For bounded real-valued function classes, uniform convergence at scale γ, agnostic learnability at γ/2, and finite fat-shattering dimension above γ are equivalent.
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Established mathematical bottlenecks in representation, optimization, complexity, and high-dimensional learning aligned with the central disappointments of early AI research periods.
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Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale
For bounded real-valued function classes, uniform convergence at scale γ, agnostic learnability at γ/2, and finite fat-shattering dimension above γ are equivalent.
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The Mathematics of AI Winters: The mathematical Taxonomy of Paradigm Fragility in AI Winter
Established mathematical bottlenecks in representation, optimization, complexity, and high-dimensional learning aligned with the central disappointments of early AI research periods.