Fanyi Yang

Jiquan Yuan, Xinyan Cao, Changjin Li et al.

As image generation technology advances, AI-based image generation has been applied in various fields and Artificial Intelligence Generated Content (AIGC) has garnered widespread attention. However, the development of AI-based image generative models also brings new problems and challenges. A significant challenge is that AI-generated images (AIGI) may exhibit unique distortions compared to natural images, and not all generated images meet the requirements of the real world. Therefore, it is of great significance to evaluate AIGIs more comprehensively. Although previous work has established several human perception-based AIGC image quality assessment (AIGCIQA) databases for text-generated images, the AI image generation technology includes scenarios like text-to-image and image-to-image, and assessing only the images generated by text-to-image models is insufficient. To address this issue, we establish a human perception-based image-to-image AIGCIQA database, named PKU-I2IQA. We conduct a well-organized subjective experiment to collect quality labels for AIGIs and then conduct a comprehensive analysis of the PKU-I2IQA database. Furthermore, we have proposed two benchmark models: NR-AIGCIQA based on the no-reference image quality assessment method and FR-AIGCIQA based on the full-reference image quality assessment method. Finally, leveraging this database, we conduct benchmark experiments and compare the performance of the proposed benchmark models. The PKU-I2IQA database and benchmarks will be released to facilitate future research on \url{https://github.com/jiquan123/I2IQA}.

Ruo Li, Pingbing Ming, Zhiyuan Sun et al.

We propose a new discontinuous Galerkin method based on the least-squares patch reconstruction for the biharmonic problem. We prove the optimal error estimate of the proposed method. The two-dimensional and three-dimensional numerical examples are presented to confirm the accuracy and efficiency of the method with several boundary conditions and several types of polygon meshes and polyhedral meshes.

Ruo Li, Qicheng Liu, Fanyi Yang et al.

In this paper, we develop an efficient preconditioned unfitted finite element method for the elliptic interface problem, based on the reconstructed discontinuous approximation. The approximation method for interface problems is originally proposed in [Li et al. SIAM J. Sci. Comput. 42(2), 2020], in which an arbitrarily high-order approximation space with one degree of freedom per element is constructed by solving local least squares fitting problems. The space can be applied within the cut discontinuous Galerkin framework, where the jump conditions across the interface are weakly enforced by the Nitsche's penalty method. In this work, the local least squares problem is modified by introducing appropriate constraints, which allows us to naturally ensure the stability near the interface by the reconstructed space, and further enables us to establish a norm equivalence between the high-order space and the lowest-order space. This equivalence property motivates us to construct a preconditioner from the piecewise constant space, and this preconditioning method is shown to be optimal in the sense that the upper bound of the condition number of the preconditioned system is independent of the mesh size, the coefficient and the interface location relative to the unfitted mesh. We also present the multigrid algorithms that serve as the inverse of the lowest-order system matrix. Numerical experiments in both two and three dimensions confirm the optimal convergence rates under error measurements and illustrate the efficiency and the robustness of the preconditioning method.

Ruo Li, Fanyi Yang

We propose a discontinuous least squares finite element method for solving the linear elasticity. The approximation space is obtained by patch reconstruction with only one unknown per element. We apply the L 2 norm least squares principle to the stress-displacement formulation based on discontinuous approximation with normal continuity across the interior faces. The optimal convergence order under the energy norm is attained. Numerical results of linear elasticity are presented to verify the error estimates. In addition to enjoying the advantages of discontinuous Galerkin method, we illustrate the great simplicity in implementation, the robustness and the improved efficiency of our method.

Ruo Li, Zhiyuan Sun, Fanyi Yang et al.

In this paper, we develop a patch reconstruction finite element method for the Stokes problem. The weak formulation of the interior penalty discontinuous Galerkin is employed. The proposed method has a great flexibility in velocity-pressure space pairs whose stability properties are confirmed by the inf-sup tests. Numerical examples show the applicability and efficiency of the proposed method.

Ziju Shen, Naohao Huang, Fanyi Yang et al.

Nowadays, formal theorem provers have made monumental progress on high-school and competition-level mathematics, but few of them generalize to more advanced mathematics. In this paper, we present REAL-Prover, a new open-source stepwise theorem prover for Lean 4 to push this boundary. This prover, based on our fine-tuned large language model (REAL-Prover-v1) and integrated with a retrieval system (Leansearch-PS), notably boosts performance on solving college-level mathematics problems. To train REAL-Prover-v1, we developed HERALD-AF, a data extraction pipeline that converts natural language math problems into formal statements, and a new open-source Lean 4 interactive environment (Jixia-interactive) to facilitate synthesis data collection. In our experiments, our prover using only supervised fine-tune achieves competitive results with a 23.7% success rate (Pass@64) on the ProofNet dataset-comparable to state-of-the-art (SOTA) models. To further evaluate our approach, we introduce FATE-M, a new benchmark focused on algebraic problems, where our prover achieves a SOTA success rate of 56.7% (Pass@64).

Fanyi Yang, Jianfeng Liu, Xin Zhang et al.

Instruction tuning has empowered large language models (LLMs) to achieve remarkable performance, yet its success heavily depends on the availability of large-scale, high-quality instruction-response pairs. To meet this demand, various methods have been developed to synthesize data at scale. However, current methods for scaling up data generation often overlook a crucial aspect: the alignment between instructions and responses. We hypothesize that the quality of instruction-response pairs is determined not by the individual quality of each component, but by the degree of mutual alignment. To address this, we propose a Mutual Alignment Framework (MAIN) which enforces coherence between instructions and responses through mutual constraints. We demonstrate that MAIN generalizes well across model architectures and sizes, achieving state-of-the-art performance on LLaMA, Mistral, and Qwen models across diverse benchmarks. This work underscores the critical role of instruction-response alignment in enabling generalizable and high-quality instruction tuning for LLMs. All code is available from our repository.

Jiquan Yuan, Fanyi Yang, Jihe Li et al.

In recent years, image generation technology has rapidly advanced, resulting in the creation of a vast array of AI-generated images (AIGIs). However, the quality of these AIGIs is highly inconsistent, with low-quality AIGIs severely impairing the visual experience of users. Due to the widespread application of AIGIs, the AI-generated image quality assessment (AIGIQA), aimed at evaluating the quality of AIGIs from the perspective of human perception, has garnered increasing interest among scholars. Nonetheless, current research has not yet fully explored this field. We have observed that existing databases are limited to images generated from single scenario settings. Databases such as AGIQA-1K, AGIQA-3K, and AIGCIQA2023, for example, only include images generated by text-to-image generative models. This oversight highlights a critical gap in the current research landscape, underscoring the need for dedicated databases catering to image-to-image scenarios, as well as more comprehensive databases that encompass a broader range of AI-generated image scenarios. Addressing these issues, we have established a large scale perceptual quality assessment database for both text-to-image and image-to-image AIGIs, named PKU-AIGIQA-4K. We then conduct a well-organized subjective experiment to collect quality labels for AIGIs and perform a comprehensive analysis of the PKU-AIGIQA-4K database. Regarding the use of image prompts during the training process, we propose three image quality assessment (IQA) methods based on pre-trained models that include a no-reference method NR-AIGCIQA, a full-reference method FR-AIGCIQA, and a partial-reference method PR-AIGCIQA. Finally, leveraging the PKU-AIGIQA-4K database, we conduct extensive benchmark experiments and compare the performance of the proposed methods and the current IQA methods.