McCoy paper: symbolic equations approximate LLM vector internals

The vector representations inside neural networks can be replaced with closed-form symbolic equations without much changing what the networks do.

That is the central claim of a new preprint by R. Thomas McCoy of Yale, Paul Soulos of Johns Hopkins, Tal Linzen of NYU and Paul Smolensky of Microsoft Research. "We can replace the network's entire representation-generating process with a closed-form equation instantiating a symbolic structure, and the network's behavior remains largely unchanged," they write.

The substitution is tested on "small-scale neural networks trained to manipulate lists" and on large language models "operating in four domains that are central in symbolic traditions: arithmetic, logic, computer code, and language." The framing answers a puzzle the paper opens with: intelligence has "traditionally been modeled as operating over structured combinations of symbols," yet modern AI runs on continuous vectors. The authors' proposal is that the two never really parted. "Despite appearances, perhaps the internal representations of neural networks implicitly realize symbolic structure."

The interpretability lever is where the paper pushes hardest. The symbolic approximation, the authors report, "allows us to modify an LLM's behavior in targeted ways via precise interventions on its internal representations," which they read as evidence the LLM is "reliant on the symbolic structures we have identified."

The abstract publishes no fidelity numbers, no per-domain accuracy figures, and does not name which LLMs were probed. Two of the researchers on our Who's Who tracker had shared the preprint within its first week.