Banach density reveals topological dichotomies in language generation: 1/2 is always achievable in 1D for finite-rank spaces but impossible in some infinite-rank cases, unlike asymptotic density; d>=2 needs nondegeneracy.
On the non-uniform generation of countable language collections
3 Pith papers cite this work. Polarity classification is still indexing.
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Defines mistake-bounded generation and gives an algorithm for finite classes achieving optimal last-mistake time Cdim(L) with floor(log2 |L|) mistakes, plus a trade-off for infinite classes and noisy extensions.
Task information structure determines ML scaling success, with code's dense verifiable signals enabling predictable progress while sparse-feedback tasks like typical RL do not.
citing papers explorer
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Banach density of generated languages: Dichotomies in topology and dimension
Banach density reveals topological dichotomies in language generation: 1/2 is always achievable in 1D for finite-rank spaces but impossible in some infinite-rank cases, unlike asymptotic density; d>=2 needs nondegeneracy.
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Mistake-Bounded Language Generation
Defines mistake-bounded generation and gives an algorithm for finite classes achieving optimal last-mistake time Cdim(L) with floor(log2 |L|) mistakes, plus a trade-off for infinite classes and noisy extensions.
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Why Code, Why Now: An Information-Theoretic Perspective on the Limits of Machine Learning
Task information structure determines ML scaling success, with code's dense verifiable signals enabling predictable progress while sparse-feedback tasks like typical RL do not.