Monodromy zeta-functions of deformations and Newton diagrams

For a one-parameter deformation of an analytic complex function germ of several variables, there is defined its monodromy zeta-function. We give a Varchenko type formula for this zeta-function if the deformation is non-degenerate with respect to its Newton diagram.For a one-parameter deformation of an analytic complex function germ of several variables, there is defined its monodromy zeta-function. We give a Varchenko type formula for this zeta-function if the deformation is non-degenerate with respect to its Newton diagram

Riemannian Optimization for Skip-Gram Negative Sampling

Skip-Gram Negative Sampling (SGNS) word embedding model, well known by its implementation in "word2vec" software, is usually optimized by stochastic gradient descent. However, the optimization of SGNS objective can be viewed as a problem of searching for a good matrix with the low-rank constraint. The most standard way to solve this type of problems is to apply Riemannian optimization framework to optimize the SGNS objective over the manifold of required low-rank matrices. In this paper, we propose an algorithm that optimizes SGNS objective using Riemannian optimization and demonstrates its superiority over popular competitors, such as the original method to train SGNS and SVD over SPPMI matrix.Comment: 9 pages, 4 figures, ACL 201

PvDeConv: Point-Voxel Deconvolution for Autoencoding CAD Construction in 3D

We propose a Point-Voxel DeConvolution (PVDeConv) module for 3D data autoencoder. To demonstrate its efficiency we learn to synthesize high-resolution point clouds of 10k points that densely describe the underlying geometry of Computer Aided Design (CAD) models. Scanning artifacts, such as protrusions, missing parts, smoothed edges and holes, inevitably appear in real 3D scans of fabricated CAD objects. Learning the original CAD model construction from a 3D scan requires a ground truth to be available together with the corresponding 3D scan of an object. To solve the gap, we introduce a new dedicated dataset, the CC3D, containing 50k+ pairs of CAD models and their corresponding 3D meshes. This dataset is used to learn a convolutional autoencoder for point clouds sampled from the pairs of 3D scans - CAD models. The challenges of this new dataset are demonstrated in comparison with other generative point cloud sampling models trained on ShapeNet. The CC3D autoencoder is efficient with respect to memory consumption and training time as compared to stateof-the-art models for 3D data generation.Comment: 2020 IEEE International Conference on Image Processing (ICIP