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. In this paper, we introduce a scalable neural architecture and loss function dedicated to learning the constraints and criteria of NP-hard reasoning problems expressed as discrete Graphical Models. Our loss function solves one of the main limitations of Besag's pseudo-loglikelihood, enabling learning of high energies. We empirically show it is able to efficiently learn how to solve NP-hard reasoning problems from natural inputs as the symbolic, visual or many-solutions Sudoku problems as well as the energy optimization formulation of the protein design problem, providing data efficiency, interpretability, and \textit{a posteriori} control over predictions.

翻译：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越来越感兴趣。本文提出了一种可扩展的神经架构和损失函数，专门用于学习表示为离散图模型的NP困难推理问题的约束条件和准则。我们的损失函数解决了Besag伪对数似然的主要局限性之一，从而能够学习高能量。我们通过实验证明，该损失函数能够高效地从自然输入中学习解决NP困难推理问题，例如符号、视觉或多解数独问题，以及蛋白质设计问题的能量优化公式，从而提供数据效率、可解释性和对预测的后验控制。