最近的一个焦点是设计在神经模型（本文中称为神经ILP）中具有非线性规划（ILP）层的架构。神经ILP架构适用于需要数据驱动约束学习的纯推理任务或需要感知（神经）和推理（ILP）的任务。最近一种用于神经ILP端到端训练的SOTA方法通过ILP黑盒明确定义了梯度（Paulus et al. 2021）-由于对minibatch中每个训练数据点的底层ILP求解器的调用，这种训练非常缓慢。作为回应，我们提出了一种替代的训练策略，是无求解器的，即，在训练时根本不调用ILP求解程序。神经ILP有一组可训练的超平面（用于ILP中的成本和约束），它们共同代表一个多面体。我们的关键思想是，训练损失应该强制最终多面体通过软余量公式将正面（满足所有约束）与负面（至少一个违反约束或次优成本值）分开。虽然正面例子作为训练数据的一部分提供，但我们设计了用于生成负面样本的新技术。我们的解决方案是灵活的，足以处理平等以及不平等的约束。在几个问题上的实验，无论是感知的还是符号的，都需要学习ILP的约束条件，表明我们的方法具有优越的性能，与纯神经基线和其他需要基于求解器的训练的最先进的模型相比，其规模要好得多。特别是，我们能够在9 x 9符号和视觉数独中获得出色的性能，而其他Neural ILP求解器无法扩展。
英文摘要：
There is a recent focus on designing architectures that have an Integer Linear Programming (ILP) layer within a neural model (referred to as Neural ILP in this paper). Neural ILP architectures are suitable for pure reasoning tasks that require data-driven constraint learning or for tasks requiring both perception (neural) and reasoning (ILP). A recent SOTA approach for end-to-end training of Neural ILP explicitly defines gradients through the ILP black box (Paulus et al. 2021) - this trains extremely slowly, owing to a call to the underlying ILP solver for every training data point in a minibatch. In response, we present an alternative training strategy that is solver-free, i.e., does not call the ILP solver at all at training time. Neural ILP has a set of trainable hyperplanes (for cost and constraints in ILP), together representing a polyhedron. Our key idea is that the training loss should impose that the final polyhedron separates the positives (all constraints satisfied) from the negatives (at least one violated constraint or a suboptimal cost value), via a soft-margin formulation. While positive example(s) are provided as part of the training data, we devise novel techniques for generating negative samples. Our solution is flexible enough to handle equality as well as inequality constraints. Experiments on several problems, both perceptual as well as symbolic, which require learning the constraints of an ILP, show that our approach has superior performance and scales much better compared to purely neural baselines and other state-of-the-art models that require solver-based training. In particular, we are able to obtain excellent performance in 9 x 9 symbolic and visual sudoku, to which the other Neural ILP solver is not able to scale.
LocalEscaper: A Weakly-supervised Framework with Regional Reconstruction for Scalable Neural TSP Solvers
School of Computer Science, Huazhong University of Science and Technology, China（华中科技大学计算机学院）；Department of Computer Science, Cornell University, United States（康奈尔大学计算机系）
Scalable h-adaptive probabilistic solver for time-independent and time-dependent systems
Department of Aerospace and Mechanical Engineering（航空航天与机械工程系）；University of Notre Dame（诺特丹大学）；Department of Applied Mechanics（应用力学系）；School of Artificial Intelligence（人工智能学院）；Indian Institute of Technology Delhi（德里印度理工学院）
