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The paper introduces Top-NMF, a framework that incorporates topological regularization via persistent homology into non-negative matrix factorization to learn interpretable and structurally coherent bases, applicable to spatially coherent image components, periodic time-series structures, and clique-like graph signals.
TopoPrimer is a framework that improves forecasting accuracy by integrating global topological structures into existing models, showing significant gains in challenging scenarios like seasonal spikes and cold starts.
This paper introduces a topology-enhanced alignment framework for LLMs, utilizing trajectory topology loss and topological preference optimization based on persistent homology to regularize semantic trajectories in hidden space.