本文提出一种基于SPINEX（基于相似度的可解释邻域探索预测，Similarity-based Predictions with Explainable Neighbors Exploration）系列的新型符号回归算法，即SPINEX_SymbolicRegression。该算法采用基于相似度的方法，识别同时满足精度与结构相似度指标的高价值表达式。我们开展了广泛的基准测试，将该算法与来自国际问题集的180余个数学基准函数进行对比，这些函数涵盖随机生成的表达式以及基于真实物理现象的表达式。随后，我们从精度、（与真实表达式相比的）算子与变量层面的表达式相似度、种群规模、收敛所需代数等维度评估了算法性能。结果显示，SPINEX_SymbolicRegression表现始终优异，部分场景下性能超越主流算法；此外，深度实验也凸显了该算法的可解释性能力。
英文摘要：
This article introduces a new symbolic regression algorithm based on the SPINEX (Similarity-based Predictions with Explainable Neighbors Exploration) family. This new algorithm (SPINEX_SymbolicRegression) adopts a similarity-based approach to identifying high-merit expressions that satisfy accuracy- and structural similarity metrics. We conducted extensive benchmarking tests comparing SPINEX_SymbolicRegression to over 180 mathematical benchmarking functions from international problem sets that span randomly generated expressions and those based on real physical phenomena. Then, we evaluated the performance of the proposed algorithm in terms of accuracy, expression similarity in terms of presence operators and variables (as compared to the actual expressions), population size, and number of generations at convergence. The results indicate that SPINEX_SymbolicRegression consistently performs well and can, in some instances, outperform leading algorithms. In addition, the algorithm's explainability capabilities are highlighted through in-depth experiments.
SPINEX-TimeSeries: Similarity-based Predictions with Explainable Neighbors Exploration for Time Series and Forecasting Problems
University of Manitoba（曼尼托巴大学）；Clemson University（克莱姆森大学）；Artificial Intelligence Research Institute for Science and Engineering (AIRISE), Clemson University（克莱姆森大学科学与工程人工智能研究院（AIRISE））
Explainable and Interpretable Diabetic Retinopathy Classification Based on Neural-Symbolic Learning
Massachusetts General Hospital（麻省总医院）；Harvard Medical School（哈佛医学院）；Singapore Eye Research Institute（新加坡眼科研究所）；Duke-NUS Medical School（杜克-新加坡国立大学医学院）；Institute for Molecular and Clinical Ophthalmology（分子与临床眼科研究所）；National University of Singapore（新加坡国立大学）
Towards Explainable Neural-Symbolic Visual Reasoning
Segula Technologies（赛古拉技术公司）；Institut des Systèmes Intelligents et de Robotique, Sorbonne Universite（索邦大学智能系统与机器人研究所）；INRIA（法国国家信息与自动化研究所）；ENSTA Paris（巴黎高等先进技术学院）
许多高性能模型都缺乏可解释性。有越来越多的工作涌入可解释的人工智能（XAI），以解开什么是XAI的意思和期望。然而，对于如何产生和判断解释，并没有普遍的共识。在本文中，我们讨论了为什么整合连接主义和符号范式的技术是为非技术用户提供解释的最有效解决方案，并且我们提出了一个基于Doran et al. [2017]（arXiv：1710.00794）定义的推理模型来解释神经网络的决策。我们使用这种解释来纠正网络决策原理中的偏差。我们根据Burns等人[2018]（arXiv：1803.09797）中的图像描述方法，为该模型提供了一个潜在用途的示例。
Explainable Moral Values: a neuro-symbolic approach to value classification
University of Pisa（比萨大学）；National Research Council（国家研究委员会）；University of Bologna（博洛尼亚大学）；Peoples' Friendship University of Russia (RUDN University)（俄罗斯人民友谊大学（RUDN大学））；Joint Institute for Nuclear Research（联合核子研究所）；Vrije Universiteit Amsterdam（阿姆斯特丹自由大学）；University of Skövde（舍夫德大学）
EXplainable Neural-Symbolic Learning (X-NeSyL) methodology to fuse deep learning representations with expert knowledge graphs: the MonuMAI cultural heritage use case
ENSTA, Institut Polytechnique Paris（巴黎综合理工学院ENSTA）；Inria（法国国家信息与自动化研究所）；DaSCI Andalusian Institute in Data Science and Computational Intelligence, University of Granada（格拉纳达大学DaSCI安达卢西亚数据科学与计算智能研究所）；University of Granada（格拉纳达大学）；Free University of Bozen-Bolzano（波尔扎诺自由大学）
