See full formalization in the prepared manuscript. Key theorem: If H is sufficiently expressive (dense w.r.t. weak topology in the ∞-topos of classifiers), then the type of weak learners is equivalent to the type of strong learners, witnessed by the boosting higher inductive type and effective descent/gluing by Giraud axioms. Connection to higher categorical Fourier reconstruction via monadic/chromatic transform of weak characters.
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The Adequacy of Boosting for All Machine Learning: Higher Categorical Equivalence of Weak and Strong Learning in ∞-Toposes
We prove the adequacy of boosting for machine learning: every sufficiently expressive hypothesis class equates weak and strong learning via higher categorical structures in ∞-toposes and HoTT. Boosting as HIT geometric realization; density implies Weak ≃ Strong; dual Fourier reconstruction.
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