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%.

arXiv:2508.19300v2 Announce Type: replace-cross Abstract: 4D live fluorescence microscopy is often compromised by prolonged high intensity illumination which induces photobleaching and phototoxic effects that generate photo-induced artifacts and severely impair image continuity and detail recovery. To address this challenge, we propose the CellINR framework, a case-specific optimization approach based on implicit neural representation. The method employs blind convolution and structure amplification strategies to map 3D spatial coordinates into the high frequency domain, enabling precise modeling and high-accuracy reconstruction of cellular structures while effectively distinguishing true signals from artifacts. Experimental results demonstrate that CellINR significantly outperforms existing techniques in artifact removal and restoration of structural continuity, and for the first time, a paired 4D live cell imaging dataset is provided for evaluating reconstruction performance, thereby offering a solid foundation for subsequent quantitative analyses and biological research. The code and dataset will be public.