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Public story · 2026-09-02 · high
McCoy and Smolensky's team swapped the math in small networks and in LLMs across four task types, and it held.
Why now: The paper posted August 30, running the swap instead of just arguing the case.
McCoy, Smolensky and co-authors swapped a trained network's representation process for one closed-form symbolic equation, per the symbolic-equivalence paper they posted August 30. Performance barely moved.
They ran the swap twice. First on small networks trained to manipulate lists. Then on large language models handling arithmetic, logic, code and natural language. The equation stood in for the network's internal math in both cases, and output quality held.
That result cuts against a working assumption in machine learning. Vector representations inside neural networks and the symbolic operations of formal reasoning are treated as separate, incompatible ways of computing. An equation replaced the vectors and the network kept working, so the vectors were carrying something like symbolic logic all along.
The paper doesn't test whether the pattern holds on a production-scale model. Its LLM tests cover four task types, arithmetic, logic, code and natural language, not the full range of what a deployed system handles.
Each link below shares sources, entities, or timing with this story.
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