Search Results for author: Shing-Tung Yau

Found 14 papers, 1 papers with code

PhyloTransformer: A Discriminative Model for Mutation Prediction Based on a Multi-head Self-attention Mechanism

no code implementations3 Nov 2021 Yingying Wu, Shusheng Xu, Shing-Tung Yau, Yi Wu

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has caused an ongoing pandemic infecting 219 million people as of 10/19/21, with a 3. 6% mortality rate.

Language Modelling

Stability of the tangent bundle through conifold transitions

no code implementations22 Feb 2021 Tristan C. Collins, Sebastien Picard, Shing-Tung Yau

Let $X$ be a compact, K\"ahler, Calabi-Yau threefold and suppose $X\mapsto \underline{X}\leadsto X_t$ , for $t\in \Delta$, is a conifold transition obtained by contracting finitely many disjoint $(-1,-1)$ curves in $X$ and then smoothing the resulting ordinary double point singularities.

Differential Geometry High Energy Physics - Theory Algebraic Geometry

Graph Laplacians, Riemannian Manifolds and their Machine-Learning

no code implementations30 Jun 2020 Yang-Hui He, Shing-Tung Yau

Graph Laplacians as well as related spectral inequalities and (co-)homology provide a foray into discrete analogues of Riemannian manifolds, providing a rich interplay between combinatorics, geometry and theoretical physics.

BIG-bench Machine Learning Topological Data Analysis


no code implementations ICLR 2020 Dongsheng An, Yang Guo, Na lei, Zhongxuan Luo, Shing-Tung Yau, Xianfeng GU

In order to tackle the both problems, we explicitly separate the manifold embedding and the optimal transportation; the first part is carried out using an autoencoder to map the images onto the latent space; the second part is accomplished using a GPU-based convex optimization to find the discontinuous transportation maps.

AE-OT-GAN: Training GANs from data specific latent distribution

no code implementations ECCV 2020 Dongsheng An, Yang Guo, Min Zhang, Xin Qi, Na lei, Shing-Tung Yau, Xianfeng GU

Though generative adversarial networks (GANs) areprominent models to generate realistic and crisp images, they often encounter the mode collapse problems and arehard to train, which comes from approximating the intrinsicdiscontinuous distribution transform map with continuousDNNs.

Super $J$-holomorphic Curves: Construction of the Moduli Space

no code implementations13 Nov 2019 Enno Keßler, Artan Sheshmani, Shing-Tung Yau

We call a map $\Phi\colon M\to N$ a super $J$-holomorphic curve if its differential maps the almost complex structure on $\mathcal{D}$ to $J$.

Differential Geometry Mathematical Physics Algebraic Geometry Mathematical Physics

Gauss-Manin connection in disguise: Genus two curves

no code implementations16 Oct 2019 Jin Cao, Hossein Movasati, Shing-Tung Yau

We describe an algebra of meromorphic functions on the Siegel domain of genus two which contains Siegel modular forms for an arithmetic index six subgroup of the symplectic group and it is closed under three canonical derivations of the Siegel domain.

Algebraic Geometry Mathematical Physics Complex Variables Mathematical Physics

Mode Collapse and Regularity of Optimal Transportation Maps

no code implementations8 Feb 2019 Na lei, Yang Guo, Dongsheng An, Xin Qi, Zhongxuan Luo, Shing-Tung Yau, Xianfeng GU

This work builds the connection between the regularity theory of optimal transportation map, Monge-Amp\`{e}re equation and GANs, which gives a theoretic understanding of the major drawbacks of GANs: convergence difficulty and mode collapse.

Latent Space Optimal Transport for Generative Models

no code implementations16 Sep 2018 Huidong Liu, Yang Guo, Na lei, Zhixin Shu, Shing-Tung Yau, Dimitris Samaras, Xianfeng GU

Experimental results on an eight-Gaussian dataset show that the proposed OT can handle multi-cluster distributions.

Geometric Understanding of Deep Learning

no code implementations26 May 2018 Na Lei, Zhongxuan Luo, Shing-Tung Yau, David Xianfeng Gu

In this work, we give a geometric view to understand deep learning: we show that the fundamental principle attributing to the success is the manifold structure in data, namely natural high dimensional data concentrates close to a low-dimensional manifold, deep learning learns the manifold and the probability distribution on it.

Machine Translation speech-recognition +2

A Geometric View of Optimal Transportation and Generative Model

no code implementations16 Oct 2017 Na Lei, Kehua Su, Li Cui, Shing-Tung Yau, David Xianfeng Gu

In this work, we show the intrinsic relations between optimal transportation and convex geometry, especially the variational approach to solve Alexandrov problem: constructing a convex polytope with prescribed face normals and volumes.

Nonlinearly Constrained MRFs: Exploring the Intrinsic Dimensions of Higher-Order Cliques

no code implementations CVPR 2013 Yun Zeng, Chaohui Wang, Stefano Soatto, Shing-Tung Yau

This paper introduces an efficient approach to integrating non-local statistics into the higher-order Markov Random Fields (MRFs) framework.

Image Segmentation Semantic Segmentation

Hyperbolic Harmonic Mapping for Constrained Brain Surface Registration

no code implementations CVPR 2013 Rui Shi, Wei Zeng, Zhengyu Su, Hanna Damasio, Zhonglin Lu, Yalin Wang, Shing-Tung Yau, Xianfeng GU

This work conquer this problem by changing the Riemannian metric on the target surface to a hyperbolic metric, so that the harmonic mapping is guaranteed to be a diffeomorphism under landmark constraints.

Homologies of path complexes and digraphs

2 code implementations12 Jul 2012 Alexander Grigor'yan, Yong Lin, Yuri Muranov, Shing-Tung Yau

In this paper we introduce a path complex that can be regarded as a generalization of the notion of a simplicial complex.

Combinatorics Algebraic Topology

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