2024: Number theory\, with Drew Sutherland\nThe focus of this week will be on the use of ML as a tool for finding and understanding statistical patterns in number-theoretic datasets\, using the recently discovered (and still largely unexplained) “murmurations” in the distribution of Frobenius traces in families of elliptic curves and other arithmetic L-functions as a motivating example.\nNumber Theory Youtube Playlist \n  \nSeptember 23–27\, 2024: Knot theory\, with Sergei Gukov\nKnot theory is a great source of labeled data that can be synthetically generated. Moreover\, many outstanding problems in knot theory and low-dimensional topology can be formulated as decision and classification tasks\, e.g. “Is the knot 123_45 slice?” or “Can two given Kirby diagrams be related by a sequence of Kirby moves?” During this focus week we will explore various ways in which AI can be applied to problems in knot theory and how\, based on these applications\, mathematical reasoning can advance development of AI algorithms. Another goal will be to develop formal knot theory libraries (e.g. contributions to mathlib) and to apply AI models to formal proof systems\, in particular in the context of knot theory.\nKnot Theory Youtube Playlist \n  \nSeptember 30: Teaching and Machine Learning Panel Discussion\, 3:30-5:30 pm ET \n  \nSeptember 30–October 4\, 2024: Graph theory and combinatorics\, with Adam Wagner\nThis week\, we will consider how machine learning can help us solve problems in combinatorics and graph theory\, broadly interpreted\, in practice. The advantage of these fields is that they deal with finite objects that are simple to set up using computers\, and programs that work for one problem can often be adapted to work for several other related problems as well. Many times\, the best constructions for a problem are easy to interpret\, making it simpler to judge how well a particular algorithm is performing. On the other hand\, there are lots of open conjectures that are simple to state\, for which the best-known constructions are counterintuitive\, making it perhaps more likely that machine learning methods can spot patterns that are difficult to understand otherwise.\nGraph Theory and Combinatorics Youtube Playlist \n  \nOctober 7–11\, 2024: More number theory\, with Drew Sutherland\nThe focus of this week will be on the use of AI as a tool to search for and/or construct interesting or extremal examples in number theory and arithmetic geometry\, using LLM-based genetic algorithms\, generative adversarial networks\, game-theoretic methods\, and heuristic tree pruning as alternatives to conventional local search strategies.\nMore Number Theory Youtube Playlist \n  \nOctober 14 –18\, 2024: Interactive theorem proving\nThis week we will discuss the use of interactive theorem proving systems such as Lean\, Coq and Isabelle in mathematical research\, and AI systems which prove theorems and translate between informal and formal mathematics.\nInteractive Theorem Proving Youtube Playlist \n  \nOctober 21–25\, 2024: Numerical Partial Differential Equations (PDE)\, with Tristan Buckmaster and Javier Gomez-Serrano\nThe focus of this week will be on constructing solutions to partial differential equations and dynamical systems (finite and infinite dimensional) more broadly defined. We will discuss several toy problems and comment on issues like sampling strategies\, optimization algorithms\, ill-posedness\, or convergence. We will also outline strategies about further developing machine-learning findings and turn them into mathematical theorems via computer-assisted approaches.\nNumerical PDEs Youtube Playlist \n  \nOctober 28–Nov. 1\, 2024: Closing Workshop: The closing workshop will provide a forum for discussing the most current research in these areas\, including work in progress and recent results from program participants.\nMath and Machine Learning Closing Workshop Youtube Playlist \n  \nSeptember 3–Nov. 1: Graduate topics in deep learning theory (Boston College) taught by Eli Grigsby\, held at the CMSA Tuesdays and Thursdays 2:30–3:45 pm Eastern Time. Course website (link).\nGraduate Topics in Deep Learning Youtube Playlist \nCourse description: This is a course on geometric aspects of deep learning theory. Broadly speaking\, we’ll investigate the question: How might human-interpretable concepts be expressed in the geometry of their data encodings\, and how does this geometry interact with the computational units and higher-level algebraic structures in various parameterized function classes\, especially neural network classes? During the portion of the course Sep. 3-Nov. 1\, the course will be presented as part of the Math and Machine Learning program at the CMSA in Cambridge. During that portion\, we will focus on the current state of research on mechanistic interpretability of transformers\, the architecture underlying large language models like Chat-GPT. \n\n\n\n\nPrerequisites: This course is targeted to graduate students and advanced undergraduates in mathematics and theoretical computer science. No prior background in machine learning or learning theory will be assumed\, but I will assume a degree of mathematical maturity (at the level of–say—the standard undergraduate math curriculum+ first-year graduate geometry/topology sequence)\n\n\n\n\n\nProgram Organizers \n\nFrancois Charton (Meta AI)\nMichael R. Douglas (Harvard CMSA)\nMichael Freedman (Harvard CMSA)\nFabian Ruehle (Northeastern)\nGeordie Williamson (Univ. of Sydney)\n\n\nProgram Schedule  \nMonday\n10:30–noon\nOpen Discussion\nRoom G10 \n12:00–1:30 pm\nGroup lunch\nCMSA Common Room \nTuesday\n2:30–3:45 pm\nTopics in deep learning theory\nRoom G10 \n4:00–5:00 pm\nOpen Discussion/Tea\nCMSA Common Room \nWednesday\n10:30 am–12:00 pm\nOpen Discussion\nRoom G10 \n2:00–3:00 pm\nNew Technologies in Mathematics Seminar\nRoom G10 \nThursday\n2:30–3:45 pm\nTopics in deep learning theory\nRoom G10 \nFriday\n10:30 am–12:00 pm\nOpen Discussion\nRoom G10 \n\nHarvard CMSA thanks Mistral AI for a generous donation of computing credit.
