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Symbolic numerical generalization through representational alignment.

Anthony Strock1, Ruizhe Liu1, Rishab Iyer1

  • 1Department of Psychiatry & Behavioral Sciences, Stanford University School of Medicine, Stanford, CA, USA.

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|September 22, 2025
PubMed
Summary
This summary is machine-generated.

Understanding how children connect quantities to numbers is key for math skills. Our study shows representational alignment is crucial for this numerical cognition bridge, especially through comparison tasks.

Keywords:
Artificial neural networkEmergence of number semanticsRepresentational alignment

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Area of Science:

  • Cognitive Neuroscience
  • Developmental Psychology
  • Computational Neuroscience

Background:

  • The ability to map nonsymbolic quantities to symbolic numbers is foundational for mathematical development.
  • Neural mechanisms underlying this symbolic-nonsymbolic integration are not well understood.
  • Investigating this cognitive bridge is crucial for understanding numerical cognition.

Purpose of the Study:

  • To investigate the computational principles of symbolic-nonsymbolic numerical integration.
  • To explore the role of representational alignment in numerical processing.
  • To understand how developmental stages impact numerical cognition.

Main Methods:

  • Utilized a biologically inspired neural network model.
  • Trained the network through developmentally inspired stages.
  • Analyzed representational alignment and divergence between numerical formats.

Main Results:

  • Representational alignment between nonsymbolic and symbolic formats is essential for generalization.
  • Cross-format comparison tasks promote stronger alignment than direct-label mapping.
  • Symbolic specialization leads to representational divergence, impairing nonsymbolic performance.

Conclusions:

  • Representational alignment is a fundamental mechanism in numerical cognition.
  • Cross-format comparison tasks may enhance mathematical learning in children.
  • Understanding these mechanisms can inform interventions for numerical processing difficulties.