Daily Papers

As medical datasets rapidly expand, creating detailed annotations of different body structures becomes increasingly expensive and time-consuming. We consider that requesting radiologists to create detailed annotations is unnecessarily burdensome and that pre-existing AI models can largely automate this process. Following the spirit don't use a sledgehammer on a nut, we find that, rather than creating annotations from scratch, radiologists only have to review and edit errors if the Best-AI Labels have mistakes. To obtain the Best-AI Labels among multiple AI Labels, we developed an automatic tool, called Label Critic, that can assess label quality through tireless pairwise comparisons. Extensive experiments demonstrate that, when incorporated with our developed Image-Prompt pairs, pre-existing Large Vision-Language Models (LVLM), trained on natural images and texts, achieve 96.5% accuracy when choosing the best label in a pair-wise comparison, without extra fine-tuning. By transforming the manual annotation task (30-60 min/scan) into an automatic comparison task (15 sec/scan), we effectively reduce the manual efforts required from radiologists by an order of magnitude. When the Best-AI Labels are sufficiently accurate (81% depending on body structures), they will be directly adopted as the gold-standard annotations for the dataset, with lower-quality AI Labels automatically discarded. Label Critic can also check the label quality of a single AI Label with 71.8% accuracy when no alternatives are available for comparison, prompting radiologists to review and edit if the estimated quality is low (19% depending on body structures).

Premise selection is a fundamental problem of automated theorem proving. Previous works often use intricate symbolic methods, rely on domain knowledge, and require significant engineering effort to solve this task. In this work, we show that Magnushammer, a neural transformer-based approach, can outperform traditional symbolic systems by a large margin. Tested on the PISA benchmark, Magnushammer achieves 59.5% proof rate compared to a 38.3% proof rate of Sledgehammer, the most mature and popular symbolic-based solver. Furthermore, by combining Magnushammer with a neural formal prover based on a language model, we significantly improve the previous state-of-the-art proof rate from 57.0% to 71.0%.

Large Language Models (LLMs) present an intriguing avenue for exploration in the field of formal theorem proving. Nevertheless, their full potential, particularly concerning the mitigation of hallucinations and refinement through prover error messages, remains an area that has yet to be thoroughly investigated. To enhance the effectiveness of LLMs in the field, we introduce the Lyra, a new framework that employs two distinct correction mechanisms: Tool Correction (TC) and Conjecture Correction (CC). To implement Tool Correction in the post-processing of formal proofs, we leverage prior knowledge to utilize predefined prover tools (e.g., Sledgehammer) for guiding the replacement of incorrect tools. Tool Correction significantly contributes to mitigating hallucinations, thereby improving the overall accuracy of the proof. In addition, we introduce Conjecture Correction, an error feedback mechanism designed to interact with prover to refine formal proof conjectures with prover error messages. Compared to the previous refinement framework, the proposed Conjecture Correction refines generation with instruction but does not collect paired (generation, error & refinement) prompts. Our method has achieved state-of-the-art (SOTA) performance on both miniF2F validation (48.0% -> 55.3%) and test (45.5% -> 51.2%). We also present 3 IMO problems solved by Lyra. We believe Tool Correction (post-process for hallucination mitigation) and Conjecture Correction (subgoal adjustment from interaction with environment) could provide a promising avenue for future research in this field.