标题： 约束和目标的高效神经符号学习 显示英文标题

标题： Efficient Neuro-Symbolic Learning of Constraints and Objective

摘要： 在将离散推理与神经网络混合的持续探索中，人们对能够从自然输入中学习解决离散推理或优化问题的神经架构的兴趣日益增加，这是一项大型语言模型似乎难以应对的任务。 目标：我们引入了一种可微的神经符号架构和一个专门用于学习解决NP难推理问题的损失函数。 方法：我们的新概率损失允许同时学习约束和目标，从而提供一个可以审查和用附加约束完成的完整模型。 通过将组合求解器移出训练循环，我们的架构还提供了可扩展的训练，而精确推理则提供了最大准确性的访问。 结果：我们实证表明，它能够高效地从自然输入中学习解决NP难推理问题。 在三个变体的数独基准测试——符号、视觉和多解——上，我们的方法所需的训练时间是其他混合方法的一小部分。 在一个视觉最小割/最大割任务上，它优化的遗憾比专注于决策的遗憾损失更好。 最后，它高效地学习了设计蛋白质这一大规模现实问题的能量优化公式。 显示英文摘要

摘要： In the ongoing quest for hybridizing discrete reasoning with neural nets, there is an increasing interest in neural architectures that can learn how to solve discrete reasoning or optimization problems from natural inputs, a task that Large Language Models seem to struggle with. Objectives: We introduce a differentiable neuro-symbolic architecture and a loss function dedicated to learning how to solve NP-hard reasoning problems. Methods: Our new probabilistic loss allows for learning both the constraints and the objective, thus delivering a complete model that can be scrutinized and completed with side constraints. By pushing the combinatorial solver out of the training loop, our architecture also offers scalable training while exact inference gives access to maximum accuracy. Results: We empirically show that it can efficiently learn how to solve NP-hard reasoning problems from natural inputs. On three variants of the Sudoku benchmark -- symbolic, visual, and many-solution --, our approach requires a fraction of training time of other hybrid methods. On a visual Min-Cut/Max-cut task, it optimizes the regret better than a Decision-Focused-Learning regret-dedicated loss. Finally, it efficiently learns the energy optimization formulation of the large real-world problem of designing proteins.