URL:https://cmsa.fas.harvard.edu/event/mml2024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Programs
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Machine-Learning-Program-poster-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240320T140000
DTEND;TZID=America/New_York:20240320T150000
DTSTAMP:20260610T100231
CREATED:20240130T215041Z
LAST-MODIFIED:20240321T140550Z
UID:10001519-1710943200-1710946800@cmsa.fas.harvard.edu
SUMMARY:Solving olympiad geometry without human demonstrations
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Trieu H. Trinh\, Google Deepmind and NYU Dept. of Computer Science \nTitle: Solving olympiad geometry without human demonstrations \nAbstract: Proving mathematical theorems at the olympiad level represents a notable milestone in human-level automated reasoning\, owing to their reputed difficulty among the world’s best talents in pre-university mathematics. Current machine-learning approaches\, however\, are not applicable to most mathematical domains owing to the high cost of translating human proofs into machine-verifiable format. The problem is even worse for geometry because of its unique translation challenges\, resulting in severe scarcity of training data. We propose AlphaGeometry\, a theorem prover for Euclidean plane geometry that sidesteps the need for human demonstrations by synthesizing millions of theorems and proofs across different levels of complexity. AlphaGeometry is a neuro-symbolic system that uses a neural language model\, trained from scratch on our large-scale synthetic data\, to guide a symbolic deduction engine through infinite branching points in challenging problems. On a test set of 30 latest olympiad-level problems\, AlphaGeometry solves 25\, outperforming the previous best method that only solves ten problems and approaching the performance of an average International Mathematical Olympiad (IMO) gold medallist. Notably\, AlphaGeometry produces human-readable proofs\, solves all geometry problems in the IMO 2000 and 2015 under human expert evaluation and discovers a generalized version of a translated IMO theorem in 2004. \n 
URL:https://cmsa.fas.harvard.edu/event/nt-32024/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-03.20.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240306T140000
DTEND;TZID=America/New_York:20240306T150000
DTSTAMP:20260610T100231
CREATED:20240108T153449Z
LAST-MODIFIED:20240306T221235Z
UID:10001129-1709733600-1709737200@cmsa.fas.harvard.edu
SUMMARY:LILO: Learning Interpretable Libraries by Compressing and Documenting Code
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Gabe Grand\, MIT CSAIL and Dept. of EE&CS \nTitle: LILO: Learning Interpretable Libraries by Compressing and Documenting Code \nAbstract: While large language models (LLMs) now excel at code generation\, a key aspect of software development is the art of refactoring: consolidating code into libraries of reusable and readable programs. In this paper\, we introduce LILO\, a neurosymbolic framework that iteratively synthesizes\, compresses\, and documents code to build libraries tailored to particular problem domains. LILO combines LLM-guided program synthesis with recent algorithmic advances in automated refactoring from Stitch: a symbolic compression system that efficiently identifies optimal lambda abstractions across large code corpora. To make these abstractions interpretable\, we introduce an auto-documentation (AutoDoc) procedure that infers natural language names and docstrings based on contextual examples of usage. In addition to improving human readability\, we find that AutoDoc boosts performance by helping LILO’s synthesizer to interpret and deploy learned abstractions. We evaluate LILO on three inductive program synthesis benchmarks for string editing\, scene reasoning\, and graphics composition. Compared to existing neural and symbolic methods – including the state-of-the-art library learning algorithm DreamCoder – LILO solves more complex tasks and learns richer libraries that are grounded in linguistic knowledge.
URL:https://cmsa.fas.harvard.edu/event/nt-3624/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-03.06.2024.png
END:VEVENT
END:VCALENDAR