3 papers
cs.LG2026
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…
cs.LG2025
Barcodes as Summary of Loss Function Topology
Serguei Barannikov, Alexander Korotin, Dmitry Oganesyan +2
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…
cs.CV2024
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…