4 papers
Loss Barcode: A Topological Measure of Escapability in Loss Landscapes
Serguei Barannikov, Daria Voronkova, Alexander Mironenko +4
Neural network training is commonly based on SGD. However, the understanding of SGD's ability to converge to good local minima, given the non-convex nature of loss functions and th…
Edge-wise Topological Divergence Gaps: Guiding Search in Combinatorial Optimization
Ilya Trofimov, Daria Voronkova, Alexander Mironenko +4
We introduce a topological feedback mechanism for the Travelling Salesman Problem (TSP) by analyzing the divergence between a tour and the minimum spanning tree (MST). Our key cont…
RTD-Lite: Scalable Topological Analysis for Comparing Weighted Graphs in Learning Tasks
Eduard Tulchinskii, Daria Voronkova, Ilya Trofimov +2
Topological methods for comparing weighted graphs are valuable in various learning tasks but often suffer from computational inefficiency on large datasets. We introduce RTD-Lite,…
Scalar Function Topology Divergence: Comparing Topology of 3D Objects
Ilya Trofimov, Daria Voronkova, Eduard Tulchinskii +2
We propose a new topological tool for computer vision - Scalar Function Topology Divergence (SFTD), which measures the dissimilarity of multi-scale topology between sublevel sets o…