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DTSTART;TZID=America/New_York:20250423T140000
DTEND;TZID=America/New_York:20250423T150000
DTSTAMP:20260404T225719
CREATED:20250128T214818Z
LAST-MODIFIED:20250311T184354Z
UID:10003709-1745416800-1745420400@cmsa.fas.harvard.edu
SUMMARY:Machine learning for analytic calculations in theoretical physics
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Matthias Wilhelm (University of Southern Denmark) \nTitle: Machine learning for analytic calculations in theoretical physics \nAbstract: In this talk\, we will present recent progress on applying machine-learning techniques to improve calculations in theoretical physics\, in which we desire exact and analytic results. One example are so-called integration-by-parts reductions of Feynman integrals\, which pose a frequent bottleneck in state-of-the-art calculations in theoretical particle and gravitational-wave physics. These reductions rely on heuristic approaches for selecting a finite set of linear equations to solve\, and the quality of the heuristics heavily influences the performance. In this talk\, we investigate the use of machine-learning techniques to find improved heuristics. We use funsearch\, a genetic programming variant based on code generation by a Large Language Model\, in order to explore possible approaches\, then use strongly typed genetic programming to zero in on useful solutions. Both approaches manage to re-discover the state-of-the-art heuristics recently incorporated into integration-by-parts solvers\, and in one example find a small advance on this state of the art.
URL:https://cmsa.fas.harvard.edu/event/newtech_42325/
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-4.23.2025.docx-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250409T140000
DTEND;TZID=America/New_York:20250409T150000
DTSTAMP:20260404T225719
CREATED:20250128T214458Z
LAST-MODIFIED:20250410T150618Z
UID:10003707-1744207200-1744210800@cmsa.fas.harvard.edu
SUMMARY:Can Transformers Do Enumerative Geometry?
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Baran Hashemi\, Technical University of Munich \nTitle: Can Transformers Do Enumerative Geometry? \nAbstract: How can Transformers model and learn enumerative geometry? What is a systematic procedure for using Transformers in abductive knowledge discovery within a mathematician-machine collaboration? In this work\, we introduce a Neural Enumerative Reasoning model for computation of ψ-class intersection numbers on the moduli space of curves. By reformulating the problem as a continuous optimization task\, we compute intersection numbers across a wide value range from 10e-45 to 10e45. To capture the recursive nature inherent in these intersection numbers\, we propose the Dynamic Range Activator (DRA)\, a new activation function that enhances the Transformer’s ability to model recursive patterns and handle severe heteroscedasticity. Given precision requirements for computing the intersections\, we quantify the uncertainty of the predictions using Conformal Prediction with a dynamic sliding window adaptive to the partitions of equivalent number of marked points. Beyond simply computing intersection numbers\, we explore the enumerative “world-model” of Transformers. Our interpretability analysis reveals that the network is implicitly modeling the Virasoro constraints in a purely data-driven manner. Moreover\, through abductive hypothesis testing\, probing\, and causal inference\, we uncover evidence of an emergent internal representation of the large-genus asymptotic of ψ-class intersection numbers. This opens up new possibilities in inferring asymptotic closed-form expressions directly from limited amount of data. \nThis talk is based on https://openreview.net/pdf?id=4X9RpKH4Ls. \n 
URL:https://cmsa.fas.harvard.edu/event/newtech_4925/
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-4.9.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250402T140000
DTEND;TZID=America/New_York:20250402T150000
DTSTAMP:20260404T225719
CREATED:20250128T214417Z
LAST-MODIFIED:20250403T144343Z
UID:10003706-1743602400-1743606000@cmsa.fas.harvard.edu
SUMMARY:Learning Dynamical Transport without Data
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Michael Albergo (Harvard) \nTitle: Learning Dynamical Transport without Data \nAbstract: Algorithms based on dynamical transport of measure\, such as score-based diffusion models\, have resulted in great progress in the field of generative modeling. However\, these algorithms rely on access to an abundance of data from the target distribution. A complementary problem to this is learning to generate samples from a target distribution when only given query access to the unnormalized log-likelihood or energy function associated to it\, with myriad application in statistical physics\, chemistry\, and Bayesian inference. I will present an algorithm based on dynamical transport to sample from a target distribution in this context\, which can be seen as an augmentation of annealed importance sampling and sequential Monte Carlo. Time permitting\, I will also discuss how to generalize these ideas to dynamics of discrete distributions. This is joint work with Eric Vanden-Eijnden\, Peter Holderrieth\, and Tommi Jaakkola. \n 
