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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 in- vestigate 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 rep- resentational alignment forms between these numerical for- mats. 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 rep- resentational alignment as a fundamental mechanism in nu- merical cognition and suggest that targeted cross-format com- parison tasks may be particularly effective in improving math- ematical learning in children with numerical processing diffi- culties. Keywords: Emergence of number semantics, Representa- tional alignment, Artificial neural network