Large language models (LLMs) struggle to accumulate evidence across multiple rounds of user interactions, failing to update their beliefs in a manner consistent with Bayesian inference. Existing solutions require fine-tuning on sensitive user interaction data, limiting their applicability in privacy-conscious settings. We propose \textsc{AdaptFuse}, a training-free framework that externalizes probabilistic computation entirely from the LLM, where a symbolic module maintains a Bayesian posterior over a discrete hypothesis set, while a frozen LLM contributes semantic reasoning via multi-sample Dirichlet aggregation. The two signals are combined through entropy-adaptive fusion, which automatically weights each source by its predictive confidence, shifting reliance from the LLM to the symbolic posterior as evidence accumulates. We evaluate across three domains: flight recommendation, hotel recommendation, and web shopping; on Gemma~2 9B, Llama~3 8B, and Qwen~2.5 7B. \textsc{AdaptFuse} consistently outperforms both prompting baselines and fine-tuned Bayesian Teaching models on all tasks, with accuracy improving monotonically over interaction rounds. These results demonstrate that principled inference-time algorithms can substitute for fine-tuning in personalized recommendation, without storing or training on sensitive user data.

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