URL:https://cmsa.fas.harvard.edu/event/newtech_4225/
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-4.2.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250327T100000
DTEND;TZID=America/New_York:20250327T110000
DTSTAMP:20260404T225719
CREATED:20250128T214249Z
LAST-MODIFIED:20250327T192309Z
UID:10003666-1743069600-1743073200@cmsa.fas.harvard.edu
SUMMARY:AlphaProof: when reinforcement learning meets formal mathematics
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Thomas Hubert (Google DeepMind) \nTitle: AlphaProof: when reinforcement learning meets formal mathematics \nAbstract: Galileo\, the renowned Italian astronomer\, physicist\, and mathematician\, famously described mathematics as the language of the universe. Progress since only confirmed his intuition as the world we live in can be described with extreme precision with just a few mathematical equations.\nIn the last 70 years\, the rise of computers has also enriched our understanding of and revolutionized the world we live in. Mathematics tremendously benefited from this digital revolution as well: while Gauss had to compute primes by hand\, computers and computation are now routinely used in research mathematics and contribute to grand problems like the Birch and Swinnerton-Dyer conjecture\, one of the Millennium Prize Problems.\nToday\, computers are entering a new age\, one in which computation can be transformed into reasoning. In this talk\, I would like to discuss two such developments that will undoubtedly have an integral role to play in the future of mathematics: the concurrent rise of formal mathematics and of machine intelligence.
URL:https://cmsa.fas.harvard.edu/event/newtech_32625/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-3.27.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250312T140000
DTEND;TZID=America/New_York:20250312T150000
DTSTAMP:20260404T225719
CREATED:20250123T195100Z
LAST-MODIFIED:20250327T194539Z
UID:10003665-1741788000-1741791600@cmsa.fas.harvard.edu
SUMMARY:Discovery in Mathematics with Automated Conjecturing
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Randy Davila\, RelationalAI and Rice University \nTitle: Discovery in Mathematics with Automated Conjecturing \nAbstract: Automated conjecturing is a form of artificial intelligence that applies heuristic-driven methods to mathematical discovery. Since the late 1980s\, systems such as Fajtlowicz’s Graffiti\, DeLaViña’s Graffiti.pc\, and TxGraffiti have collectively contributed to over 130 publications in mathematical journals. In this talk\, we outline the evolution of automated conjecturing\, focusing on TxGraffiti\, a program that employs linear optimization methods and several distinct heuristics to generate mathematically meaningful conjectures. We will then introduce GraphMind\, a dueling framework where the Optimist proposes conjectures while the Pessimist seeks counterexamples\, fostering a feedback loop that strengthens automated reasoning. Finally\, we will present GraffitiAI\, a Python package that extends automated conjecturing across various mathematical domains. \nBio: Randy R. Davila is a Lecturer in the Department of Computational Applied Mathematics & Operations Research at Rice University and a Library Engineer at RelationalAI\, specializing in relational knowledge graph systems for intelligent data management. He earned his PhD in Mathematics from the University of Johannesburg in 2019\, with research focused on graph theory and combinatorial optimization. His work explores artificial intelligence in mathematical conjecture generation\, graph theory\, and neural network applications to combinatorial problems. As the creator of TxGraffiti\, he has developed AI-driven systems that have contributed to numerous mathematical publications. His recent projects include GraphMind\, a dueling agent-based framework that pairs conjecture generation with counterexample discovery\, and GraffitiAI\, a Python package for automated conjecturing across mathematical disciplines. \n 
URL:https://cmsa.fas.harvard.edu/event/newtech_31225/
LOCATION:Hybrid – G10
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-3.12.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250305T140000
DTEND;TZID=America/New_York:20250305T150000
DTSTAMP:20260404T225719
CREATED:20250123T192715Z
LAST-MODIFIED:20250307T154830Z
UID:10003664-1741183200-1741186800@cmsa.fas.harvard.edu
SUMMARY:Machine Learning G2 Geometry
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Elli Heyes\, Imperial College \nTitle: Machine Learning G2 Geometry \nAbstract: 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. Since 2017 machine-learning techniques have been applied extensively to study Calabi-Yau manifolds but until 2024 no similar work had been carried out on holonomy G2 manifolds. In this talk\, I will firstly show how topological properties of these manifolds can be learnt using neural networks. I will then discuss how one could try to numerically learn metrics on compact holonomy G2 manifolds using machine-learning and why these approximations would be useful in M-theory.
