Neural networks are already symbolic: paper shows LLM vectors approximate symbolic structure
tallinzen · x · 2026-10-23
A new arXiv paper by R. Thomas McCoy (Yale), Tal Linzen and Paul Smolensky (NYU), "The Emergent Symbolic Structure of Artificial Neural Networks," pushes back on the claim that LLMs "run on vectors, not symbols":
- Vector representations of various neural networks can be closely approximated by symbolic structures: replacing the network's entire representation-generating process with a closed-form equation instantiating a symbolic structure leaves behavior largely unchanged.
- The finding holds for small networks trained on list manipulation and for LLMs across four central symbolic domains: arithmetic, logic, code, and language.
- The symbolic approximation also enables targeted behavioral modification via precise interventions on internal representations.
Co-author Tall Linzen's takeaway: "Neural networks are already symbolic."
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