Although Answer Set Programming (ASP) allows constraining neural-symbolic (NeSy) systems, its employment is hindered by the prohibitive costs of computing stable models and the CPU-bound nature of state-of-the-art solvers. To this end, we propose Answer Set Networks (ASN), a NeSy solver. Based on Graph Neural Networks (GNN), ASNs are a scalable approach to ASP-based Deep Probabilistic Logic Programming (DPPL). Specifically, we show how to translate ASPs into ASNs and demonstrate how ASNs can efficiently solve the encoded problem by leveraging GPU's batching and parallelization capabilities. Our experimental evaluations demonstrate that ASNs outperform state-of-the-art CPU-bound NeSy systems on multiple tasks. Simultaneously, we make the following two contributions based on the strengths of ASNs. Namely, we are the first to show the finetuning of Large Language Models (LLM) with DPPLs, employing ASNs to guide the training with logic. Further, we show the "constitutional navigation" of drones, i.e., encoding public aviation laws in an ASN for routing Unmanned Aerial Vehicles in uncertain environments.

翻译：尽管答案集编程（ASP）能够约束神经符号（NeSy）系统，但其应用受到稳定模型计算的高昂成本以及当前最先进求解器受限于CPU性能的阻碍。为此，我们提出答案集网络（ASN），一种基于图神经网络（GNN）的NeSy求解器。ASN是一种可扩展的、基于ASP的深度概率逻辑编程（DPPL）方法。具体而言，我们展示了如何将ASP问题转化为ASN，并证明ASN如何通过利用GPU的批处理和并行化能力高效求解编码后的问题。实验评估表明，ASN在多项任务上优于当前最先进的受限于CPU的NeSy系统。同时，基于ASN的优势，我们做出了以下两项贡献：我们首次展示了使用DPPL对大语言模型（LLM）进行微调，利用ASN通过逻辑指导训练；此外，我们实现了无人机的"法规导航"，即将公共航空法规编码到ASN中，用于在不确定环境中为无人机规划路径。