URL:https://cmsa.fas.harvard.edu/event/newtech_3525/
LOCATION:Hybrid
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-3.5.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250226T140000
DTEND;TZID=America/New_York:20250226T150000
DTSTAMP:20260404T225719
CREATED:20250124T154400Z
LAST-MODIFIED:20250623T124501Z
UID:10003663-1740578400-1740582000@cmsa.fas.harvard.edu
SUMMARY:Datasets for Math: From AIMO Competitions to Math Copilots for Research
DESCRIPTION:  \nNew Technologies in Mathematics Seminar \nSpeaker: Simon Frieder\, Oxford \nTitle: Datasets for Math: From AIMO Competitions to Math Copilots for Research \nAbstract: This talk begins with a brief exposition of the AI Mathematical Olympiad (AIMO) on Kaggle\, now in its second iteration\, outlining datasets and models available to contestants. Taking a broader perspective\, I then examine 1) the overarching issues the current datasets suffer from—such as binary evaluation or constrained sets of use cases— and 2) the trajectory they set for competition-style mathematical problem-solving\, which is different from mathematical research practice. I argue for a fundamental shift in dataset structure and composition\, both for training and evaluation\, and introduce the idea of mapping mathematical workflows to data\, a key example underscoring the need for this shift. I touch upon new thinking LLMs and their role in redefining LLM math evaluation\, highlighting their implications for dataset design. Finally\, I propose general improvements to the current state of mathematical datasets\, including mathematical adaptations of dataset documentation (e.g.\, datasheets). \n 
URL:https://cmsa.fas.harvard.edu/event/newtech_22625/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/1740494700974-e6086db9-08ab-4681-9ecd-580092fe27b62025-1_1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250212T140000
DTEND;TZID=America/New_York:20250212T150000
DTSTAMP:20260404T225719
CREATED:20250123T194306Z
LAST-MODIFIED:20250228T212617Z
UID:10003661-1739368800-1739372400@cmsa.fas.harvard.edu
SUMMARY:Discovering Data Structures: Nearest Neighbor Search and Beyond
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Omar Salemohamed\, Mila \nTitle: Discovering Data Structures: Nearest Neighbor Search and Beyond \nAbstract: As neural networks learn increasingly sophisticated tasks—from image recognition to mastering the game of Go—we ask: can deep learning discover data structures entirely from scratch? We introduce a general framework for data structure discovery\, which adapts to the underlying data distribution and provides fine-grained control over query and space complexity. For nearest neighbor (NN) search\, our model (re)discovers classic algorithms like binary search in one dimension and learns structures reminiscent of k-d trees and locality-sensitive hashing in higher dimensions. Additionally\, the model learns useful representations of high-dimensional data such as images and exploits them to design effective data structures. Beyond NN search\, we believe the framework could be a powerful tool for data structure discovery for other problems and adapt our framework to the problem of estimating frequencies over a data stream. To encourage future work in this direction\, we conclude with a discussion on some of the opportunities and remaining challenges of learning data structures end-to-end.
