Daniil Emtsev

Stefan Lionar, Daniil Emtsev, Dusan Svilarkovic et al.

Learning-based 3D reconstruction using implicit neural representations has shown promising progress not only at the object level but also in more complicated scenes. In this paper, we propose Dynamic Plane Convolutional Occupancy Networks, a novel implicit representation pushing further the quality of 3D surface reconstruction. The input noisy point clouds are encoded into per-point features that are projected onto multiple 2D dynamic planes. A fully-connected network learns to predict plane parameters that best describe the shapes of objects or scenes. To further exploit translational equivariance, convolutional neural networks are applied to process the plane features. Our method shows superior performance in surface reconstruction from unoriented point clouds in ShapeNet as well as an indoor scene dataset. Moreover, we also provide interesting observations on the distribution of learned dynamic planes.

Serguei Barannikov, Alexander Korotin, Dmitry Oganesyan et al.

We propose to study neural networks' loss surfaces by methods of topological data analysis. We suggest to apply barcodes of Morse complexes to explore topology of loss surfaces. An algorithm for calculations of the loss function's barcodes of local minima is described. We have conducted experiments for calculating barcodes of local minima for benchmark functions and for loss surfaces of small neural networks. Our experiments confirm our two principal observations for neural networks' loss surfaces. First, the barcodes of local minima are located in a small lower part of the range of values of neural networks' loss function. Secondly, increase of the neural network's depth and width lowers the barcodes of local minima. This has some natural implications for the neural network's learning and for its generalization properties.