Algorithmic Principles For Multiclass Learning Are Hard To Come By: Limits of Regularization and Proper Learning

arXiv:2608.26516 · cs.LG, stat.ML · Submitted 2026-08-27 · Read on arXiv

cs.LG, stat.ML

Submitted: 2026-08-27

Updated: 2026-08-27

Terminology

• Regularization — 42× in this paper · explained in 3 episodes
• Core — 13× in this paper · explained in 2 episodes
• Sample Complexity — 12× in this paper · explained in 15 episodes
• Consistency — 9× in this paper · explained in 3 episodes
• Aggregation — 3× in this paper · explained in 1 episode
• Generalization — 3× in this paper · explained in 13 episodes
• Structural Risk Minimization — 3× in this paper
• Axioms — 2× in this paper · explained in 2 episodes
• VC Dimension — 2× in this paper · explained in 2 episodes
• Annual Symposium on Foundations of Computer Science — 1× in this paper
• Anticoncentration — 1× in this paper · explained in 1 episode
• Empirical Risk Minimization — 1× in this paper
• List Learning — 1× in this paper · explained in 2 episodes
• Loss Function — 1× in this paper · explained in 2 episodes

Sources

• An Optimal Sauer Lemma Over $k$-ary Alphabets
• Local Regularization Does Not Characterize Multiclass PAC Learnability
• The Optimal Sample Complexity of Multiclass and List Learning
• Majority-of-Three is Optimal

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