arXiv:2604.03925v1 Announce Type: cross Abstract: Large language models struggle to accumulate evidence across multiple rounds of user interaction, 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 AdaptFuse, a training-free framework that externalizes probabilistic computation entirely from the LLM: 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. 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. All the code and materials will be open-sourced.

Oncogene, Published online: 14 March 2026; doi:10.1038/s41388-026-03714-y

LINC-AC092535.5 regulates MICAL2 mRNA level to inhibit p53-mediated ferroptosis in nasopharyngeal carcinoma

arXiv:2410.15756v3 Announce Type: replace-cross Abstract: Ensuring correctness is crucial for code generation. Formal verification offers a definitive assurance of correctness, but demands substantial human effort in proof construction and hence raises a pressing need for automation. The primary obstacle lies in the severe lack of data-there is much fewer proofs than code snippets for Large Language Models (LLMs) to train upon. In this paper, we introduce SAFE, a framework that overcomes the lack of human-written proofs to enable automated proof generation of Rust code. SAFE establishes a self-evolving cycle where data synthesis and fine-tuning collaborate to enhance the model capability, leveraging the definitive power of a symbolic verifier in telling correct proofs from incorrect ones. SAFE also re-purposes the large number of synthesized incorrect proofs to train the self-debugging capability of the fine-tuned models, empowering them to fix incorrect proofs based on the verifier's feedback. SAFE demonstrates superior efficiency and precision compared to GPT-4o. Through tens of thousands of synthesized proofs and the self-debugging mechanism, we improve the capability of open-source models, initially unacquainted with formal verification, to automatically write proofs for Rust code. This advancement leads to a significant improvement in performance, achieving a 52.52% accuracy rate in a benchmark crafted by human experts, a significant leap over GPT-4o's performance of 14.39%.