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Why Neural Network Can Discover Symbolic Structures with Gradient-based Training: An Algebraic and Geometric Foundation for Neurosymbolic Reasoning

  • Researchers have developed a theoretical framework explaining how neural networks can naturally discover discrete symbolic structures through gradient-based training.
  • By lifting neural parameters to a measure space and utilizing Wasserstein gradient flow, the framework demonstrates the emergence of symbolic phenomena under geometric constraints like group invariance.
  • The framework highlights the decoupling of gradient flow into independent optimization trajectories based on potential functions and a reduction in degrees of freedom, leading to the encoding of algebraic constraints relevant to the task.
  • The research establishes data scaling laws connecting representational capacity to group invariance, enabling neural networks to transition from high-dimensional exploration to compositional representations aligned with algebraic operations, offering insights for designing neurosymbolic systems.

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