A composite Collapse Index based on incremental discrete Morse homology provides low-latency early warning of representational collapse during neural network training.
Morse theory for cell complexes.Advances in Mathematics, 134(1):90–145, 1998
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A persistence-augmented neural network framework encodes local gradient flow regions and their hierarchy via the Morse-Smale complex to retain multi-scale localized topological information, outperforming global TDA descriptors on histopathology classification and 3D porous material regression while,
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Monitoring Neural Training with Topology: A Footprint-Predictable Collapse Index
A composite Collapse Index based on incremental discrete Morse homology provides low-latency early warning of representational collapse during neural network training.
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Persistence-Augmented Neural Networks
A persistence-augmented neural network framework encodes local gradient flow regions and their hierarchy via the Morse-Smale complex to retain multi-scale localized topological information, outperforming global TDA descriptors on histopathology classification and 3D porous material regression while,