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DTSTART;TZID=America/New_York:20251201T163000
DTEND;TZID=America/New_York:20251201T173000
DTSTAMP:20260508T191057
CREATED:20251007T152747Z
LAST-MODIFIED:20251201T144411Z
UID:10003807-1764606600-1764610200@cmsa.fas.harvard.edu
SUMMARY:Asymptotic Theory of Attention: In-Context Learning and Sparse Token Detection
DESCRIPTION:Colloquium \nSpeaker: Yue M. Lu\, Harvard University \nTitle: Asymptotic Theory of Attention: In-Context Learning and Sparse Token Detection \nAbstract: Attention-based architectures exhibit striking emergent abilities—from learning tasks directly from context to detecting rare\, weak features in long sequences—yet a rigorous theory explaining these behaviors remains limited. In this talk\, I will present two recent exactly solvable models that develop a high-dimensional asymptotic theory of attention. \n(i) In-context learning. For linear attention pretrained on linear regression tasks\, we derive sharp asymptotics in a regime where token dimension\, context length\, and task diversity all scale proportionally\, while the number of pretraining examples scales quadratically. The resulting learning curve exhibits double descent and a phase transition separating a low-diversity memorization regime from a high-diversity regime of genuine in-context generalization. These predictions closely track empirical behavior in both linear-attention models and nonlinear Transformer architectures. \n(ii) Sparse-token classification. For detecting weak signals embedded in a small\, randomly located subset of tokens\, we analyze a single-layer attention classifier and determine its representational and learnability thresholds. Attention succeeds with only logarithmic signal scaling in the sequence length L\, outperforming linear baselines that require √L scaling. In a proportional high-dimensional regime\, we prove that two gradient descent steps yield nontrivial alignment between the query vector and the hidden signal\, leading to signal-adaptive attention. Exact formulas for the test error\, training loss\, and separability capacity quantify this advantage.
URL:https://cmsa.fas.harvard.edu/event/colloquium-12125/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-12.1.2025-scaled.png
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DTSTART;TZID=America/New_York:20251208T163000
DTEND;TZID=America/New_York:20251208T173000
DTSTAMP:20260508T191057
CREATED:20251202T153625Z
LAST-MODIFIED:20251202T162404Z
UID:10003843-1765211400-1765215000@cmsa.fas.harvard.edu
SUMMARY:Recent Advances in Probabilistically Checkable Proofs
DESCRIPTION:Colloquium \nSpeaker: Dor Minzer (MIT) \nTitle: Recent Advances in Probabilistically Checkable Proofs \nAbstract: The PCP Theorem is a cornerstone of computer science\, with applications to hardness of approximation\, verification\, interactive protocols and more. It asserts a witness for the satisfiability of a given 3CNF formula can be encoded in a robust way that allows local checking.In this talk we discuss recent developments in PCPs\, and their connection with distributed protocols\, high-dimensional expanders and discrete Fourier analysis. Based on joint works with Kai Zhe Zheng\, Mitali Bafna\, Noam Lifshitz\, Nikhil Vyas.
URL:https://cmsa.fas.harvard.edu/event/colloquium-12825/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-12.8.2025.docx-scaled.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20251215T163000
DTEND;TZID=America/New_York:20251215T173000
DTSTAMP:20260508T191057
CREATED:20251124T150428Z
LAST-MODIFIED:20251211T145044Z
UID:10003836-1765816200-1765819800@cmsa.fas.harvard.edu
SUMMARY:The active Young-Dupré equation
DESCRIPTION:Colloquium \nSpeaker: Julien Tailleur\, MIT \nTitle: The active Young-Dupré equation \nAbstract: The Young-Dupré equation is a cornerstone of the equilibrium theory of capillary and wetting phenomena. In the biological world\, interfacial phenomena are ubiquitous\, from the spreading of bacterial colonies to tissue growth and flocking of birds\, but the description of such active systems escapes the realm of equilibrium physics. I will show how a microscopic\, mechanical definition of surface tension allows building an Active Young-Dupré equation able to account for the partial wetting observed in simulations of active particles interacting via pairwise forces. Remarkably\, the equation shows that the corresponding steady interfaces do not result from a simple balance between the surface tensions at play but instead emerge from a complex feedback mechanism. The interfaces are indeed stabilized by a drag force due to the emergence of steady currents\, which are themselves a by-product of the symmetry breaking induced by the interfaces. These currents also lead to new physics by selecting the sizes and shapes of adsorbed droplets\, breaking the equilibrium scale-free nature of the problem. Finally\, I will demonstrate a spectacular consequence of the negative value of the liquid-gas surface tensions in systems undergoing motility-induced phase separation: partially-immersed objects are expelled from the liquid phase\, in stark contrast with what is observed in passive systems. These results lay the foundations for a theory of wetting in active systems.
URL:https://cmsa.fas.harvard.edu/event/colloquium-121525/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-12.15.2025.docx-scaled.png
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