This paper proves that under O(d)-equivariant gradient flow, neural network training on reasoning tasks decouples into independent monomial potentials and reduces effective dimensionality, yielding algebraic compositions of symbolic solutions.
On the planning abilities of large language models-a critical investigation
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Why Neural Network Can Discover Symbolic Structures with Gradient-based Training: An Algebraic and Geometric Foundation for Neurosymbolic Reasoning
This paper proves that under O(d)-equivariant gradient flow, neural network training on reasoning tasks decouples into independent monomial potentials and reduces effective dimensionality, yielding algebraic compositions of symbolic solutions.