4 citations · 10 across the 6 of their papers we have counts for
5 papers · 1 filter
Data-driven discovery of non-Newtonian astronomy via learning non-Euclidean Hamiltonian
Oswin So, Gongjie Li, Evangelos A. Theodorou +1
Incorporating the Hamiltonian structure of physical dynamics into deep learning models provides a powerful way to improve the interpretability and prediction accuracy. While previo…
Data-driven Prediction of General Hamiltonian Dynamics via Learning Exactly-Symplectic Maps
Renyi Chen, Molei Tao
We consider the learning and prediction of nonlinear time series generated by a latent symplectic map. A special case is (not necessarily separable) Hamiltonian systems, whose solu…
Why Do Deep Residual Networks Generalize Better than Deep Feedforward Networks? -- A Neural Tangent Kernel Perspective
Kaixuan Huang, Yuqing Wang, Molei Tao +1
Deep residual networks (ResNets) have demonstrated better generalization performance than deep feedforward networks (FFNets). However, the theory behind such a phenomenon is still…
Stochasticity of Deterministic Gradient Descent: Large Learning Rate for Multiscale Objective Function
Lingkai Kong, Molei Tao
This article suggests that deterministic Gradient Descent, which does not use any stochastic gradient approximation, can still exhibit stochastic behaviors. In particular, it shows…
Variational Optimization on Lie Groups, with Examples of Leading (Generalized) Eigenvalue Problems
Molei Tao, Tomoki Ohsawa
The article considers smooth optimization of functions on Lie groups. By generalizing NAG variational principle in vector space (Wibisono et al., 2016) to Lie groups, continuous Li…