Symbolic numerical generalization through representational alignment.

Abstract

The mapping between nonsymbolic quantities and symbolic numbers lays the foundation for mathematical development in children. However, the neural mechanisms underlying this crucial cognitive bridge remain unclear. Here, we investigate the computational principles governing symbolic-nonsymbolic integration using a biologically inspired neural network trained through developmentally inspired stages. Our investigation reveals that generalization from nonsymbolic to symbolic numerical processing emerges specifically when representational alignment forms between these numerical formats. Notably, this alignment appears to be stronger in cross-format comparison-based mapping compared to direct-label-based mapping. Furthermore, we demonstrate that subsequent symbolic specialization creates a representational divergence that impairs nonsymbolic performance while maintaining the ordinal structure of the mapping. These findings highlight representational alignment as a fundamental mechanism in numerical cognition and suggest that targeted cross-format comparison tasks may be particularly effective in improving mathematical learning in children with numerical processing difficulties.