一周活动预告（6.26-7.2）
请查收。
变分方法及其应用的若干问题 （邹文明）
https://mathcenter.ctgu.edu.cn/info/1028/2031.htm
Learning functionals using deep ReLU networks（樊军）
https://math.fudan.edu.cn/bc/44/c30472a506948/page.htm
Thinking Fast with Transformers: Algorithmic Reasoning via Shortcuts (Bingbin Liu) https://www.mis.mpg.de/calendar/lectures/2023/abstract-35914.html
1. 变分方法及其应用的若干问题
报告人: 邹文明（清华大学）
报告时间: 2023-06-26 15:00
报告地点: 腾讯会议ID: 498-372-609
信息来源:
https://mathcenter.ctgu.edu.cn/info/1028/2031.htm
报告摘要:
介绍变分方法及其应用方面若干进展和存在的问题，包括临界椭圆方程、Lane-Emden方程孤立奇点分析、Dancer 猜想、约束变分问题等等。
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2. Learning functionals using deep ReLU networks
报告人: 樊军（香港浸会大学）
报告时间: 2023-06-27 10:30-12:00
报告地点: 腾讯会议ID: 273-665-687 密码: 200433
信息来源: https://math.fudan.edu.cn/bc/44/c30472a506948/page.htm
报告摘要:
Functional neural networks have been proposed and studied as a means of approximating nonlinear continuous functionals defined on Lp spaces. However, their theoretical properties are largely unknown beyond the universality of approximation or the existing analysis does not apply to the rectified linear unit (ReLU) activation function. In this talk, I will present functional deep ReLU networks and explore their convergence rates of approximation and generalization errors under different regularity conditions. Additionally, I will discuss their applications to functional data analysis. This talk is based on joint works with Dirong Chen, Ying Liu, Linhao Song, and Dingxuan Zhou.
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3. Thinking Fast with Transformers: Algorithmic Reasoning via Shortcuts
Speaker: Bingbin Liu (Carnegie Mellon University)
Time: 2023-6-29, 17:00, Berlin Time, 23:00 Beijing Time
Registration and Source Link:
https://www.mis.mpg.de/calendar/lectures/2023/abstract-35914.html
Abstract:
Algorithmic reasoning requires capabilities which are most naturally understood through recurrent models of computation, like the Turing machine. However, Transformer models, while lacking recurrence, are able to perform such reasoning using far fewer layers than the number of reasoning steps. This raises the question: what solutions are these shallow and non-recurrent models finding? In this talk, we will formalize reasoning in the setting of automata, and show that the computation of an automaton on an input sequence of length T can be replicated exactly by Transformers with o(T) layers, which we call "shortcuts". We provide two constructions, with O(log T) layers for all automata and O(1) layers for solvable automata. Empirically, our results from synthetic experiments show that shallow solutions can also be found in practice.
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