In recent years there has been increased use of machine learning (ML) techniques within mathematics, including symbolic computation where it may be applied safely to optimise or select algorithms. This paper explores whether using explainable AI (XAI) techniques on such ML models can offer new insight for symbolic computation, inspiring new implementations within computer algebra systems that do not directly call upon AI tools. We present a case study on the use of ML to select the variable ordering for cylindrical algebraic decomposition. It has already been demonstrated that ML can make the choice well, but here we show how the SHAP tool for explainability can be used to inform new heuristics of a size and complexity similar to those human-designed heuristics currently commonly used in symbolic computation. [ABSTRACT FROM AUTHOR]
This paper introduces an innovative bilevel optimization approach to elevate the deblurring process. By integrating a weights variable nonlocal model with a spatially varying attached term, the methodology aims to achieve enhanced restoration outcomes. Theoretical scrutiny is dedicated to unraveling the solution of the model, paving the way for the development of an efficient algorithm meticulously crafted to compute the clean image. This algorithm excels in learning both the weights parameter and the balanced L 2 - L 1 attached parameter concurrently, thereby ensuring optimal performance. Through careful parameter selection, the proposed nonlocal deblurring model showcases superior effectiveness, surpassing existing models in terms of both performance and efficacy. [ABSTRACT FROM AUTHOR]