CV模型能模拟人类数学认知发展过程,揭示视觉学习与抽象思维的关联。
Computer Vision Modeling of the Development of Geometric and Numerical Concepts in Humans
- 用图像分类训练的ResNet-50模型展现几何与数感的发育轨迹
- 部分几何概念(如欧氏几何)和数的“心理数轴”随训练逐步出现
- 适合研究认知发展、脑启发模型的学者参考
数学思维是人类认知的核心。认知科学家研究了我们进行几何与数理思考的机制,发展科学家则记录了这些能力在人一生中的演变轨迹。先前研究发现,仅通过图像分类任务训练的计算机视觉(CV)模型,仍会习得与成人相似的几何与数理概念隐式表征。本研究进一步考察这些模型是否也表现出发展一致性:即其性能提升是否与儿童的认知发展路径一致。通过对ResNet-50模型的详细案例研究,我们发现:在几何与拓扑方面,某些概念类别(欧氏几何、几何图形、度量属性、拓扑)展现出发展一致性,但另一些(手性图形、几何变换、对称图形)则未体现;在数理方面,模型随着训练经验的积累,逐步出现类人的“心理数轴”表征。这些结果表明,计算机视觉模型有望成为理解人类数学认知发展的新工具,为未来探索更多模型架构和构建更大基准提供方向。
原文摘要 · Abstract (English)
Mathematical thinking is a fundamental aspect of human cognition. Cognitive scientists have investigated the mechanisms that underlie our ability to thinking geometrically and numerically, to take two prominent examples, and developmental scientists have documented the trajectories of these abilities over the lifespan. Prior research has shown that computer vision (CV) models trained on the unrelated task of image classification nevertheless learn latent representations of geometric and numerical concepts similar to those of adults. Building on this demonstrated cognitive alignment, the current study investigates whether CV models also show developmental alignment: whether their performance improvements across training to match the developmental progressions observed in children. In a detailed case study of the ResNet-50 model, we show that this is the case. For the case of geometry and topology, we find developmental alignment for some classes of concepts (Euclidean Geometry, Geometrical Figures, Metric Properties, Topology) but not others (Chiral Figures, Geometric Transformations, Symmetrical Figures). For the case of number, we find developmental alignment in the emergence of a human-like ``mental number line'' representation with experience. These findings show the promise of computer vision models for understanding the development of mathematical understanding in humans. They point the way to future research exploring additional model architectures and building larger benchmarks.
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