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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Higher-order Hamiltonian generalization evolution equations
高阶 哈密顿 广义演化方程
2023/11/13
In this talk, I will review several classes of higher-order generalizations of the integrable Camassa-Holm equation in the Hamiltonian forms. Then, I talk about some new results for one generalized Ca...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Robust Generalization Requires Exponentially Large Models
鲁棒泛化 指数级大 模型
2023/5/15
It is well-known that modern neural networks are vulnerable to adversarial examples. To mitigate this problem, a series of robust learning algorithms have been proposed. However, although the robust t...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Generalization of Graph Neural Networks and Graph Structural Learning for Robust Representation
图神经网络 泛化 图结构学习 鲁棒表示
2023/4/18
This report consists of two parts associated with graph neural networks: generalization and graph structural learning. We first study the Rademacher complexity of GNNs, as one of independent-algorithm...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Lines on holomorphic contact manifolds and a generalization of (2,3,5)-distributions to higher dimensions
全纯接触流形 线和 （2，3，5） 高维度推广
2023/4/19
Since the celebrated work by Cartan, distributions with small growth vector (2,3,5) have been studied extensively. In the holomorphic setting, there is a natural correspondence between holomorphic (2,...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Implicit biases of optimization algorithms for neural networks and their effects on generalization
神经网络 优化算法 隐式偏差 泛化的影响
2023/4/26
Modern neural networks are usually over-parameterized—the number of parameters exceeds the number of training data. In this case the loss functions tend to have many (or even infinite) global minima, ...