TopoFisher optimizes trainable filtrations, vectorizations, and compressors in persistent homology to maximize Fisher information, yielding higher information than fixed cosmological summaries and approaching neural baselines with far fewer parameters while generalizing better under simulator shifts
Bulletin of the American Mathematical Society , volume=
3 Pith papers cite this work. Polarity classification is still indexing.
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Empirical tests with quad-mesh filling indicate that decision regions in modern image classifiers are simply connected.
MAPLE estimates conditional class probabilities by local averaging over Mapper-graph neighborhoods with data-driven cover selection and proves consistency under regularity conditions.
citing papers explorer
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TopoFisher: Learning Topological Summary Statistics by Maximizing Fisher Information
TopoFisher optimizes trainable filtrations, vectorizations, and compressors in persistent homology to maximize Fisher information, yielding higher information than fixed cosmological summaries and approaching neural baselines with far fewer parameters while generalizing better under simulator shifts
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Empirical Evidence for Simply Connected Decision Regions in Image Classifiers
Empirical tests with quad-mesh filling indicate that decision regions in modern image classifiers are simply connected.
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MAPLE: Mapper Based Localized Prediction with Data Driven Cover Selection for High dimensional Data
MAPLE estimates conditional class probabilities by local averaging over Mapper-graph neighborhoods with data-driven cover selection and proves consistency under regularity conditions.