We contribute NeuralSolver, a novel recurrent solver that can efficiently and consistently extrapolate, i.e., learn algorithms from smaller problems (in terms of observation size) and execute those algorithms in large problems. Contrary to previous recurrent solvers, NeuralSolver can be naturally applied in both same-size problems, where the input and output sizes are the same, and in different-size problems, where the size of the input and output differ. To allow for this versatility, we design NeuralSolver with three main components: a recurrent module, that iteratively processes input information at different scales, a processing module, responsible for aggregating the previously processed information, and a curriculum-based training scheme, that improves the extrapolation performance of the method. To evaluate our method we introduce a set of novel different-size tasks and we show that NeuralSolver consistently outperforms the prior state-of-the-art recurrent solvers in extrapolating to larger problems, considering smaller training problems and requiring less parameters than other approaches.

翻译：本文提出NeuralSolver，一种新型循环求解器，能够高效且一致地进行外推，即从较小规模（观测尺寸）问题中学习算法，并在大规模问题中执行这些算法。与现有循环求解器不同，NeuralSolver可自然适用于输入输出尺寸相同的等规模问题，以及输入输出尺寸不同的异规模问题。为实现这种通用性，我们设计了包含三个核心组件的NeuralSolver：循环模块（迭代处理多尺度输入信息）、处理模块（负责聚合已处理信息）以及基于课程学习的训练方案（提升方法的外推性能）。为评估本方法，我们构建了一系列新型异规模任务，实验表明在训练问题规模更小、参数量更少的条件下，NeuralSolver在外推至更大规模问题时持续优于现有最先进的循环求解器。