GNN和Transformer能通过嵌入空间推理几何约束，还原隐藏图形。
Geometric Reasoning in the Embedding Space
- 用图神经网络和Transformer从约束预测2D网格中点的位置。
- 模型在嵌入空间中自发形成2D结构，反映网格邻接关系。
- 所提GNN比Transformer性能更优且更易扩展，适合几何推理任务。
本文证明图神经网络和Transformer能够学习几何约束推理。我们训练它们根据一组唯一描述隐藏图形的约束条件，预测离散2D网格中点的空间位置。两种模型不仅能准确预测点的位置，还令人惊讶地在推理过程中于嵌入空间中重构出输入约束所描述的隐藏图形。分析表明，训练过程中模型恢复了网格结构，使得对应点的嵌入自组织为二维子空间，并反映网格的邻近关系。此外，我们设计的图神经网络在该任务上显著优于Transformer，且更易于扩展。
原文摘要 · Abstract (English)
In this contribution, we demonstrate that Graph Neural Networks and Transformers can learn to reason about geometric constraints. We train them to predict spatial position of points in a discrete 2D grid from a set of constraints that uniquely describe hidden figures containing these points. Both models are able to predict the position of points and interestingly, they form the hidden figures described by the input constraints in the embedding space during the reasoning process. Our analysis shows that both models recover the grid structure during training so that the embeddings corresponding to the points within the grid organize themselves in a 2D subspace and reflect the neighborhood structure of the grid. We also show that the Graph Neural Network we design for the task performs significantly better than the Transformer and is also easier to scale.
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