A new attention mechanism adds persistent homology and Euler-based topological structure to time-series models via validation-gated residuals, yielding RMSE reductions of 12.5-47.8% in paired tests on synthetic and real datasets when geometry is predictive.
Statistical topological data analysis using persistence landscapes.Journal of Machine Learning Research, 16(3):77–102
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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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Global and Local Topology-Aware Attention with Persistent Homology and Euler Biases for Time-Series Forecasting
A new attention mechanism adds persistent homology and Euler-based topological structure to time-series models via validation-gated residuals, yielding RMSE reductions of 12.5-47.8% in paired tests on synthetic and real datasets when geometry is predictive.
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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,