URL:https://cmsa.fas.harvard.edu/event/newtech_21225/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-2.12.2025.docx-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241204T140000
DTEND;TZID=America/New_York:20241204T150000
DTSTAMP:20260404T225719
CREATED:20240907T180227Z
LAST-MODIFIED:20241212T205959Z
UID:10003410-1733320800-1733324400@cmsa.fas.harvard.edu
SUMMARY:Can Transformers Reason Logically? A Study in SAT-Solving
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Leyan Pan\, Georgia Tech \nTitle: Can Transformers Reason Logically? A Study in SAT-Solving \nAbstract: Transformer-based LLMs have apparently demonstrated capabilities that resembles human reasoning. In our recent work\, we investigated the Boolean reasoning abilities of decoder-only Transformers equipped with Chain-of-Thought\, establishing that a Transformer model can decide all 3-SAT instances up to a bounded size (i.e.\, number of variables and clauses). In this talk\, I will first review recent studies that formally examine the expressiveness of Transformer models. Next\, I will explain how we establish an equivalence between Chain-of-Thought reasoning and algorithm\, in our case\, the DPLL SAT-solving algorithm. I will then discuss how to encode 3-SAT formulas and partial assignments as vectors so that the high-level operations in DPLL can be represented as vector operations and implemented using attention mechanisms within Transformers. Finally\, I will present experimental results that support our theoretical predictions. I will also address why standard Transformers can only solve reasoning problems of bounded length\, leading to failures in length-generalization\, and discuss potential solutions to overcome this limitation.
URL:https://cmsa.fas.harvard.edu/event/newtech_12424/
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-12.4.24.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241120T100000
DTEND;TZID=America/New_York:20241120T230000
DTSTAMP:20260404T225719
CREATED:20241017T153402Z
LAST-MODIFIED:20241115T183929Z
UID:10003614-1732096800-1732143600@cmsa.fas.harvard.edu
SUMMARY:Thinking Like Transformers - A Practical Session
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Gail Weiss\, EPFL \nTitle: Thinking Like Transformers – A Practical Session \nAbstract: With the help of the RASP programming language\, we can better imagine how transformers—the powerful attention based sequence processing architecture—solve certain tasks. Some tasks\, such as simply repeating or reversing an input sequence\, have reasonably straightforward solutions\, but many others are more difficult. To unlock a fuller intuition of what can and cannot be achieved with transformers\, we must understand not just the RASP operations but also how to use them effectively.\nIn this session\, I would like to discuss some useful tricks with you in more detail. How is the powerful selector_width operation yielded from the true RASP operations? How can a fixed-depth RASP program perform arbitrary length long-addition\, despite the equally large number of potential carry operations such a computation entails? How might a transformer perform in-context reasoning? And are any of these solutions reasonable\, i.e.\, realisable in practice? I will begin with a brief introduction of the base RASP operations to ground our discussion\, and then walk us through several interesting task solutions. Following this\, and armed with this deeper intuition of how transformers solve several tasks\, we will conclude with a discussion of what this implies for how knowledge and computations must spread out in transformer layers and embeddings in practice.
URL:https://cmsa.fas.harvard.edu/event/newtech_112024/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-11.20.24.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20241113T100000
DTEND;TZID=America/New_York:20241113T230000
DTSTAMP:20260404T225719
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:20260404T225719
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:20260404T225719
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:20260404T225719
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:20260404T225719
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:20260404T225719
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:20260404T225719
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:20260404T225719
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:20260404T225719
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:20260404T225719
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:20260404T225719
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:20260404T225719
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:20260404T225719
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:20260404T225719
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:20260404T225719
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:20260404T225719
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:20260404T225719
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:20260404T225719
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:20260404T225719
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:20260404T225719
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
END:VCALENDAR