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Found 14 papers, 2 papers with code
PhyloTransformer: A Discriminative Model for Mutation Prediction Based on a Multi-head Self-attention Mechanism
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.
Stability of the tangent bundle through conifold transitions
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
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.
AE-OT: A NEW GENERATIVE MODEL BASED ON EXTENDED SEMI-DISCRETE OPTIMAL TRANSPORT
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
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
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
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
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
Experimental results on an eight-Gaussian dataset show that the proposed OT can handle multi-cluster distributions.
Geometric Understanding of Deep Learning
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.
A Geometric View of Optimal Transportation and Generative Model
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.
Hyperbolic Harmonic Mapping for Constrained Brain Surface Registration
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.
Nonlinearly Constrained MRFs: Exploring the Intrinsic Dimensions of Higher-Order Cliques
This paper introduces an efficient approach to integrating non-local statistics into the higher-order Markov Random Fields (MRFs) framework.
Homologies of path complexes and digraphs
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
