发表机构
Centro de Investigación en Computación, Instituto Politécnico Nacional; School of Informatics, University of Edinburgh（国家理工学院计算研究中心; 爱丁堡大学信息学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
Soft-PNet通过Metropolis游走和原型分布实现无损失工程的软符号接地，在稀缺监督下匹配或超越现有原型网络，并降低训练时间。
AI 中文摘要
神经符号模型通常仅在最终标签上接受监督训练，中间概念保持未观察状态。由于许多概念分配与给定标签一致，训练可能正确预测标签却恢复出错误的概念，这种失败被称为推理捷径。原型网络通过将每个概念锚定到少量带标签示例来减少捷径，但现有方法仍通过手工设计、任务特定的可微损失来耦合感知与推理，该损失必须为每个任务重新设计。我们引入Soft-PNet，它移除了这种损失：将概念接地重新表述为在预计算的可行符号解缓存上的Metropolis游走，由从每个概念单个带标签锚点构建的原型分布引导，并针对原型加权缓存与网络概念预测之间的一个KL目标进行训练。该目标在不同任务间相同，且在解空间无法枚举时仍然适用。在稀缺监督下的MNIST-EvenOdd、Visual Sudoku和Kand-Logic上，Soft-PNet在概念和标签层面匹配了损失工程化的原型网络，并恢复了软接地基线遗漏的概念，无需损失工程且训练时间更短。
英文摘要
Neuro-symbolic models are usually trained with supervision only on final labels, leaving the intermediate concepts unobserved. Since many concept assignments are consistent with a given label, training can predict labels correctly while recovering the wrong concepts, a failure known as a reasoning shortcut. Prototypical networks reduce shortcuts by anchoring each concept to a few labeled examples, but existing methods still couple perception and reasoning through a hand-crafted, task-specific differentiable loss that must be redesigned for every task. We introduce \textbf{Soft-PNet}, which removes this loss: it reframes concept grounding as a Metropolis walk over a precomputed cache of feasible symbolic solutions, guided by a prototype distribution built from a single labeled anchor per concept, and trains against one KL objective between the prototype-weighted cache and the network's concept predictions. The objective is identical across tasks and remains applicable when the solution space cannot be enumerated. On \texttt{MNIST-EvenOdd}, Visual Sudoku, and \texttt{Kand-Logic} under scarce supervision, Soft-PNet matches loss-engineered prototypical networks at the concept and label levels and recovers concepts that soft-grounding baselines miss, with no loss engineering and lower training time.
Comments20th Conference on Neurosymbolic Learning and Reasoning (NeSy 2026)
