Wei Wang

Jing Wang, Bo Han, Wei Wang

Image reconstruction of EIT mathematically is a typical nonlinear and severely ill-posed inverse problem. Appropriate priors or penalties are required to enable the reconstruction. The commonly used L2-norm can enforce the stability to preserve local smoothness, and the current L1-norm can enforce the sparsity to preserve sharp edges. Considering the fact that L2-norm penalty always makes the solution overly smooth and L1-norm penalty always makes the solution too sparse, elastic-net regularization approach with a convex combination term of L1-norm and L2-norm emerges for fully nonlinear EIT inverse problems. Our aim is to combine the strength of both terms: sparsity in the transform domain and smoothness in the physical domain, in an attempt to improve the reconstruction resolution and robustness to noise. Nonlinearity and non-smoothness of the generated composite minimization problem make it challenging to find an efficient numerical solution. Then we develop one simple and fast numerical optimization scheme based on the split Bregman technique for the joint penalties regularization. The method is validated using simulated data for some typical conductivity distributions. Results indicate that the proposed inversion model with an appropriate parameter choice achieves an efficient regularization solution and enhances the quality of the reconstructed image.

Zhengyu Chen, Yudong Wang, Teng Xiao et al. · pku

Recent advancements in improving the reasoning capabilities of Large Language Models have underscored the efficacy of Process Reward Models (PRMs) in addressing intermediate errors through structured feedback mechanisms. This study analyzes PRMs from multiple perspectives, including training methodologies, scalability, and generalization capabilities. We investigate the interplay between pre-training and reward model training FLOPs to assess their influence on PRM efficiency and accuracy in complex reasoning tasks. Our analysis reveals a pattern of diminishing returns in performance with increasing PRM scale, highlighting the importance of balancing model size and computational cost. Furthermore, the diversity of training datasets significantly impacts PRM performance, emphasizing the importance of diverse data to enhance both accuracy and efficiency. We further examine test-time scaling strategies, identifying Monte Carlo Tree Search as the most effective method when computational resources are abundant, while Best-of-N Sampling serves as a practical alternative under resource-limited conditions. Notably, our findings indicate that PRMs trained on mathematical datasets exhibit performance comparable to those tailored for code generation, suggesting robust cross-domain generalization. Employing a gradient-based metric, we observe that PRMs exhibit a preference for selecting responses with similar underlying patterns, further informing their optimization.