Robots are increasingly entering human-interactive scenarios that require understanding of quantity. How intelligent systems acquire abstract numerical concepts from sensorimotor experience remains a fundamental challenge in cognitive science and artificial intelligence. Here we investigate embodied numerical learning using a neural network model trained to perform sequential counting through naturalistic robotic interaction with a Franka Panda manipulator. We demonstrate that embodied models achieve 96.8\% counting accuracy with only 10\% of training data, compared to 60.6\% for vision-only baselines. This advantage persists when visual-motor correspondences are randomized, indicating that embodiment functions as a structural prior that regularizes learning rather than as an information source. The model spontaneously develops biologically plausible representations: number-selective units with logarithmic tuning, mental number line organization, Weber-law scaling, and rotational dynamics encoding numerical magnitude ($r = 0.97$, slope $= 30.6°$/count). The learning trajectory parallels children's developmental progression from subset-knowers to cardinal-principle knowers. These findings demonstrate that minimal embodiment can ground abstract concepts, improve data efficiency, and yield interpretable representations aligned with biological cognition, which may contribute to embodied mathematics tutoring and safety-critical industrial applications.
翻译:机器人正越来越多地进入需要理解数量的人类交互场景。智能系统如何从感觉运动经验中获得抽象数字概念,仍然是认知科学和人工智能领域的一个基本挑战。在此,我们研究了具身数字学习,使用一个神经网络模型,该模型通过Franka Panda机械臂的自然主义机器人交互来训练执行顺序计数。我们证明,具身模型仅使用10%的训练数据即可达到96.8%的计数准确率,而纯视觉基线为60.6%。当视觉-运动对应关系被随机化时,这一优势依然存在,表明具身性作为一种结构先验,正则化了学习过程,而非作为信息源。该模型自发地发展了具有生物合理性的表征:具有对数调谐的数字选择性单元、心理数字线组织、韦伯定律缩放,以及编码数值大小的旋转动力学($r = 0.97$,斜率 $= 30.6°$/计数)。学习轨迹与儿童从子集知晓者到基数原则知晓者的发展进程平行。这些发现表明,最小具身性可以奠定抽象概念的基础,提高数据效率,并产生与生物认知一致的可解释表征,这可能有助于具身数学辅导和安全关键型工业应用。