Power-Law Correlations Without Apparent Temperature-Tuned Criticality in Fixed-Tree Hierarchical Languages
Sampling temperature can substantially reshape autoregressive generation, but it is unclear when temperature changes in long-range correlations reflect a genuine phase transition rather than a smooth change in statistics. We study this question in a controlled analogue of temperature sampling: a finite-depth probabilistic context-free grammar on a fixed hierarchical tree, where exact next-token conditionals are computed by belief propagation and then rescaled by a softmax temperature before autoregressive sampling. We measure two-point mutual information between tokens as a function of separation. Across the tested temperatures and grammar ensembles, mutual information remains well descri...
| Authors | Marcel Kühn, Bernd Rosenow |
|---|---|
| Primary category | cs.LG |
| Published | 17 October 2026 |
| Last updated at source | 17 October 2026 |
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