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To address this, we propose Canopy Entropy ($\\mathrm{CE}^\\star$), a measure that views language generation from a tree perspective, where ``canopy'' represents the space of all possible rollouts, making $\\mathrm{CE}^\\star$ naturally quantify the effective size of the generation space. $\\mathrm{CE}^\\star$ jointly captures uncertainty in both the output length $N$ and the generated sequence $Y_{1:N}$ -- indeed, we show that it equals to total Shannon entropy $H(N, Y_{1:N}\\mid X)$, where $X$ denotes the prompt. This formulation yields interpretable metrics, including a length-entropy correlation term $\\rho(N, r_N)$, where $r_N$ is the entropy rate, quantifying information conveyance effici","title":"Fine-Tuning Improves Information Conveyance in Language Models","url":"https://arxiv.org/abs/2605.30844","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.30844v1 Announce Type: cross \nAbstract: Fine-tuning is often believed to reduce uncertainty and diversity in large language models, but existing analyses overlook output length, a key confounder, and therefore fail to capture how uncertainty is distributed across an entire generation rollout. To address this, we propose Canopy Entropy ($\\mathrm{CE}^\\star$), a measure that views language generation from a tree perspective, where ``canopy'' represents the space of all possible rollouts, making $\\mathrm{CE}^\\star$ naturally quantify the effective size of the generation space. $\\mathrm{CE}^\\star$ jointly captures uncertainty in both the output length $N$ and the generated sequence $Y_{1:N}$ -- indeed, we show that it equals to total Shannon entropy $H(N, Y_{1:N}\\mid X)$, where $X$ denotes the prompt. 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