McCoy, Smolensky and Co-Authors Replace a Network's Entire Representation Process With a Closed-Form Symbolic Equation and Behavior Barely Changes

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arXiv 2608.29530, submitted August 30, 2026 by R. Thomas McCoy, Paul Soulos, Tal Linzen and Paul Smolensky, argues that neural network internal representations implicitly realize symbolic structure. The strong claim is empirical: they substitute a closed-form equation instantiating a symbolic structure for the network's whole representation-generating process and find behavior largely unchanged, across small networks trained on list manipulation and across large language models in arithmetic, logic, code, and natural language. It is a direct attack on the assumption that continuous vector representations and symbolic accounts of intelligence are incompatible.