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This paper presents TGO-IV, a topological framework using persistent homology to analyze how transformer representations evolve across layers, complementing prior spectral and geometric observatories.
The paper studies the topology of learned representations in predictive coding networks using persistent homology, finding that smaller models simplify topology earlier than larger ones and that earlier simplification correlates with worse reconstruction performance.
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.