Multiclass Classification Sample Complexity Resolved: Decades-Old ML Theory Gap Closed

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Pabbaraju closes the longstanding open problem of optimal sample complexity for multiclass classification in terms of the DS dimension. While binary classification's optimal bounds via VC dimension are well-established, multiclass had a persistent √DS gap between upper and lower bounds despite decades of community effort. Building on recent algebraic characterizations from Hanneke et al. (2026), this achieves tight bounds — a fundamental result that completes the learning-theoretic picture.