Research·arXiv cs.LG·6d ago

High-arity Sample Compression

Learning theorists have extended sample compression, a foundational concept in computational learning theory, into the high-arity regime where multiple learning tasks interact simultaneously. This work establishes that non-trivial high-arity compression schemes guarantee PAC learnability in product spaces, bridging classical sample complexity bounds with multi-task and federated learning settings. The result matters for practitioners building systems that must learn efficiently across correlated domains or distributed data, tightening the theoretical guarantees that underpin generalization in complex learning scenarios.

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Explainer

The paper doesn't just apply sample compression to multiple tasks; it proves that compression schemes in high-arity settings are equivalent to PAC learnability itself, closing a gap between classical bounds and what actually happens when learning tasks interact.

This connects directly to the data allocation problem surfaced in the GRPO and on-policy distillation work from May 12. That paper showed practitioners need principled strategies for rationing labeled data across training phases. High-arity sample compression provides the theoretical foundation for why such rationing works: if you can compress across correlated tasks, you've proven you can learn efficiently even when data is scarce. The same logic applies to federated and multi-domain settings where tasks share structure. This is the theory underneath the empirical pipeline optimization.

If federated learning systems or multi-task practitioners cite this result when justifying reduced per-task sample budgets in production deployments over the next 6 months, the theory has crossed into practice. If it remains confined to learning theory venues without adoption signals, it's elegant but not yet actionable.

Coverage we drew on

Beyond GRPO and On-Policy Distillation: An Empirical Sparse-to-Dense Reward Principle for Language-Model Post-Training · arXiv cs.LG

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MentionsPAC learning · sample compression · high-arity learning theory

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