Yang Li

Xiaokai Zhang, Na Zhu, Yiming He et al.

This is the first paper in a series of work we have accomplished over the past three years. In this paper, we have constructed a consistent formal plane geometry system. This will serve as a crucial bridge between IMO-level plane geometry challenges and readable AI automated reasoning. Within this formal framework, we have been able to seamlessly integrate modern AI models with our formal system. AI is now capable of providing deductive reasoning solutions to IMO-level plane geometry problems, just like handling other natural languages, and these proofs are readable, traceable, and verifiable. We propose the geometry formalization theory (GFT) to guide the development of the geometry formal system. Based on the GFT, we have established the FormalGeo, which consists of 88 geometric predicates and 196 theorems. It can represent, validate, and solve IMO-level geometry problems. we also have crafted the FGPS (formal geometry problem solver) in Python. It serves as both an interactive assistant for verifying problem-solving processes and an automated problem solver. We've annotated the formalgeo7k and formalgeo-imo datasets. The former contains 6,981 (expand to 133,818 through data augmentation) geometry problems, while the latter includes 18 (expand to 2,627 and continuously increasing) IMO-level challenging geometry problems. All annotated problems include detailed formal language descriptions and solutions. Implementation of the formal system and experiments validate the correctness and utility of the GFT. The backward depth-first search method only yields a 2.42% problem-solving failure rate, and we can incorporate deep learning techniques to achieve lower one. The source code of FGPS and datasets are available at https://github.com/BitSecret/FGPS.

Changjian Chen, Pengcheng Wang, Fei Lyu et al.

Hybrid rice breeding crossbreeds different rice lines and cultivates the resulting hybrids in fields to select those with desirable agronomic traits, such as higher yields. Recently, genomic selection has emerged as an efficient way for hybrid rice breeding. It predicts the traits of hybrids based on their genes, which helps exclude many undesired hybrids, largely reducing the workload of field cultivation. However, due to the limited accuracy of genomic prediction models, breeders still need to combine their experience with the models to identify regulatory genes that control traits and select hybrids, which remains a time-consuming process. To ease this process, in this paper, we proposed a visual analysis method to facilitate interactive hybrid rice breeding. Regulatory gene identification and hybrid selection naturally ensemble a dual-analysis task. Therefore, we developed a parametric dual projection method with theoretical guarantees to facilitate interactive dual analysis. Based on this dual projection method, we further developed a gene visualization and a hybrid visualization to verify the identified regulatory genes and hybrids. The effectiveness of our method is demonstrated through the quantitative evaluation of the parametric dual projection method, identified regulatory genes and desired hybrids in the case study, and positive feedback from breeders.