#persistent-homology News & Analysis

4 articles tagged with #persistent-homology. AI-curated summaries with sentiment analysis and key takeaways from 50+ sources.

4 articles

AINeutralarXiv – CS AI · Jun 256/10

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TopoCast: A Topological Fidelity Framework for Evaluating Transformer-Based Time Series Forecasting

Researchers introduce TopoCast, a topology-based evaluation framework for time series forecasting that moves beyond traditional error metrics to assess structural fidelity in deep learning models. The framework uses persistent homology to detect phase shifts, oscillatory distortions, and timing errors that conventional metrics like MSE overlook, revealing that models with similar numerical accuracy can exhibit substantially different structural quality.

AINeutralarXiv – CS AI · Jun 236/10

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The Topology of Ill-Posed Questions: Persistent Homology for Detection and Steering in LLMs

Researchers demonstrate that persistent homology—a topological data analysis technique—can detect and classify ill-posed questions (ambiguous, underspecified, or contradictory queries) in large language models by analyzing hidden state geometry across transformer layers. The method achieves 78-88% accuracy on benchmark datasets and enables targeted activation steering to improve response quality, offering a principled approach to handling inherently problematic inputs.

AINeutralarXiv – CS AI · Jun 45/10

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Incremental Sheaf Cohomology on Cellular Complexes: O(1)-in-n Lazy Edit Processing under Bounded Local Geometry

Researchers present an algorithmic framework for efficiently maintaining sheaf cohomology computations on dynamically evolving cellular complexes, reducing edit processing time from O(mn³) to O(1) per operation under bounded local geometry assumptions. The method demonstrates practical viability through experiments on large-scale graphs with millions of vertices and streaming edits, achieving microsecond-level latency while maintaining zero computational drift.

AINeutralarXiv – CS AI · May 116/10

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TopoPrune: Robust Data Pruning via Unified Latent Space Topology

TopoPrune introduces a topology-based framework for data pruning that addresses instability issues in geometric methods by leveraging intrinsic data structure rather than extrinsic geometry. The approach combines manifold approximation with persistent homology to achieve high accuracy at extreme pruning rates (90%) while maintaining robustness across architectures and noise conditions.