Learning to solve geometric construction problems from images
This addresses the challenge of automating geometric reasoning in educational or AI contexts, though it is incremental as it adapts existing neural architectures.
The paper tackles the problem of solving geometric construction problems from images using a purely image-based method, achieving 92% accuracy on known problem types and solving 31 out of 68 types on new problems.
We describe a purely image-based method for finding geometric constructions with a ruler and compass in the Euclidea geometric game. The method is based on adapting the Mask R-CNN state-of-the-art image processing neural architecture and adding a tree-based search procedure to it. In a supervised setting, the method learns to solve all 68 kinds of geometric construction problems from the first six level packs of Euclidea with an average 92% accuracy. When evaluated on new kinds of problems, the method can solve 31 of the 68 kinds of Euclidea problems. We believe that this is the first time that a purely image-based learning has been trained to solve geometric construction problems of this difficulty.