Symbolic Imitation Learning: From Black-Box to Explainable Driving Policies
Department of Science and Engineering, the George Washington University（科学与工程系，乔治·华盛顿大学）；Autonomous Vehicles Lab, Department of Mechanical Engineering, University of Surrey（自主车辆实验室，机械工程系，萨里大学）
The Road to Learning Explainable Inverse Kinematic Models: Graph Neural Networks as Inductive Bias for Symbolic Regression
Faculty of Computer Science, Otto-von-Guericke-University Magdeburg（马格德堡奥托·冯·格里克大学计算机科学学院）；Fraunhofer Institute for Transportation and Infrastructure Systems IVI（弗劳恩霍夫运输与基础设施系统研究所IVI）
ANSR-DT: A Neuro-Symbolic Framework for Adaptive and Explainable Digital Twins
Department of Information Systems, University of Maryland Baltimore County（信息系统系，马里兰大学巴尔的摩县分校）；Department of Computer Science and Engineering, University at Buffalo（计算机科学与工程系，布法罗大学）；Department of Computer Science, University of Colorado Boulder（计算机科学系，科罗拉多大学波德分校）
Interpretable and Explainable Logical Policies via Neurally Guided Symbolic Abstraction
Technical University of Darmstadt（达姆施塔特工业大学）；National Research Center for Applied Cybersecurity（国家应用网络安全研究中心）；Eindhoven University of Technology（埃因霍温理工大学）；Hessian Center for AI (hessian.AI)（黑森人工智能中心）；German Research Center for AI (DFKI)（德国人工智能研究中心）
A Verifier-Guided Explainable Reasoning Framework with Gold-Anchored QLoRA, Task-Aware Mixture-of-Experts, and Group-Relative RLVR
University of Information Technology (UIT)（信息科技大学）；Ho Chi Minh City University of Technology (HCMUT)（胡志明市理工大学）；Vietnam National University, Ho Chi Minh City（越南国家大学胡志明市分校）；University of Economics Ho Chi Minh City (UEH)（胡志明市经济大学）
ECSEL: Explainable Classification via Signomial Equation Learning
Amsterdam Business School, University of Amsterdam, Amsterdam, the Netherlands（阿姆斯特丹大学阿姆斯特丹商学院）；Institute for Informatics, University of Amsterdam（阿姆斯特丹大学信息学院）；Institute for Logic, Language and Computation, University of Amsterdam（阿姆斯特丹大学逻辑、语言与计算研究所）
Greybox XAI: a Neural-Symbolic learning framework to produce interpretable predictions for image classification
ENSTA, Institut Polytechnique Paris（巴黎理工学院ENSTA）；Inria（法国国家信息与自动化研究所）；Segula Technologies（赛科集团）；Sorbonne Université（索邦大学）；TECNALIA（泰克尼亚研究中心）；University of the Basque Country (UPV/EHU)（巴斯克大学）；Andalusian Research Institute in Data Science and Computational Intelligence (DaSCI)（安达卢西亚数据科学与计算智能研究所）；University of Granada（格拉纳达大学）
Combining feature-based approaches with graph neural networks and symbolic regression for synergistic performance and interpretability
Laboratory of Applied Materials and Interfaces, Federal University of Rio Grande do Sul（南里奥格兰德联邦大学应用材料与界面实验室）；Institute of Condensed Matter and Nanosciences, Université Catholique de Louvain（鲁汶天主教大学凝聚态与纳米科学研究所）；Ruhr-Universität Bochum（波鸿鲁尔大学）
SRLR: Symbolic Regression based Logic Recovery to Counter Programmable Logic Controller Attacks
Beijing University of Posts and Telecommunications, China（北京邮电大学）；Aalborg University, Denmark（奥胡斯大学）；Singapore University of Technology and Design, Singapore（新加坡科技设计大学）
Board gender diversity and emissions performance: Insights from panel regressions, machine learning, and explainable AI
NTNU Business School, Norwegian University of Science and Technology（挪威科技大学NTNU商学院）；Smith School of Enterprise and the Environment, University of Oxford（牛津大学史密斯企业与环境学院）；Faculty of Technology, Natural and Maritime Sciences, University of South-Eastern Norway（东南挪威大学技术、自然与海事科学学院）
