Hierarchical synthetic languages require Ω(n) context length for faithful autoregressive sampling but only Θ(log n) working memory with reasoning for exact generation from the true distribution.
Conditioned on the root, each retains the signal with probabilityρindependently, and given they all do, the corresponding means areM d,ρ,h−1(1) = (dρ)h−1
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A Hierarchical Language Model with Predictable Scaling Laws and Provable Benefits of Reasoning
Hierarchical synthetic languages require Ω(n) context length for faithful autoregressive sampling but only Θ(log n) working memory with reasoning for exact generation from the true distribution.